Author name code: priest ADS astronomy entries on 2022-09-14 author:"Priest, Eric" ------------------------------------------------------------------------ Title: Magnetic reconnection: MHD theory and modelling Authors: Pontin, David I.; Priest, Eric R. Bibcode: 2022LRSP...19....1P Altcode: In this review we focus on the fundamental theory of magnetohydrodynamic reconnection, together with applications to understanding a wide range of dynamic processes in the solar corona, such as flares, jets, coronal mass ejections, the solar wind and coronal heating. We summarise only briefly the related topics of collisionless reconnection, non-thermal particle acceleration, and reconnection in systems other than the corona. We introduce several preliminary topics that are necessary before the subtleties of reconnection can be fully described: these include null points (Sects. 2.1-2.2), other topological and geometrical features such as separatrices, separators and quasi-separatrix layers (Sects. 2.3, 2.6), the conservation of magnetic flux and field lines (Sect. 3), and magnetic helicity (Sect. 4.6). Formation of current sheets in two- and three-dimensional fields is reviewed in Sect. 5. These set the scene for a discussion of the definition and properties of reconnection in three dimensions that covers the conditions for reconnection, the failure of the concept of a flux velocity, the nature of diffusion, and the differences between two-dimensional and three-dimensional reconnection (Sect. 4). Classical 2D models are briefly presented, including magnetic annihilation (Sect. 6), slow and fast regimes of steady reconnection (Sect. 7), and non-steady reconnection such as the tearing mode (Sect. 8). Then three routes to fast reconnection in a collisional or collisionless medium are described (Sect. 9). The remainder of the review is dedicated to our current understanding of how magnetic reconnection operates in three dimensions and in complex magnetic fields such as that of the Sun's corona. In Sects. 10-12, 14.1 the different regimes of reconnection that are possible in three dimensions are summarised, including at a null point, separator, quasi-separator or a braid. The role of 3D reconnection in solar flares (Sect. 13) is reviewed, as well as in coronal heating (Sect. 14), and the release of the solar wind (Sect. 15.2). Extensions including the role of reconnection in the magnetosphere (Sect. 15.3), the link between reconnection and turbulence (Sect. 16), and the role of reconnection in particle acceleration (Sect. 17) are briefly mentioned. Title: Ambipolar diffusion: Self-similar solutions and MHD code testing. Cylindrical symmetry Authors: Moreno-Insertis, F.; Nóbrega-Siverio, D.; Priest, E. R.; Hood, A. W. Bibcode: 2022A&A...662A..42M Altcode: 2022arXiv220306272M Context. Ambipolar diffusion is a process occurring in partially ionised astrophysical systems that imparts a complicated mathematical and physical nature to Ohm's law. The numerical codes that solve the magnetohydrodynamic (MHD) equations have to be able to deal with the singularities that are naturally created in the system by the ambipolar diffusion term.
Aims: The global aim is to calculate a set of theoretical self-similar solutions to the nonlinear diffusion equation with cylindrical symmetry that can be used as tests for MHD codes which include the ambipolar diffusion term.
Methods: First, following the general methods developed in the applied mathematics literature, we obtained the theoretical solutions as eigenfunctions of a nonlinear ordinary differential equation. Phase-plane techniques were used to integrate through the singularities at the locations of the nulls, which correspond to infinitely sharp current sheets. In the second half of the paper, we consider the use of these solutions as tests for MHD codes. To that end, we used the Bifrost code, thereby testing the capabilities of these solutions as tests as well as (inversely) the accuracy of Bifrost's recently developed ambipolar diffusion module.
Results: The obtained solutions are shown to constitute a demanding, but nonetheless viable, test for MHD codes that incorporate ambipolar diffusion. Detailed tabulated runs of the solutions have been made available at a public repository. The Bifrost code is able to reproduce the theoretical solutions with sufficient accuracy up to very advanced diffusive times. Using the code, we also explored the asymptotic properties of our theoretical solutions in time when initially perturbed with either small or finite perturbations.
Conclusions: The functions obtained in this paper are relevant as physical solutions and also as tests for general MHD codes. They provide a more stringent and general test than the simple Zeldovich-Kompaneets-Barenblatt-Pattle solution.

Movies associated to Figs. 4 and 7 are available at https://www.aanda.org Title: Fast plasmoid-mediated reconnection in a solar flare Authors: Yan, Xiaoli; Xue, Zhike; Jiang, Chaowei; Priest, E. R.; Kliem, Bernhard; Yang, Liheng; Wang, Jincheng; Kong, Defang; Song, Yongliang; Feng, Xueshang; Liu, Zhong Bibcode: 2022NatCo..13..640Y Altcode: Magnetic reconnection is a multi-faceted process of energy conversion in astrophysical, space and laboratory plasmas that operates at microscopic scales but has macroscopic drivers and consequences. Solar flares present a key laboratory for its study, leaving imprints of the microscopic physics in radiation spectra and allowing the macroscopic evolution to be imaged, yet a full observational characterization remains elusive. Here we combine high resolution imaging and spectral observations of a confined solar flare at multiple wavelengths with data-constrained magnetohydrodynamic modeling to study the dynamics of the flare plasma from the current sheet to the plasmoid scale. The analysis suggests that the flare resulted from the interaction of a twisted magnetic flux rope surrounding a filament with nearby magnetic loops whose feet are anchored in chromospheric fibrils. Bright cusp-shaped structures represent the region around a reconnecting separator or quasi-separator (hyperbolic flux tube). The fast reconnection, which is relevant for other astrophysical environments, revealed plasmoids in the current sheet and separatrices and associated unresolved turbulent motions. Title: Scaling theory of three-dimensional magnetic reconnection spreading and applications Authors: Arencibia, Milton; Cassak, Paul; Shay, Michael; Priest, Eric Bibcode: 2021AGUFMSM35E2015A Altcode: We develop a first-principles scaling theory of the spreading of three-dimensional (3D) magnetic reconnection of finite extent in the out of plane direction. The results provide a theoretical framework for understanding spreading and are important for applications including two-ribbon solar flares and reconnection in Earth's magnetosphere. This theory addresses systems with or without an out of plane (guide) magnetic field, and with or without Hall physics. The theory reproduces known spreading speeds and directions with and without guide fields, unifying previous knowledge in a single theory. New results include: (1) Reconnection spreads in a particular direction if an x-line is induced at the interface between reconnecting and non-reconnecting regions, which is controlled by the out of plane gradient of the electric field in the outflow direction. (2) The spreading mechanism for anti-parallel collisionless reconnection is convection, as is known, but for guide field reconnection it is magnetic field bending. We confirm the theory using 3D two-fluid and resistive-magnetohydrodynamics simulations. (3) The theory explains why anti-parallel reconnection in resistive-magnetohydrodynamics does not spread. (4) The simulation domain aspect ratio, associated with the free magnetic energy, influences whether reconnection spreads or convects with a fixed x-line length. (5) We perform a simulation initiating anti-parallel collisionless reconnection with a pressure pulse instead of a magnetic perturbation, finding spreading is unchanged rather than spreading at the magnetosonic speed as previously suggested. Title: Scaling theory of three-dimensional magnetic reconnection spreading Authors: Arencibia, Milton; Cassak, P. A.; Shay, M. A.; Priest, E. R. Bibcode: 2021PhPl...28h2104A Altcode: 2021arXiv210800294A We develop a first-principles scaling theory of the spreading of three-dimensional (3D) magnetic reconnection of finite extent in the out of plane direction. This theory addresses systems with or without an out of plane (guide) magnetic field, and with or without Hall physics. The theory reproduces known spreading speeds and directions with and without guide fields, unifying previous knowledge in a single theory. New results include the following: (1) reconnection spreads in a particular direction if an x-line is induced at the interface between reconnecting and non-reconnecting regions, which is controlled by the out of plane gradient of the electric field in the outflow direction. (2) The spreading mechanism for anti-parallel collisionless reconnection is convection, as is known, but for guide field reconnection it is magnetic field bending. We confirm the theory using 3D two-fluid and resistive-magnetohydrodynamics simulations. (3) The theory explains why anti-parallel reconnection in resistive-magnetohydrodynamics does not spread. (4) The simulation domain aspect ratio, associated with the free magnetic energy, influences whether reconnection spreads or convects with a fixed x-line length. (5) We perform a simulation initiating anti-parallel collisionless reconnection with a pressure pulse instead of a magnetic perturbation, finding spreading is unchanged rather than spreading at the magnetosonic speed as previously suggested. The results provide a theoretical framework for understanding spreading beyond systems studied here and are important for applications including two-ribbon solar flares and reconnection in Earth's magnetosphere. Title: Dynamic Evolution Of A Solar Flare Current Sheet Authors: Chitta, L.; Priest, E. R.; Cheng, X. Bibcode: 2021AAS...23830301C Altcode: Current sheets play a key role in solar flares as they are the locations where magnetic energy is liberated through reconnection and is converted to other forms. Yet, their formation and evolution during the impulsive phase of a flare remain elusive. In this talk, we will report new observations of a current-sheet formation and subsequent evolution in the early stages of a solar flare. In particular, we will present multi-phase evolution of a dynamic current sheet from its formation to quasi-stable evolution and disruption. Implications for the onset and evolution of reconnection will be discussed. Title: Chromospheric and coronal heating and jet acceleration due to reconnection driven by flux cancellation. II. Cancellation of two magnetic polarities of unequal flux Authors: Syntelis, P.; Priest, E. R. Bibcode: 2021A&A...649A.101S Altcode: 2021arXiv210316184S Context. Recent observations have shown that magnetic flux cancellation occurs at the photosphere more frequently than previously thought.
Aims: In order to understand the energy release by reconnection driven by flux cancellation, we previously studied a simple model of two cancelling polarities of equal flux. Here, we further develop our analysis to achieve a more general setup where the two cancelling polarities have unequal magnetic fluxes and where many new features are revealed.
Methods: We carried out an analytical study of the cancellation of two magnetic fragments of unequal and opposite flux that approach one another and are located in an overlying horizontal magnetic field.
Results: The energy release as microflares and nanoflares occurs in two main phases. During phase 1a, a separator is formed and reconnection is driven at it as it rises to a maximum height and then moves back down to the photosphere, heating the plasma and accelerating plasma jets in the process. During phase 1b, once the separator moves back to the photosphere, it bifurcates into two null points. Reconnection is no longer driven at the separator and an isolated magnetic domain connecting the two polarities is formed. During phase 2, the polarities cancel out at the photosphere as magnetic flux submerges below the photosphere and as reconnection occurs at and above the photosphere and plasma jets and a mini-filament eruption can be produced. Title: Three-dimensional magnetic reconnection in astrophysical plasmas Authors: Li, Ting; Priest, Eric; Guo, Ruilong Bibcode: 2021RSPSA.47700949L Altcode: 2021arXiv210405174L Magnetic reconnection is a fundamental process in laboratory, magnetospheric, solar and astrophysical plasmas, whereby magnetic energy is converted into heat, bulk kinetic energy and fast particle energy. Its nature in two dimensions is much better understood than that in three dimensions, where its character is completely different and has many diverse aspects that are currently being explored. Here, we focus on the magnetohydrodynamics of three-dimensional reconnection in the plasma environment of the Solar System, especially solar flares. The theory of reconnection at null points, separators and quasi-separators is described, together with accounts of numerical simulations and observations of these three types of reconnection. The distinction between separator and quasi-separator reconnection is a theoretical one that is unimportant for the observations of energy release. A new paradigm for solar flares, in which three-dimensional reconnection plays a central role, is proposed. Title: From Formation to Disruption: Observing the Multiphase Evolution of a Solar Flare Current Sheet Authors: Chitta, L. P.; Priest, E. R.; Cheng, X. Bibcode: 2021ApJ...911..133C Altcode: 2021arXiv210302352C A current sheet, where magnetic energy is liberated through reconnection and converted to other forms, is thought to play the central role in solar flares, the most intense explosions in the heliosphere. However, the evolution of a current sheet and its subsequent role in flare-related phenomena such as particle acceleration is poorly understood. Here we report observations obtained with NASA's Solar Dynamics Observatory that reveal a multiphase evolution of a current sheet in the early stages of a solar flare, from its formation to quasi-stable evolution and disruption. Our observations have implications for the understanding of the onset and evolution of reconnection in the early stages of eruptive solar flares. Title: Chromospheric and coronal heating and jet acceleration due to reconnection driven by flux cancellation. I. At a three-dimensional current sheet Authors: Priest, E. R.; Syntelis, P. Bibcode: 2021A&A...647A..31P Altcode: 2021arXiv210104600P Context. The recent discovery of much greater magnetic flux cancellation taking place at the photosphere than previously realised has led us in our previous works to suggest magnetic reconnection driven by flux cancellation as the cause of a wide range of dynamic phenomena, including jets of various kinds and solar atmospheric heating.
Aims: Previously, the theory considered energy release at a two-dimensional current sheet. Here we develop the theory further by extending it to an axisymmetric current sheet in three dimensions without resorting to complex variable theory.
Methods: We analytically study reconnection and treat the current sheet as a three-dimensional structure. We apply the theory to the cancellation of two fragments of equal but opposite flux that approach each another and are located in an overlying horizontal magnetic field.
Results: The energy release occurs in two phases. During Phase 1, a separator is formed and reconnection is driven at it as it rises to a maximum height and then moves back down to the photosphere, heating the plasma and accelerating a plasma jet as it does so. During Phase 2 the fluxes cancel in the photosphere and accelerate a mixture of cool and hot plasma upwards. Title: Scaling theory of magnetic reconnection spreading Authors: Arencibia, M.; Cassak, P.; Liang, H.; Shay, M.; Jiong, Q.; Priest, E. R. Bibcode: 2020AGUFMSM0200006A Altcode: Observations of magnetic reconnection at the dayside magnetopause, magnetotail and in two-ribbon solar flares suggest that the magnetic reconnection process often begins in a localized region and spreads in the out-of-plane direction as it proceeds. Much has been learned from 3D numerical simulations of quasi-2D current sheets about how reconnection spreads, including an empirical understanding of the direction and the out-of-plane spreading speed as a function of system parameters for idealized systems. For anti-parallel reconnection the spreading occurs at the speed and direction of the current carriers, while for reconnection with a large out-of-plane (guide) magnetic field it spreads bi-directionally at the Alfven speed. However, the understanding of the physics of reconnection spreading from first principles remains primitive. We develop a scaling theory of 3D magnetic reconnection spreading from first principles. We identify the key micro- and meso-scale physics causing the spreading of reconnection with and without a guide field, and predict the spreading speed in current sheets with uniform and non-uniform thicknesses. For current sheets with uniform equilibrium thickness, the predictions reproduce previous empirical results. For spreading with no guide field in current sheets with a non-uniform equilibrium thickness, a key prediction is that in the thicker regions, the spreading is slower than the local current carriers. We confirm these predictions via a parametric study using 3D two-fluid numerical simulations. The results are potentially important for understanding systems in which reconnection spreads, including why the observed spreading speed is often at sub-Alfvenic speeds in two-ribbon solar flares and the dayside magnetopause. The results also have applications to laboratory reconnection experiments and in the solar wind. Title: Impulsive coronal heating during the interaction of surface magnetic fields in the lower solar atmosphere Authors: Chitta, L. P.; Peter, H.; Priest, E. R.; Solanki, S. K. Bibcode: 2020A&A...644A.130C Altcode: 2020arXiv201012560C Coronal plasma in the cores of solar active regions is impulsively heated to more than 5 MK. The nature and location of the magnetic energy source responsible for such impulsive heating is poorly understood. Using observations of seven active regions from the Solar Dynamics Observatory, we found that a majority of coronal loops hosting hot plasma have at least one footpoint rooted in regions of interacting mixed magnetic polarity at the solar surface. In cases when co-temporal observations from the Interface Region Imaging Spectrograph space mission are available, we found spectroscopic evidence for magnetic reconnection at the base of the hot coronal loops. Our analysis suggests that interactions of magnetic patches of opposite polarity at the solar surface and the associated energy release during reconnection are key to impulsive coronal heating.

Movies are available at https://www.aanda.org Title: Reconnection Spreading Theory and Application to Two-Ribbon Flares Authors: Arencibia, M.; Cassak, P.; Liang, H.; Priest, E.; Shay, M.; Qiu, J. Bibcode: 2020SPD....5121109A Altcode: Observations of solar flare ribbons and prominence eruptions suggest that the magnetic reconnection process underlying them begins locally and spreads in the out-of-plane direction as it proceeds. Much has been learned from 3D numerical simulations of quasi-2D current sheets about how reconnection spreads, including an empirical understanding of the direction and the out-of-plane spreading speed as a function of system parameters for idealized systems. It has been shown that in the absence of an out-of-plane (guide) magnetic field, the spreading occurs at the speed and direction of the current carriers; with a guide field, the spreading is bi-directional at the Alfven speed. Here, we advance upon previous knowledge in two key ways. First, we develop a first principles theory of 3D magnetic reconnection spreading. We identify the key micro- and meso-scale physics causing the spreading of reconnection with and without a guide field, and predict the scaling for the spreading speed in these configurations. The predictions reproduce the previously determined empirical results for both configurations. Second, we use the theory to predict the spreading speed for current sheets of non-uniform thickness. We confirm these predictions via a parametric study using 3D two-fluid numerical simulations. A key result is that the spreading with no guide field in non-uniform current sheets is slower than the speed of the current carriers in the thicker regions of the current sheet. The results are potentially important for understanding observations in which reconnection spreads, including why the observed spreading speed is often at sub-Alfvénic speeds. The result may also have applications to Earth's magnetosphere, laboratory reconnection experiments, and reconnection in the solar wind. Title: Coronal Mini-jets in an Activated Solar Tornado-like Prominence Authors: Chen, Huadong; Zhang, Jun; De Pontieu, Bart; Ma, Suli; Kliem, Bernhard; Priest, Eric Bibcode: 2020ApJ...899...19C Altcode: 2020arXiv200608252C High-resolution observations from the Interface Region Imaging Spectrometer reveal the existence of a particular type of small solar jet, which arose singly or in clusters from a tornado-like prominence suspended in the corona. In this study, we perform a detailed statistical analysis of 43 selected mini-jets in the tornado event. Our results show that the mini-jets typically have (1) a projected length of 1.0-6.0 Mm, (2) a width of 0.2-1.0 Mm, (3) a lifetime of 10-50 s, (4) a velocity of 100-350 km s-1, and (5) an acceleration of 3-20 km s-2. Based on spectral diagnostics and EM-Loci analysis, these jets seem to be multithermal small-scale plasma ejections with an estimated average electron density of ∼2.4 × 1010 cm-3 and an approximate mean temperature of ∼2.6 × 105 K. Their mean kinetic energy density, thermal energy density, and dissipated magnetic field strength are roughly estimated to be ∼9 erg cm-3, 3 erg cm-3, and 16 G, respectively. The accelerations of the mini-jets, the UV and EUV brightenings at the footpoints of some mini-jets, and the activation of the host prominence suggest that the tornado mini-jets are probably created by fine-scale external or internal magnetic reconnections (a) between the prominence field and the enveloping or background field or (b) between twisted or braided flux tubes within the prominence. The observations provide insight into the geometry of such reconnection events in the corona and have implications for the structure of the prominence magnetic field and the instability that is responsible for the eruption of prominences and coronal mass ejections. Title: The Creation of Twist by Reconnection of Flux Tubes Authors: Priest, E. R.; Longcope, D. W. Bibcode: 2020SoPh..295...48P Altcode: A fundamental process in a plasma is the magnetic reconnection of one pair of flux tubes (such as solar coronal loops) to produce a new pair. During this process magnetic helicity is conserved, but mutual helicity can be transformed to self-helicity, so that the new tubes acquire twist. However, until recently, when Wright (Astrophys. J.878, 102, 2019) supplied a solution, the partition of self-helicity between the two tubes was an outstanding puzzle. Here we examine Wright's result in detail and apply it to a variety of cases. The simplest case, which Wright himself used to illustrate the result, is that of thin ribbons or flux sheets. We first explicitly apply his method to the usually expected standard case (when the tubes approach one another without twisting before reconnection) and confirm his result is valid for flux sheaths and tubes as well as sheets. Title: A Cancellation Nanoflare Model for Solar Chromospheric and Coronal Heating. III. 3D Simulations and Atmospheric Response Authors: Syntelis, P.; Priest, E. R. Bibcode: 2020ApJ...891...52S Altcode: 2020arXiv200110456S Inspired by recent observations suggesting that photospheric magnetic flux cancellation occurs much more frequently than previously thought, we analytically estimated the energy released from reconnection driven by photospheric flux cancellation, and propose that it can act as a mechanism for chromospheric and coronal heating. Using two-dimensional simulations we validated the analytical estimates and studied the resulting atmospheric response. In the present work, we set up 3D resistive MHD simulations of two canceling polarities in a stratified atmosphere with a horizontal external field to further validate and improve upon the analytical estimates. The computational evaluation of the parameters associated with the energy release are in good qualitative agreement with the analytical estimates. The computational Poynting energy flux into the current sheet is in good qualitative agreement with the analytical estimates, after correcting the analytical expression to better account for the horizontal extent of the current sheet. The atmospheric response to the cancellation is the formation of hot ejections, cool ejections, or a combination of both hot and cool ejections, which can appear with a time difference and/or be spatially offset, depending on the properties of the canceling region and the resulting height of the reconnection. Therefore, during the cancellation, a wide spectrum of ejections can be formed, which can account for the variety of multi-thermal ejections associated with Ellerman bombs, UV bursts, and IRIS bombs, and also other ejections associated with small-scale canceling regions and spicules. Title: Quantifying the Toroidal Flux of Preexisting Flux Ropes of Coronal Mass Ejections Authors: Xing, C.; Cheng, X.; Qiu, Jiong; Hu, Qiang; Priest, E. R.; Ding, M. D. Bibcode: 2020ApJ...889..125X Altcode: 2019arXiv191210623X In past decades, much progress has been achieved in understanding the origin and evolution of coronal mass ejections (CMEs). In situ observations of the counterparts of CMEs, especially magnetic clouds (MCs) near the Earth, have provided measurements of the structure and total flux of CME flux ropes. However, it has been difficult to measure these properties in an erupting CME flux rope, in particular in a preexisting flux rope. In this work, we propose a model to estimate the toroidal flux of a preexisting flux rope by subtracting the flux contributed by magnetic reconnection during the eruption from the flux measured in the MC. The flux contributed by the reconnection is derived from geometric properties of two-ribbon flares based on a quasi-2D reconnection model. We then apply the model to four CME/flare events and find that the ratio of toroidal flux in the preexisting flux rope to that in the associated MC lies in the range 0.40-0.88. This indicates that the toroidal flux of the preexisting flux rope makes an important contribution to that of the CME flux rope and is usually at least as large as the flux arising from the eruption process for the selected events. Title: Sub-Alfvènic Spreading of 3D Collisionless Magnetic Reconnection and Application to Two-Ribbon Solar Flares Authors: Arencibia, M.; Cassak, P.; Liang, H.; Priest, E. R.; Qiu, J.; Longcope, D. W. Bibcode: 2019AGUFMSH13D3421A Altcode: Ribbons in two-ribbon solar flares are observed to elongate in time along the polarity inversion line in addition to their well-known apparent motion away from it. This has been attributed to the spreading of initially localized magnetic reconnection in time. Similar spreading of reconnection has been observed in other settings, including laboratory experiments, Earth's magnetotail, and Earth's dayside magnetopause. Understanding how reconnection spreads is an important aspect of understanding flare evolution including plasma energization and particle acceleration, since these phenomena are associated with the properties of the magnetic reconnection including its physical size. An interesting observational result, both in solar flares and Earth's magnetosphere, is that the reconnection tends to spread slower than the Alfven speed. We investigate the effect of the thickness of the current sheet being non-uniform on the speed of 3D spreading of magnetic reconnection. We perform a parametric study using 3D two-fluid numerical simulations of initially localized anti-parallel magnetic reconnection and present a theory for the out-of-plane spreading velocity as a function of the initial current sheet thicknesses of the fluted current sheet. We find the spreading in fluted current sheets is slower than spreading in uniform sheets with the same thickness in as its broader region. This result provides a potential explanation of why 3D reconnection can spread at sub-Alfvenic speeds. Title: Evidence for downflows in the narrow plasma sheet of 10 Sep 2017, and their significance for flare reconnection Authors: Longcope, Dana; Unverferth, John E.; Klein, Courtney; McCarthy, Marika; Priest, Eric R. Bibcode: 2019AAS...23421604L Altcode: Current sheets are believed to form in the wakes of erupting flux ropes and to enable the magnetic reconnection responsible for an associated flare. Multi-wavelength observations of an eruption on 10 Sep 2017 show a long, linear feature widely taken as evidence of a current sheet viewed edge-on. The relation between the high-temperature, high-density plasma thus observed and any current sheet is not yet entirely clear. We estimate the magnetic field strength surrounding the sheet, and from that conclude that approximately one-third of all flux in the active region was opened by the eruption. Subsequently decreasing field strength suggests that the open flux closed down over the next several hours through reconnection at a rate dΦ/dt = 5 × 1017 Mx/s. We find in AIA observations evidence of downward moving, dark structures analogous to either supra-arcade downflows more typically observed above flare arcades viewed face-on, or to supra-arcade downflowing loops, previously reported in flares viewed in this perspective. This suggests that the plasma sheet is composed of the magnetic flux retracting after being reconnected high above the arcade. We use a model of flux tube retraction following reconnection to show that this process can generate high densities and temperatures as observed in the plasma sheet. The retracting flux tubes reach their highest temperatures at the end of their retraction, well below the site of reconnection. Previous analysis of AIA and EIS data had revealed a peak in the plasma temperature very near the base of this particular sheet. This is consistent with our hypothesis that downflows descend from a higher reconnection point.

This work supported by grants from NASA/HSR and NSF/REU Title: A Cancellation Nanoflare Model for Solar Chromospheric and Coronal Heating. II. 2D Theory and Simulations Authors: Syntelis, P.; Priest, E. R.; Chitta, L. P. Bibcode: 2019ApJ...872...32S Altcode: 2019arXiv190102798S Recent observations at high spatial resolution have shown that magnetic flux cancellation occurs on the solar surface much more frequently than previously thought, and so this led Priest et al. (2018) to propose magnetic reconnection driven by photospheric flux cancellation as a mechanism for chromospheric and coronal heating. In particular, they estimated analytically the amount of energy released as heat and the height of the energy release during flux cancellation. In the present work, we take the next step in the theory by setting up a two-dimensional resistive MHD simulation of two canceling polarities in the presence of a horizontal external field and a stratified atmosphere in order to check and improve upon the analytical estimates. Computational evaluation of the energy release during reconnection is found to be in good qualitative agreement with the analytical estimates. In addition, we go further and undertake an initial study of the atmospheric response to reconnection. We find that, during the cancellation, either hot ejections or cool ones or a combination of both hot and cool ejections can be formed, depending on the height of the reconnection location. The hot structures can have the density and temperature of coronal loops, while the cooler structures are suggestive of surges and large spicules. Title: Chapter 7 - Magnetohydrodynamics and Solar Dynamo Action Authors: Priest, E. R. Bibcode: 2019sgsp.book..239P Altcode: Magnetohydrodynamics (MHD) describes the complex interaction between magnetic fields and plasmas that are responsible for much dynamic behavior in the Sun and many other cosmic objects. This chapter introduces the fundamental equations and their physical effects, including the basic physics inherent in the equations of induction and motion and the key process of magnetic reconnection for converting magnetic energy into other forms. MHD is important in astrophysical processes such as magnetoconvection, magnetic flux emergence, flux ropes, spots, atmospheric heating, wind acceleration, flares, and eruptions. In particular, the focus is on the generation of magnetic fields by dynamo action. Title: Evidence for Downflows in the Narrow Plasma Sheet of 2017 September 10 and Their Significance for Flare Reconnection Authors: Longcope, Dana; Unverferth, John; Klein, Courtney; McCarthy, Marika; Priest, Eric Bibcode: 2018ApJ...868..148L Altcode: Current sheets are believed to form in the wakes of erupting flux ropes and to enable the magnetic reconnection responsible for an associated flare. Multiwavelength observations of an eruption on 2017 September 10 show a long, linear feature widely taken as evidence of a current sheet viewed edge-on. The relation between the high-temperature, high-density plasma thus observed and any current sheet is not yet entirely clear. We estimate the magnetic field strength surrounding the sheet and conclude that approximately one-third of all flux in the active region was opened by the eruption. Subsequently decreasing field strength suggests that the open flux closed down over the next several hours through reconnection at a rate \dot{{{Φ }}}≃ 5× {10}17 Mx s-1. We find in AIA observations evidence of downward-moving, dark structures analogous to either supra-arcade downflows, more typically observed above flare arcades viewed face-on, or supra-arcade downflowing loops, previously reported in flares viewed in this perspective. These features suggest that the plasma sheet is composed of the magnetic flux retracting after being reconnected high above the arcade. We model flux tube retraction following reconnection to show that this process can generate high densities and temperatures as observed in the plasma sheet. The retracting flux tubes reach their highest temperatures at the end of their retraction, well below the site of reconnection, consistent with previous analysis of AIA and EIS data showing a peak in the plasma temperature near the base of this particular sheet. Title: Self-similar Approach for Rotating Magnetohydrodynamic Solar and Astrophysical Structures Authors: Luna, M.; Priest, E.; Moreno-Insertis, F. Bibcode: 2018ApJ...863..147L Altcode: 2018arXiv180702473L Rotating magnetic structures are common in astrophysics, from vortex tubes and tornadoes in the Sun all the way to jets in different astrophysical systems. The physics of these objects often combine inertial, magnetic, gas pressure, and gravitational terms. Also, they often show approximate symmetries that help simplify the otherwise rather intractable equations governing their morphology and evolution. Here we propose a general formulation of the equations assuming axisymmetry and a self-similar form for all variables: in spherical coordinates (r, θ, ϕ), the magnetic field and plasma velocity are taken to be of the form {\boldsymbol{B}}={\boldsymbol{f}}(θ )/{r}n and {\boldsymbol{v}}={\boldsymbol{g}}(θ )/{r}m, with corresponding expressions for the scalar variables like pressure and density. Solutions are obtained for potential, force-free, and non-force-free magnetic configurations. Potential field solutions can be found for all values of n. Nonpotential force-free solutions possess an azimuthal component B ϕ and exist only for n ≥ 2 the resulting structures are twisted and have closed field lines but are not collimated around the system axis. In the non-force-free case, including gas pressure, the magnetic field lines acquire an additional curvature to compensate for an outward pointing pressure gradient force. We have also considered a pure rotation situation with no gravity, in the zero-β limit: the solution has cylindrical geometry and twisted magnetic field lines. The latter solutions can be helpful in producing a collimated magnetic field structure; but they exist only when n < 0 and m < 0: for applications they must be matched to an external system at a finite distance from the origin. Title: A Cancellation Nanoflare Model for Solar Chromospheric and Coronal Heating Authors: Priest, E. R.; Chitta, L. P.; Syntelis, P. Bibcode: 2018ApJ...862L..24P Altcode: 2018arXiv180708161P Nanoflare models for heating the solar corona usually assume magnetic braiding and reconnection as the source of the energy. However, recent observations at record spatial resolution from the SUNRISE balloon mission suggest that photospheric magnetic flux cancellation is much more common than previously realized. We therefore examine the possibility of three-dimensional reconnection driven by flux cancellation as a cause of chromospheric and coronal heating. In particular, we estimate how the heights and amount of energy release produced by flux cancellation depend on flux size, flux cancellation speed, and overlying field strength. Title: Flux Rope Formation Due to Shearing and Zipper Reconnection Authors: Threlfall, J.; Hood, A. W.; Priest, E. R. Bibcode: 2018SoPh..293...98T Altcode: 2018arXiv180606760T Zipper reconnection has been proposed as a mechanism for creating most of the twist in the flux tubes that are present prior to eruptive flares and coronal mass ejections. We have conducted a first numerical experiment on this new regime of reconnection, where two initially untwisted parallel flux tubes are sheared and reconnected to form a large flux rope. We describe the properties of this experiment, including the linkage of magnetic flux between concentrated flux sources at the base of the simulation, the twist of the newly formed flux rope, and the conversion of mutual magnetic helicity in the sheared pre-reconnection state into the self-helicity of the newly formed flux rope. Title: The Eruption of a Small-scale Emerging Flux Rope as the Driver of an M-class Flare and of a Coronal Mass Ejection Authors: Yan, X. L.; Jiang, C. W.; Xue, Z. K.; Wang, J. C.; Priest, E. R.; Yang, L. H.; Kong, D. F.; Cao, W. D.; Ji, H. S. Bibcode: 2017ApJ...845...18Y Altcode: 2017arXiv170700073Y Solar flares and coronal mass ejections are the most powerful explosions in the Sun. They are major sources of potentially destructive space weather conditions. However, the possible causes of their initiation remain controversial. Using high-resolution data observed by the New Solar Telescope of Big Bear Solar Observaotry, supplemented by Solar Dynamics Observatory observations, we present unusual observations of a small-scale emerging flux rope near a large sunspot, whose eruption produced an M-class flare and a coronal mass ejection. The presence of the small-scale flux rope was indicated by static nonlinear force-free field extrapolation as well as data-driven magnetohydrodynamics modeling of the dynamic evolution of the coronal three-dimensional magnetic field. During the emergence of the flux rope, rotation of satellite sunspots at the footpoints of the flux rope was observed. Meanwhile, the Lorentz force, magnetic energy, vertical current, and transverse fields were increasing during this phase. The free energy from the magnetic flux emergence and twisting magnetic fields is sufficient to power the M-class flare. These observations present, for the first time, the complete process, from the emergence of the small-scale flux rope, to the production of solar eruptions. Title: 3D Simulation Study of the Spreading/Elongation of Ribbons in Two-Ribbon Flares Authors: Arencibia, Milton; Cassak, Paul; Qiu, Jiong; Longscope, Dana; Priest, Eric R. Bibcode: 2017SPD....4810812A Altcode: Two-ribbon solar flares are characterized by the appearance in pairs of bright ribbons on the surface of the Sun. The ribbons separate from each other in time, which has been cited as one of many pieces of evidence that magnetic reconnection participates in the release of magnetic energy in solar flares. In addition to moving apart from each other, observations have revealed that ribbons also elongate (or spread) in time along the polarity inversion line. This is likely related to the spreading of the magnetic reconnection process in the corona. Recent observations have shown ribbons can elongate either unidirectionally or bidirectionally. We investigate the physics of reconnection spreading and its potential relation to two-ribbon flares via a parametric study using 3D numerical simulations with the two-fluid (MHD + Hall effect + electron inertia) model. We study how anti-parallel reconnection spreads in current sheets with a non-uniform thickness in the out-of-plane direction. Previous numerical work on spreading in current sheets of uniform thickness revealed that anti-parallel reconnection spreads at a speed given by the current carriers, but it is not obvious how the spreading occurs in a current sheet with non-uniform thickness. We compare spreading in this system with spreading in current sheets of uniform thickness that are thicker than the dissipation scale. The results may be useful not just for solar flares, but also for Earth’s magnetotail, laboratory reconnection experiments, and reconnection in the solar wind. Title: A Complex Solar Coronal Jet with Two Phases Authors: Chen, Jie; Su, Jiangtao; Deng, Yuanyong; Priest, E. R. Bibcode: 2017ApJ...840...54C Altcode: 2017arXiv170402072C Jets often occur repeatedly from almost the same location. In this paper, a complex solar jet was observed with two phases to the west of NOAA AR 11513 on 2012 July 2. If it had been observed at only moderate resolution, the two phases and their points of origin would have been regarded as identical. However, at high resolution we find that the two phases merge into one another and the accompanying footpoint brightenings occur at different locations. The phases originate from different magnetic patches rather than being one phase originating from the same patch. Photospheric line of sight (LOS) magnetograms show that the bases of the two phases lie in two different patches of magnetic flux that decrease in size during the occurrence of the two phases. Based on these observations, we suggest that the driving mechanism of the two successive phases is magnetic cancellation of two separate magnetic fragments with an opposite-polarity fragment between them. Title: Our Dynamic Sun (Hannes Alfvén Medal Lecture) Authors: Priest, Eric Bibcode: 2017EGUGA..19.2273P Altcode: The Sun, an object of worship for early civilisations, is the main source of light and life on Earth and of our space weather, with many subtle effects on our environment. The lecture will introduce you to the Sun and its dynamic phenomena, and will aim to show how our understanding of many aspects of the Sun has been revolutionized over the past few years by current spacecraft observations and models. Much of the dynamic behaviour is driven by the magnetic field since, in the outer atmosphere (or corona), it represents by far the largest source of energy. The interior of the Sun, revealed by solar seismology, possesses a strong shear layer at the base of the convection zone, where sunspot magnetic fields are generated. But a small-scale dynamo is also operating near the surface of the Sun, generating magnetic fields that thread the lowest layer of the solar atmosphere, the photosphere, in a turbulent convective state. Above the photosphere lies the highly dynamic fine-scale chromosphere and beyond that the rare corona at high temperatures exceeding one million degrees K. Magnetic mechanisms for heating the corona (an intriguing puzzle) will be described. Other puzzles include the structure of giant flux ropes, known as prominences, which have complex fine structure. Occasionally, they erupt and produce huge ejections of mass and magnetic field (coronal mass ejections), which can disrupt the space environment of the Earth. When such eruptions originate in active regions around sunspots, they are also associated with solar flares, where magnetic energy is converted to kinetic, heat and fast particle energy. A new theory will be presented for the origin of the twist that is observed in erupting prominences. Title: Elongation of Flare Ribbons Authors: Qiu, Jiong; Longcope, Dana W.; Cassak, Paul A.; Priest, Eric R. Bibcode: 2017ApJ...838...17Q Altcode: 2017arXiv170702478Q We present an analysis of the apparent elongation motion of flare ribbons along the polarity inversion line (PIL), as well as the shear of flare loops in several two-ribbon flares. Flare ribbons and loops spread along the PIL at a speed ranging from a few to a hundred km s-1. The shear measured from conjugate footpoints is consistent with the measurement from flare loops, and both show the decrease of shear toward a potential field as a flare evolves and ribbons and loops spread along the PIL. Flares exhibiting fast bidirectional elongation appear to have a strong shear, which may indicate a large magnetic guide field relative to the reconnection field in the coronal current sheet. We discuss how the analysis of ribbon motion could help infer properties in the corona where reconnection takes place. Title: Imaging Observations of Magnetic Reconnection in a Solar Eruptive Flare Authors: Li, Y.; Sun, X.; Ding, M. D.; Qiu, J.; Priest, E. R. Bibcode: 2017ApJ...835..190L Altcode: 2016arXiv161209417L Solar flares are among the most energetic events in the solar atmosphere. It is widely accepted that flares are powered by magnetic reconnection in the corona. An eruptive flare is usually accompanied by a coronal mass ejection, both of which are probably driven by the eruption of a magnetic flux rope (MFR). Here we report an eruptive flare on 2016 March 23 observed by the Atmospheric Imaging Assembly on board the Solar Dynamics Observatory. The extreme-ultraviolet imaging observations exhibit the clear rise and eruption of an MFR. In particular, the observations reveal solid evidence of magnetic reconnection from both the corona and chromosphere during the flare. Moreover, weak reconnection is observed before the start of the flare. We find that the preflare weak reconnection is of tether-cutting type and helps the MFR to rise slowly. Induced by a further rise of the MFR, strong reconnection occurs in the rise phases of the flare, which is temporally related to the MFR eruption. We also find that the magnetic reconnection is more of 3D-type in the early phase, as manifested in a strong-to-weak shear transition in flare loops, and becomes more 2D-like in the later phase, as shown by the apparent rising motion of an arcade of flare loops. Title: Flux-Rope Twist in Eruptive Flares and CMEs: Due to Zipper and Main-Phase Reconnection Authors: Priest, E. R.; Longcope, D. W. Bibcode: 2017SoPh..292...25P Altcode: 2017arXiv170100147P The nature of three-dimensional reconnection when a twisted flux tube erupts during an eruptive flare or coronal mass ejection is considered. The reconnection has two phases: first of all, 3D "zipper reconnection" propagates along the initial coronal arcade, parallel to the polarity inversion line (PIL); then subsequent quasi-2D "main-phase reconnection" in the low corona around a flux rope during its eruption produces coronal loops and chromospheric ribbons that propagate away from the PIL in a direction normal to it. One scenario starts with a sheared arcade: the zipper reconnection creates a twisted flux rope of roughly one turn (2 π radians of twist), and then main-phase reconnection builds up the bulk of the erupting flux rope with a relatively uniform twist of a few turns. A second scenario starts with a pre-existing flux rope under the arcade. Here the zipper phase can create a core with many turns that depend on the ratio of the magnetic fluxes in the newly formed flare ribbons and the new flux rope. Main phase reconnection then adds a layer of roughly uniform twist to the twisted central core. Both phases and scenarios are modeled in a simple way that assumes the initial magnetic flux is fragmented along the PIL. The model uses conservation of magnetic helicity and flux, together with equipartition of magnetic helicity, to deduce the twist of the erupting flux rope in terms the geometry of the initial configuration. Interplanetary observations show some flux ropes have a fairly uniform twist, which could be produced when the zipper phase and any pre-existing flux rope possess small or moderate twist (up to one or two turns). Other interplanetary flux ropes have highly twisted cores (up to five turns), which could be produced when there is a pre-existing flux rope and an active zipper phase that creates substantial extra twist. Title: The Formation of an Inverse S-shaped Active-region Filament Driven by Sunspot Motion and Magnetic Reconnection Authors: Yan, X. L.; Priest, E. R.; Guo, Q. L.; Xue, Z. K.; Wang, J. C.; Yang, L. H. Bibcode: 2016ApJ...832...23Y Altcode: 2016arXiv160904871Y We present a detailed study of the formation of an inverse S-shaped filament prior to its eruption in active region NOAA 11884 from 2013 October 31 to November 2. In the initial stage, clockwise rotation of a small positive sunspot around the main negative trailing sunspot formed a curved filament. Then the small sunspot cancelled with the negative magnetic flux to create a longer active-region filament with an inverse S-shape. At the cancellation site a brightening was observed in UV and EUV images and bright material was transferred to the filament. Later the filament erupted after cancellation of two opposite polarities below the upper part of the filament. Nonlinear force-free field extrapolation of vector photospheric fields suggests that the filament may have a twisted structure, but this cannot be confirmed from the current observations. Title: 3D MHD modeling of twisted coronal loops Authors: Reale, F.; Orlando, S.; Guarrasi, M.; Mignone, A.; Peres, G.; Hood, A. W.; Priest, E. R. Bibcode: 2016ApJ...830...21R Altcode: 2016arXiv160705500R We perform MHD modeling of a single bright coronal loop to include the interaction with a non-uniform magnetic field. The field is stressed by random footpoint rotation in the central region and its energy is dissipated into heating by growing currents through anomalous magnetic diffusivity that switches on in the corona above a current density threshold. We model an entire single magnetic flux tube in the solar atmosphere extending from the high-β chromosphere to the low-β corona through the steep transition region. The magnetic field expands from the chromosphere to the corona. The maximum resolution is ∼30 km. We obtain an overall evolution typical of loop models and realistic loop emission in the EUV and X-ray bands. The plasma confined in the flux tube is heated to active region temperatures (∼3 MK) after ∼2/3 hr. Upflows from the chromosphere up to ∼100 km s-1 fill the core of the flux tube to densities above 109 cm-3. More heating is released in the low corona than the high corona and is finely structured both in space and time. Title: Direct imaging of a classical solar eruptive flare Authors: Li, Y.; Sun, X. D.; Ding, M. D.; Qiu, J.; Priest, E. R.; Longcope, D. W. Bibcode: 2016usc..confE..21L Altcode: Solar flares are the most energetic events in the solar system that have a potential hazard on Earth. Although a standard model for the eruptive flare accompanied by a coronal mass ejection has been outlined and elaborated for decades, some key aspects are still under debate, such as what drives the eruption, what is the role of magnetic reconnection, and how the flare loops evolve. Here we present an excellent event exhibiting nearly all the key elements involved in the standard flare model. Using extreme-ultraviolet imaging observations, we detect the unambiguous rise and eruption of a magnetic flux rope, solid evidence for magnetic reconnection, and evident slipping and rising motions in flare loops. Modeled coronal magnetic field supports the interpretation of a pre-existing flux rope that persists after the eruption with reduced twist. This flare, from the observational view, shows a clear and comprehensive picture of how a classical solar eruptive flare occurs and evolves, and helps to clarify some of the controversial topics in the standard flare model. Title: Magnetic reconnection between a solar filament and nearby coronal loops Authors: Li, Leping; Zhang, Jun; Peter, Hardi; Priest, Eric; Chen, Huadong; Guo, Lijia; Chen, Feng; Mackay, Duncan Bibcode: 2016NatPh..12..847L Altcode: 2016arXiv160503320L Magnetic reconnection is difficult to observe directly but coronal structures on the Sun often betray the magnetic field geometry and its evolution. Here we report the observation of magnetic reconnection between an erupting filament and its nearby coronal loops, resulting in changes in the filament connection. X-type structures form when the erupting filament encounters the loops. The filament becomes straight, and bright current sheets form at the interfaces. Plasmoids appear in these current sheets and propagate bi-directionally. The filament disconnects from the current sheets, which gradually disperse and disappear, then reconnects to the loops. This evolution suggests successive magnetic reconnection events predicted by theory but rarely detected with such clarity in observations. Our results confirm the three-dimensional magnetic reconnection theory and have implications for the evolution of dissipation regions and the release of magnetic energy for reconnection in many magnetized plasma systems. Title: Evolution of Magnetic Helicity During Eruptive Flares and Coronal Mass Ejections Authors: Priest, E. R.; Longcope, D. W.; Janvier, M. Bibcode: 2016SoPh..291.2017P Altcode: 2016arXiv160703874P; 2016SoPh..tmp..130P During eruptive solar flares and coronal mass ejections, a non-potential magnetic arcade with much excess magnetic energy goes unstable and reconnects. It produces a twisted erupting flux rope and leaves behind a sheared arcade of hot coronal loops. We suggest that the twist of the erupting flux rope can be determined from conservation of magnetic flux and magnetic helicity and equipartition of magnetic helicity. It depends on the geometry of the initial pre-eruptive structure. Two cases are considered, in the first of which a flux rope is not present initially but is created during the eruption by the reconnection. In the second case, a flux rope is present under the arcade in the pre-eruptive state, and the effect of the eruption and reconnection is to add an amount of magnetic helicity that depends on the fluxes of the rope and arcade and the geometry. Title: MHD Structures in Three-Dimensional Reconnection Authors: Priest, E. Bibcode: 2016ASSL..427..101P Altcode: This review of three-dimensional reconnection focusses on the MHD aspects of the process. It describes the different structures where current tends to concentrate and so lead to reconnection, namely, null points (where the magnetic field vanishes), separators (which are magnetic field lines joining null points) and quasi-separators. Then the role of topological invariants such as magnetic helicity (which describes the twist and linkage of magnetic structures) is described, together with the conditions for flux and field-line conservation and for reconnection itself. The surprising and crucial differences between 2D and 3D reconnection are highlighted and finally the different regimes for 3D reconnection are summarised. Title: Are Tornado-Like Magnetic Structures Able to Support Solar Prominence Plasma? Authors: Ogunjo, S. T.; Luna Bennasar, M.; Moreno-Insertis, F.; Priest, E. R. Bibcode: 2015AGUFMSH53B2483O Altcode: Recent high-resolution and high-cadence observations have surprisingly suggested that prominence barbs exhibit apparent rotating motions suggestive of a tornado-like structure. Additional evidence has been provided by Doppler measurements. The observations reveal opposite velocities for both hot and cool plasma on the two sides of a prominence barb. This motion is persistent for several hours and has been interpreted in terms of rotational motion of prominence feet. Several authors suggest that such barb motions are rotating helical structures around a vertical axis similar to tornadoes on Earth. One of the difficulties of such a proposal is how to support cool prominence plasma in almost-vertical structures against gravity. In this work we model analytically a tornado-like structure and try to determine possible mechanisms to support the prominence plasma. We have found that the Lorentz force can indeed support the barb plasma provided the magnetic structure is sufficiently twisted and/or significant poloidal flows are present. Title: Are Tornado-like Magnetic Structures Able to Support Solar Prominence Plasma? Authors: Luna, M.; Moreno-Insertis, F.; Priest, E. Bibcode: 2015ApJ...808L..23L Altcode: 2015arXiv150701455L Recent high-resolution and high-cadence observations have surprisingly suggested that prominence barbs exhibit apparent rotating motions suggestive of a tornado-like structure. Additional evidence has been provided by Doppler measurements. The observations reveal opposite velocities for both hot and cool plasma on the two sides of a prominence barb. This motion is persistent for several hours and has been interpreted in terms of rotational motion of prominence feet. Several authors suggest that such barb motions are rotating helical structures around a vertical axis similar to tornadoes on Earth. One of the difficulties of such a proposal is how to support cool prominence plasma in almost-vertical structures against gravity. In this work we model analytically a tornado-like structure and try to determine possible mechanisms to support the prominence plasma. We have found that the Lorentz force can indeed support the barb plasma provided the magnetic structure is sufficiently twisted and/or significant poloidal flows are present. Title: Extreme ultraviolet imaging of three-dimensional magnetic reconnection in a solar eruption Authors: Sun, J. Q.; Cheng, X.; Ding, M. D.; Guo, Y.; Priest, E. R.; Parnell, C. E.; Edwards, S. J.; Zhang, J.; Chen, P. F.; Fang, C. Bibcode: 2015NatCo...6.7598S Altcode: 2015NatCo...6E7598S; 2015arXiv150608255S Magnetic reconnection, a change of magnetic field connectivity, is a fundamental physical process in which magnetic energy is released explosively, and it is responsible for various eruptive phenomena in the universe. However, this process is difficult to observe directly. Here, the magnetic topology associated with a solar reconnection event is studied in three dimensions using the combined perspectives of two spacecraft. The sequence of extreme ultraviolet images clearly shows that two groups of oppositely directed and non-coplanar magnetic loops gradually approach each other, forming a separator or quasi-separator and then reconnecting. The plasma near the reconnection site is subsequently heated from ~1 to >=5 MK. Shortly afterwards, warm flare loops (~3 MK) appear underneath the hot plasma. Other observational signatures of reconnection, including plasma inflows and downflows, are unambiguously revealed and quantitatively measured. These observations provide direct evidence of magnetic reconnection in a three-dimensional configuration and reveal its origin. Title: The nature of separator current layers in MHS equilibria. I. Current parallel to the separator Authors: Stevenson, J. E. H.; Parnell, C. E.; Priest, E. R.; Haynes, A. L. Bibcode: 2015A&A...573A..44S Altcode: 2014arXiv1410.8691S Context. Separators, which are in many ways the three-dimensional equivalent to two-dimensional nulls, are important sites for magnetic reconnection. Magnetic reconnection occurs in strong current layers which have very short length scales.
Aims: The aim of this work is to explore the nature of current layers around separators. A separator is a special field line which lies along the intersection of two separatrix surfaces and forms the boundary between four topologically distinct flux domains. In particular, here the current layer about a separator that joins two 3D nulls and lies along the intersection of their separatrix surfaces is investigated.
Methods: A magnetic configuration containing a single separator embedded in a uniform plasma with a uniform electric current parallel to the separator is considered. This initial magnetic setup, which is not in equilibrium, relaxes in a non-resistive manner to form an equilibrium. The relaxation is achieved using the 3D MHD code, Lare3d, with resistivity set to zero. A series of experiments with varying initial current are run to investigate the characteristics of the resulting current layers present in the final (quasi-)equilibrium states.
Results: In each experiment, the separator collapses and a current layer forms along it. The dimensions and strength of the current layer increase with initial current. It is found that separator current layers formed from current parallel to the separator are twisted. Also the collapse of the separator is a process that evolves like an infinite-time singularity where the length, width and peak current in the layer grow slowly whilst the depth of the current layer decreases. Title: Hinode 7: Conference summary and future suggestions Authors: Priest, Eric Bibcode: 2014PASJ...66S..18P Altcode: 2014arXiv1405.3523P; 2014PASJ..tmp..104P This conclusion to the seventh Hinode science meeting (2013 November in Takayama, Japan) attempts to summarise what we have learnt during the conference (mainly from the review talks) about new observations from Hinode and about theories stimulated by them. Suggestions for future study are also offered. Title: The formation and stability of Petschek reconnection Authors: Baty, H.; Forbes, T. G.; Priest, E. R. Bibcode: 2014PhPl...21k2111B Altcode: No abstract at ADS Title: A Life of Fun Playing with Solar Magnetic Fields (Special Historical Review) Authors: Priest, E. R. Bibcode: 2014SoPh..289.3579P Altcode: 2014SoPh..tmp...93P; 2014arXiv1405.3481P This invited memoire describes my fortunate life, which has been enriched by meeting many wonderful people. The story starts at home and university, and continues with accounts of St Andrews and trips to the USA, together with musings on the book Solar MHD. The nature and results of collaborations with key people from abroad and with students is mentioned at length. Finally, other important aspects of my life are mentioned briefly before wrapping up. Title: Catastrophe versus Instability for the Eruption of a Toroidal Solar Magnetic Flux Rope Authors: Kliem, B.; Lin, J.; Forbes, T. G.; Priest, E. R.; Török, T. Bibcode: 2014ApJ...789...46K Altcode: 2014arXiv1404.5922K The onset of a solar eruption is formulated here as either a magnetic catastrophe or as an instability. Both start with the same equation of force balance governing the underlying equilibria. Using a toroidal flux rope in an external bipolar or quadrupolar field as a model for the current-carrying flux, we demonstrate the occurrence of a fold catastrophe by loss of equilibrium for several representative evolutionary sequences in the stable domain of parameter space. We verify that this catastrophe and the torus instability occur at the same point; they are thus equivalent descriptions for the onset condition of solar eruptions. Title: Magnetohydrodynamics of the Sun Authors: Priest, Eric Bibcode: 2014masu.book.....P Altcode: Preface; 1. A description of the Sun; 2. Basic equations of MHD; 3. Magnetohydrostatics; 4. Waves; 5. Shock waves; 6. Magnetic reconnection; 7. Instability; 8. Dynamo theory; 9. Magnetoconvection and sunspots; 10. Heating of the upper atmosphere; 11. Prominences; 12. Solar flares and coronal mass ejections; 13. The solar wind; Appendices; References; Index. Title: The solar cycle variation of topological structures in the global solar corona Authors: Platten, S. J.; Parnell, C. E.; Haynes, A. L.; Priest, E. R.; Mackay, D. H. Bibcode: 2014A&A...565A..44P Altcode: 2014arXiv1406.5333P Context. The complicated distribution of magnetic flux across the solar photosphere results in a complex web of coronal magnetic field structures. To understand this complexity, the magnetic skeleton of the coronal field can be calculated. The skeleton highlights the (separatrix) surfaces that divide the field into topologically distinct regions, allowing open-field regions on the solar surface to be located. Furthermore, separatrix surfaces and their intersections with other separatrix surfaces (i.e., separators) are important likely energy release sites.
Aims: The aim of this paper is to investigate, throughout the solar cycle, the nature of coronal magnetic-field topologies that arise under the potential-field source-surface approximation. In particular, we characterise the typical global fields at solar maximum and minimum.
Methods: Global magnetic fields are extrapolated from observed Kitt Peak and SOLIS synoptic magnetograms, from Carrington rotations 1645 to 2144, using the potential-field source-surface model. This allows the variations in the coronal skeleton to be studied over three solar cycles.
Results: The main building blocks which make up magnetic fields are identified and classified according to the nature of their separatrix surfaces. The magnetic skeleton reveals that, at solar maximum, the global coronal field involves a multitude of topological structures at all latitudes criss-crossing throughout the atmosphere. Many open-field regions exist originating anywhere on the photosphere. At solar minimum, the coronal topology is heavily influenced by the solar magnetic dipole. A strong dipole results in a simple large-scale structure involving just two large polar open-field regions, but, at short radial distances between ± 60° latitude, the small-scale topology is complex. If the solar magnetic dipole if weak, as in the recent minimum, then the low-latitude quiet-sun magnetic fields may be globally significant enough to create many disconnected open-field regions between ± 60° latitude, in addition to the two polar open-field regions. Title: Prominences: Conference Summary and Suggestions for the Future Authors: Priest, Eric R. Bibcode: 2014IAUS..300..379P Altcode: In this conclusion to the conference, I shall attempt to summarise what we knew before about solar prominences and what we have learnt during the conference (mainly from the review talks), as well as to make suggestions for their future study. Title: On the Nature of Reconnection at a Solar Coronal Null Point above a Separatrix Dome Authors: Pontin, D. I.; Priest, E. R.; Galsgaard, K. Bibcode: 2013ApJ...774..154P Altcode: 2013arXiv1307.6874P Three-dimensional magnetic null points are ubiquitous in the solar corona and in any generic mixed-polarity magnetic field. We consider magnetic reconnection at an isolated coronal null point whose fan field lines form a dome structure. Using analytical and computational models, we demonstrate several features of spine-fan reconnection at such a null, including the fact that substantial magnetic flux transfer from one region of field line connectivity to another can occur. The flux transfer occurs across the current sheet that forms around the null point during spine-fan reconnection, and there is no separator present. Also, flipping of magnetic field lines takes place in a manner similar to that observed in the quasi-separatrix layer or slip-running reconnection. Title: The nature and significance of solar minima Authors: Priest, Eric Bibcode: 2012IAUS..286....3P Altcode: As an introduction to the theme of this symposium, I give a simple review of the photospheric magnetic field, the properties of the solar cycle, the way in which the magnetic field is thought to be generated by dynamo action, and finally the unusual properties of the recent solar minimum. This has awakened an interest in improving predictions of the solar cycle and in the nature of solar minima not just as gaps between maxima but as phenomena of intrinsic interest in their own right. Title: The onset of impulsive bursty reconnection at a two-dimensional current layer Authors: Fuentes-Fernández, J.; Parnell, C. E.; Priest, E. R. Bibcode: 2012PhPl...19g2901F Altcode: 2012arXiv1205.2120F The sudden reconnection of a non-force free 2D current layer, embedded in a low-beta plasma, triggered by the onset of an anomalous resistivity, is studied in detail. The resulting behaviour consists of two main phases. First, a transient reconnection phase, in which the current in the layer is rapidly dispersed and some flux is reconnected. This dispersal of current launches a family of small amplitude magnetic and plasma perturbations, which propagate away from the null at the local fast and slow magnetosonic speeds. The vast majority of the magnetic energy released in this phase goes into internal energy of the plasma, and only a tiny amount is converted into kinetic energy. In the wake of the outwards propagating pulses, an imbalance of Lorentz and pressure forces creates a stagnation flow which drives a regime of impulsive bursty reconnection, in which fast reconnection is turned on and off in a turbulent manner as the current density exceeds and falls below a critical value. During this phase, the null current density is continuously built up above a certain critical level, then dissipated very rapidly, and built up again, in a stochastic manner. Interestingly, the magnetic energy converted during this quasi-steady phase is greater than that converted during the initial transient reconnection phase. Again essentially all the energy converted during this phase goes directly to internal energy. These results are of potential importance for solar flares and coronal heating, and set a conceptually important reference for future 3D studies. Title: Consequences of spontaneous reconnection at a two-dimensional non-force-free current layer Authors: Fuentes-Fernández, J.; Parnell, C. E.; Hood, A. W.; Priest, E. R.; Longcope, D. W. Bibcode: 2012PhPl...19b2901F Altcode: 2012arXiv1202.0161F Magnetic neutral points, where the magnitude of the magnetic field vanishes locally, are potential locations for energy conversion in the solar corona. The fact that the magnetic field is identically zero at these points suggests that for the study of current sheet formation and of any subsequent resistive dissipation phase, a finite beta plasma should be considered, rather than neglecting the plasma pressure as has often been the case in the past. The rapid dissipation of a finite current layer in non-force-free equilibrium is investigated numerically, after the sudden onset of an anomalous resistivity. The aim of this study is to determine how the energy is redistributed during the initial diffusion phase, and what is the nature of the outward transmission of information and energy. The resistivity rapidly diffuses the current at the null point. The presence of a plasma pressure allows the vast majority of the free energy to be transferred into internal energy. Most of the converted energy is used in direct heating of the surrounding plasma, and only about 3% is converted into kinetic energy, causing a perturbation in the magnetic field and the plasma which propagates away from the null at the local fast magnetoacoustic speed. The propagating pulses show a complex structure due to the highly non-uniform initial state. It is shown that this perturbation carries no net current as it propagates away from the null. The fact that, under the assumptions taken in this paper, most of the magnetic energy released in the reconnection converts internal energy of the plasma, may be highly important for the chromospheric and coronal heating problem. Title: Cosmic magnetic fields in the Sun: Current Outstanding Problems (Invited Review) Authors: Priest, Eric Bibcode: 2011IAUS..273....1P Altcode: In the Sun there has been much progress towards answering fundamental problems with profound implications for the behaviour of cosmic magnetic fields in other stars. A review is given here of such problems, including identifying some of the outstanding questions that remain. In the solar interior, the main dynamo operates at the base of the convection zone, but its details have not been identified. In the solar surface, recent observations have revealed many new and surprising properties of magnetic fields, but understanding the key processes of flux emergence, fragmentation, merging and cancellation is rudimentary. Sunspots have until very recently been an enigma. In the atmosphere, there are many new ideas for coronal heating and solar wind acceleration, but the mechanisms have not yet been pinned down. Also, the detailed mechanisms for solar flares and coronal mass ejections remain controversial. In future, new generations of space and ground-based measurements and computational modelling should enable a definitive physical understanding of these puzzles. Title: The Flux Tube Tectonics model for coronal heating Authors: Priest, Eric R. Bibcode: 2011JASTP..73..271P Altcode: An account is presented of the Flux Tube Tectonics model for heating the solar corona, in which a multitude of current sheets are continually forming and dissipating. In addition, a model is summarised for the time-dependent response of the corona to the sudden dissipation of one such current sheet. Title: Nonlinear Plasma Physics of the Solar Corona Authors: Priest, Eric R. Bibcode: 2011AIPC.1320....3P Altcode: As a tribute to Dennis Papadopoulos, we present a review of some recent ideas in solar coronal plasma physics. In particular we discuss some models of coronal heating, notably the coronal tectonics model, as well as some ideas on the nature of reconnection in three dimensions. In addition, we summarise a model for the time-dependent response of the corona to the sudden dissipation of a current sheet. Title: MHD reconnection Authors: Priest, Eric Bibcode: 2011SchpJ...6.2371P Altcode: No abstract at ADS Title: Opening Remarks Authors: Priest, E. Bibcode: 2010ASSP...19...10P Altcode: 2010mcia.conf...10P I would like to add my warm welcome to this meeting on behalf of the Scientific Organizing Committee. I am delighted that so many of the world's leading solar physicists have agreed to attend this meeting. Title: Interaction of twisted curved flux tubes Authors: Selwa, Malgorzata; Parnell, Clare; Priest, Eric Bibcode: 2010cosp...38.1947S Altcode: 2010cosp.meet.1947S Most solar eruptions are initiated from sigmoidal structures. We perform 3D MHD numerical experiments of the interaction of force-free dipolar flux tubes. The magnetic configuration is initialized as either a potential or a force-free dipole with a constant density. Next we perturb the dipoles by twisting or rotating them leading to reconnection in a resistive MHD regime. We compare the connectivity, energetics and topological features in both models, vary the contact angle of the dipoles and check if the initial configuration (sigmoidal or not) affects flares and eruption initiation leading to faster and stronger reconnection. Title: Three-dimensional null point reconnection regimes Authors: Priest, E. R.; Pontin, D. I. Bibcode: 2009PhPl...16l2101P Altcode: 2009arXiv0910.3043P Recent advances in theory and computational experiments have shown the need to refine the previous categorization of magnetic reconnection at three-dimensional null points-points at which the magnetic field vanishes. We propose here a division into three different types, depending on the nature of the flow near the spine and fan of the null. The spine is an isolated field line which approaches the null (or recedes from it), while the fan is a surface of field lines which recede from it (or approach it). So-called torsional spine reconnection occurs when field lines in the vicinity of the fan rotate, with current becoming concentrated along the spine so that nearby field lines undergo rotational slippage. In torsional fan reconnection field lines near the spine rotate and create a current that is concentrated in the fan with a rotational flux mismatch and rotational slippage. In both of these regimes, the spine and fan are perpendicular and there is no flux transfer across spine or fan. The third regime, called spine-fan reconnection, is the most common in practice and combines elements of the previous spine and fan models. In this case, in response to a generic shearing motion, the null point collapses to form a current sheet that is focused at the null itself, in a sheet that locally spans both the spine and fan. In this regime the spine and fan are no longer perpendicular and there is flux transfer across both of them. Title: Dynamic non-null magnetic reconnection in three dimensions-II: composite solutions Authors: Wilmot-Smith, A. L.; Hornig, G.; Priest, E. R. Bibcode: 2009GApFD.103..515W Altcode: 2008arXiv0811.4621W In this series of papers we examine magnetic reconnection in a domain where the magnetic field does not vanish and the non-ideal region is localised in space. In a previous paper we presented a technique for obtaining analytical solutions to the stationary resistive MHD equations in such a situation and examined specific examples of non-ideal reconnective solutions. Here we further develop the model, noting that certain ideal solutions may be superimposed onto the fundamental non-ideal solutions and examining the effect of imposing various such flows. Significant implications are found for the evolution of magnetic flux in the reconnection process. It is shown that, in contrast to the two-dimensional case, in three-dimensions there is a very wide variety of physically different steady reconnection solutions. Title: Relationship between the topological skeleton, current concentrations, and 3D magnetic reconnection sites in the solar atmosphere Authors: Maclean, R. C.; Büchner, J.; Priest, E. R. Bibcode: 2009A&A...501..321M Altcode: Aims: The aim of this work is to determine the relationship between the 3D structure of the coronal magnetic field, diagnosed by the topological skeleton, and current concentrations as potential sites of 3D reconnection.
Methods: We utilised the results of 3D numerical MHD simulations of an observed EUV bright point (BP) in the solar atmosphere. The simulations are based on MDI line-of-sight magnetogram data from 13 June 1998. We analysed the results of the simulations using the method of magnetic charge topology. Three different methods of reducing the magnetogram to a set of point magnetic sources are tested.
Results: Observations of the BP show a rotation of one of its main magnetic source regions. Numerical simulations of this rotational motion result in a localised build-up of parallel electric current, which is dissipated by anomalous resistivity, causing 3D magnetic reconnection and BP heating. The magnetic topological structure of the simulated BP was also calculated, and a portion of the topological separatrix surface bounding the magnetic flux of the rotating source region is found to correspond to the locations of current build-up and heating. All three magnetogram reduction methods produce similar results for the large-scale magnetic field structure.
Conclusions: Magnetic topology is a useful method for predicting the locations of coronal current concentrations, insofar as the results of our simulations show that strong integrated parallel electric fields are found only along topological separatrix surfaces. However, further investigation is necessary to determine exactly which parts of the reconstructed separatrices will host the electric currents. Topological magnetic field reconstructions also cast light on the location of coronal BP heating, which occurs as a result of the dissipation of the currents by 3D reconnection. The choice of the magnetogram reduction algorithm does not greatly affect the large-scale topological features of the resulting reconstructed magnetic field. Further work is required to compare these results with data for other observed BPs. Title: Slip-Squashing Factors as a Measure of Three-Dimensional Magnetic Reconnection Authors: Titov, V. S.; Forbes, T. G.; Priest, E. R.; Mikić, Z.; Linker, J. A. Bibcode: 2009ApJ...693.1029T Altcode: 2008arXiv0807.2892T A general method for describing magnetic reconnection in arbitrary three-dimensional magnetic configurations is proposed. The method is based on the field-line mapping technique previously used only for the analysis of a magnetic structure at a given time. This technique is extended here so as to analyze the evolution of a magnetic structure. Such a generalization is made with the help of new dimensionless quantities called "slip-squashing factors." Their large values define the surfaces that border the reconnected or to-be-reconnected magnetic flux tubes for a given period of time during the magnetic evolution. The proposed method is universal, since it assumes only that the time sequence of evolving magnetic field and the tangential boundary flows are known. The application of the method is illustrated for simple examples, one of which was considered previously by Hesse and coworkers in the framework of the general magnetic reconnection theory. The examples help us to compare these two approaches; it reveals also that, just as for magnetic null points, hyperbolic and cusp minimum points of a magnetic field serve as favorable sites for magnetic reconnection. The new method admits a straightforward numerical implementation and provides a powerful tool for the diagnostics of magnetic reconnection in numerical models of solar-flare-like phenomena in space and laboratory plasmas. Title: The Solar-Stellar Connection: Our New Sun Authors: Priest, Eric R. Bibcode: 2009AIPC.1094....3P Altcode: 2009csss...15....3P Our view of the Sun has changed dramatically over the past 10 years due mainly to a series of space satellites such as Yohkoh, SoHO and TRACE. This state of ferment will continue with the coming onto line last year of two other satellites, Hinode and STEREO, and next year SDO. Here we give a brief overview of the progress made in answering fundamental questions about the nature of the Sun which may have profound implications for other stars.

In the interior, helioseismology has revealed the internal rotation structure and suggested that the main solar dynamo responsible for active regions is located at the tachocline, although the details are highly uncertain and there may be a second dynamo responsible for generating small-scale ephemeral regions. In the photosphere, flux is mainly concentrated at the edges of supergranule cells, but recent high-resolution observations have suggested that extra flux is also located at granulation boundaries and Hinode has discovered much horizontal flux.

The solar corona is likely to be heated in myriads of tiny current sheets by reconnection, according to the Coronal Tectonics Model. Observations suggest that all the coronal field lines reconnect every 1.5 hours. Theory has shown that reconnection in 3D has many features that are completely different from the standard 2D picture. The solar wind is highly dynamic and complex and its acceleration mechanism may possibly be high-frequency ion-cyclotron waves. Many new features of solar flares and coronal mass ejections have been discovered, but it is not known whether the cause of the eruption is an instability or a lack of equilibrium. Title: Slip-Squashing Factors as a Measure of Three-Dimensional Magnetic Reconnection Authors: Titov, V. S.; Forbes, T. G.; Priest, E. R.; Mikic, Z.; Linker, J. A. Bibcode: 2008AGUFMSM31A1713T Altcode: A general method for describing magnetic reconnection in arbitrary three-dimensional magnetic configurations is proposed. The method is based on the field-line mapping technique previously used only for the analysis of magnetic structure at a given time. This technique is extended here so as to analyze the evolution of magnetic structure. Such a generalization is made with the help of new dimensionless quantities called "slip-squashing factors". Their large values define the surfaces that border the reconnected or to-be-reconnected magnetic flux tubes for a given period of time during the magnetic evolution. The proposed method is universal, since it assumes only that the time sequence of the evolving magnetic field and the tangential boundary flows are known. The application of the method is illustrated for simple examples, one of which was considered previously by Hesse and coworkers in the framework of the general magnetic reconnection theory. The examples help to compare these two approaches; they reveal also that, just as for magnetic null points, hyperbolic and cusp minimum points of a magnetic field may serve as favorable sites for magnetic reconnection. The new method admits a straightforward numerical implementation and provides a powerful tool for the diagnostics of magnetic reconnection in numerical models of solar-flare-like phenomena in space and laboratory plasmas. Research partially supported by NASA and NSF. Title: Coronal Alfvén speeds in an isothermal atmosphere. I. Global properties Authors: Régnier, S.; Priest, E. R.; Hood, A. W. Bibcode: 2008A&A...491..297R Altcode: 2008arXiv0809.1155R Aims: Estimating Alfvén speeds is of interest in modelling the solar corona, studying the coronal heating problem and understanding the initiation and propagation of coronal mass ejections (CMEs).
Methods: We assume here that the corona is in a magnetohydrostatic equilibrium and that, because of the low plasma β, one may decouple the magnetic forces from pressure and gravity. The magnetic field is then described by a force-free field for which we perform a statistical study of the magnetic field strength with height for four different active regions. The plasma along each field line is assumed to be in a hydrostatic equilibrium. As a first approximation, the coronal plasma is assumed to be isothermal with a constant or varying gravity with height. We study a bipolar magnetic field with a ring distribution of currents, and apply this method to four active regions associated with different eruptive events.
Results: By studying the global properties of the magnetic field strength above active regions, we conclude that (i) most of the magnetic flux is localized within 50 Mm of the photosphere; (ii) most of the energy is stored in the corona below 150 Mm; (iii) most of the magnetic field strength decays with height for a nonlinear force-free field slower than for a potential field. The Alfvén speed values in an isothermal atmosphere can vary by two orders of magnitude (up to 100 000 km s-1). The global properties of the Alfvén speed are sensitive to the nature of the magnetic configuration. For an active region with highly twisted flux tubes, the Alfvén speed is significantly increased at the typical height of the twisted flux bundles; in flaring regions, the average Alfvén speeds are above 5000 km s-1 and depart highly from potential field values.
Conclusions: We discuss the implications of this model for the reconnection rate and inflow speed, the coronal plasma β and the Alfvén transit time. Title: Highlights from Hinode Authors: Priest, E. R. Bibcode: 2008ASPC..397..147P Altcode: A personal summary is presented of the main results that have been presented at the conference. Particular emphasis is given to the new discoveries that have made use of the SOT, XRT and EIS instruments on board Hinode. Title: Global properties of Alfven speeds in the corona Authors: Regnier, Stephane; Priest, Eric; Hood, Alan Bibcode: 2008cosp...37.2585R Altcode: 2008cosp.meet.2585R We investigate the values and distribution of the Alfvén speed in the solar corona. We assume e that the coronal magnetic field is force-free and the plasma is isothermal and in hydrostatic equilibrium. Firstly we consider a bipolar configuration in order to study the effect of parameters such as the pressure scale-height and the density at the base of the corona. Secondly, we apply the model to four active regions at different stages of their evolution (before and after a flare or a CME). At a given height in the low corona, the Alfvén speed values can vary by two e orders of magnitude (up to 100000 km·s-1 ). For an active region with highly twisted flux tubes, the Alfvén speed is significantly increased at the typical height of the twisted flux bundles; in e flaring regions, the average Alfvén speeds are above 5000 km·s-1 and depart strongly from e potential field values. We discuss implications for coronal heating models and CME models in terms of the plasma β, the inflow speed and the reconnection rate. Title: Free Magnetic Energy in Solar Active Regions above the Minimum-Energy Relaxed State Authors: Régnier, S.; Priest, E. R. Bibcode: 2007ApJ...669L..53R Altcode: 2008arXiv0805.1619R To understand the physics of solar flares, including the local reorganization of the magnetic field and the acceleration of energetic particles, we have first to estimate the free magnetic energy available for such phenomena, which can be converted into kinetic and thermal energy. The free magnetic energy is the excess energy of a magnetic configuration compared to the minimum-energy state, which is a linear force-free field if the magnetic helicity of the configuration is conserved. We investigate the values of the free magnetic energy estimated from either the excess energy in extrapolated fields or the magnetic virial theorem. For four different active regions, we have reconstructed the nonlinear force-free field and the linear force-free field corresponding to the minimum-energy state. The free magnetic energies are then computed. From the energy budget and the observed magnetic activity in the active region, we conclude that the free energy above the minimum-energy state gives a better estimate and more insights into the flare process than the free energy above the potential field state. Title: Topological Aspects of Global Magnetic Field Reversal in the Solar Corona Authors: Maclean, R. C.; Priest, E. R. Bibcode: 2007SoPh..243..171M Altcode: Every eleven years on average, the dipolar component of the Sun's global coronal magnetic field reverses in sign - a consequence of the sunspot cycle. In this paper we begin to investigate the complex changes in coronal structure during the reversal. We present a simplified model of the solar cycle containing six time-varying photospheric sources of magnetic field and analyse the evolution of the global coronal field using the technique of magnetic charge topology. Surprisingly, a sequence of seventeen topological changes takes place in the model between one solar minimum state and the next; many of the resultant topological configurations correspond to observable magnetic field structures in the real corona. We also show how descriptions of all the six-source topological states from the model can be built up in terms of combinations of simpler four-source states, providing a framework for future descriptions of even more complicated topological states. Title: Nonlinear force-free models for the solar corona. I. Two active regions with very different structure Authors: Régnier, S.; Priest, E. R. Bibcode: 2007A&A...468..701R Altcode: 2007astro.ph..3756R Context: With the development of new instrumentation providing measurements of solar photospheric vector magnetic fields, we need to develop our understanding of the effects of current density on coronal magnetic field configurations.
Aims: The object is to understand the diverse and complex nature of coronal magnetic fields in active regions using a nonlinear force-free model.
Methods: From the observed photospheric magnetic field we derive the photospheric current density for two active regions: one is a decaying active region with strong currents (AR8151), and the other is a newly emerged active region with weak currents (AR8210). We compare the three-dimensional structure of the magnetic fields for both active region when they are assumed to be either potential or nonlinear force-free. The latter is computed using a Grad-Rubin vector-potential-like numerical scheme. A quantitative comparison is performed in terms of the geometry, the connectivity of field lines, the magnetic energy and the magnetic helicity content.
Results: For the old decaying active region the connectivity and geometry of the nonlinear force-free model include strong twist and strong shear and are very different from the potential model. The twisted flux bundles store magnetic energy and magnetic helicity high in the corona (about 50 Mm). The newly emerged active region has a complex topology and the departure from a potential field is small, but the excess magnetic energy is stored in the low corona and is enough to trigger powerful flares. Title: News and Views: Does the Sun affect the Earth's climate? Authors: Priest, Eric; Lockwood, Mike; Solanki, Sami; Wolfendale, Arnold; Coustenis, A. Bibcode: 2007A&G....48c...7P Altcode: 2007A&G....48c...7C Svensmark's article in the February issue (A&G 2007 48 1.18) presented a possible mechanism for the way the Sun could influence the Earth's climate. He suggested that water droplets condense in the ionization trail left by cosmic rays, whose flux varies inversely with solar activity: when the magnetic field of the solar wind is stronger, it shields the Earth from galactic cosmic rays and so decreases their flux on the Earth; according to Svensmark's ideas, this produces fewer clouds and thereby heats the Earth. Title: Magnetohydrodynamic evolution of magnetic skeletons Authors: Haynes, A. L.; Parnell, C. E.; Galsgaard, K.; Priest, E. R. Bibcode: 2007RSPSA.463.1097H Altcode: 2007astro.ph..2604H The heating of the solar corona is probably due to reconnection of the highly complex magnetic field that threads throughout its volume. We have run a numerical experiment of an elementary interaction between the magnetic field of two photospheric sources in an overlying field that represents a fundamental building block of the coronal heating process. The key to explaining where, how and how much energy is released during such an interaction is to calculate the resulting evolution of the magnetic skeleton. A skeleton is essentially the web of magnetic flux surfaces (called separatrix surfaces) that separate the coronal volume into topologically distinct parts. For the first time, the skeleton of the magnetic field in a three-dimensional numerical magnetohydrodynamic experiment is calculated and carefully analysed, as are the ways in which it bifurcates into different topologies. A change in topology normally changes the number of magnetic reconnection sites.

In our experiment, the magnetic field evolves through a total of six distinct topologies. Initially, no magnetic flux joins the two sources. Then, a new type of bifurcation, called a global double-separator bifurcation, takes place. This bifurcation is probably one of the main ways in which new separators are created in the corona (separators are field lines at which three-dimensional reconnection takes place). This is the first of five bifurcations in which the skeleton becomes progressively more complex before simplifying. Surprisingly, for such a simple initial state, at the peak of complexity there are five separators and eight flux domains present. Title: Magnetic Reconnection Authors: Priest, Eric; Forbes, Terry Bibcode: 2007mare.book.....P Altcode: Preface; 1. Introduction; 2. Current-sheet formation; 3. Magnetic annihilation; 4. Steady reconnection: the classical solutions; 5. Steady reconnection: new generation of fast regimes; 6. Unsteady reconnection: the tearing mode; 7. Unsteady reconnection: other approaches; 8. Reconnection in three dimensions; 9. Laboratory applications; 10. Magnetospheric applications; 11. Solar applications; 12. Astrophysical applications; 13. Particle acceleration; References; Appendices; Index. Title: Reconnection of Magnetic Fields Authors: Birn, J.; Priest, E. R. Bibcode: 2007rmf..book.....B Altcode: Preface; Part I. Introduction: 1.1 The Sun E. R. Priest; 1.2 Earth's magnetosphere J. Birn; Part II. Basic Theory of MHD Reconnection: 2.1 Classical theory of two-dimensional reconnection T. G. Forbes; 2.2 Fundamental concepts G. Hornig; 2.3 Three-dimensional reconnection in the absence of magnetic null points G. Hornig; 2.4 Three-dimensional reconnection at magnetic null points D. Pontin; 2.5 Three-dimensional flux tube reconnection M. Linton; Part III. Basic Theory of Collisionless Reconnection: 3.1 Fundamentals of collisionless reconnection J. Drake; 3.2 Diffusion region physics M. Hesse; 3.3 Onset of magnetic reconnection P. Pritchett; 3.4 Hall-MHD reconnection A. Bhattacharjee and J. Dorelli; 3.5 Role of current-aligned instabilities J. Büchner and W. Daughton; 3.6 Nonthermal particle acceleration M. Hoshino; Part IV. Reconnection in the Magnetosphere: 4.1 Reconnection at the magnetopause: concepts and models J. G. Dorelli and A. Bhattacharjee; 4.2 Observations of magnetopause reconnection K.-H. Trattner; 4.3 On the stability of the magnetotail K. Schindler; 4.4 Simulations of reconnection in the magnetotail J. Birn; 4.5 Observations of tail reconnection W. Baumjohann and R. Nakamura; 4.6 Remote sensing of reconnection M. Freeman; Part V. Reconnection in the Sun's Atmosphere: 5.1 Coronal heating E. R. Priest; 5.2 Separator reconnection D. Longcope; 5.3 Pinching of coronal fields V. Titov; 5.4 Numerical experiments on coronal heating K. Galsgaard; 5.5 Solar flares K. Kusano; 5.6 Particle acceleration in flares: theory T. Neukirch; 5.7 Fast particles in flares: observations L. Fletcher; 6. Open problems J. Birn and E. R. Priest; Bibliography; Index. Title: Reconnection of magnetic fields : magnetohydrodynamics and collisionless theory and observations Authors: Birn, J.; Priest, E. R. Bibcode: 2007rmfm.book.....B Altcode: No abstract at ADS Title: Solar Atmosphere Authors: Priest, E. R. Bibcode: 2007hste.book...56P Altcode: No abstract at ADS Title: Transition-Region Explosive Events: Reconnection Modulated by p-Mode Waves Authors: Chen, P. F.; Priest, E. R. Bibcode: 2006SoPh..238..313C Altcode: 2006SoPh..tmp...61C Transition-region explosive events (TREEs) have long been proposed as a consequence of magnetic reconnection. However, several critical issues have not been well addressed, such as the location of the reconnection site, their unusually short lifetime (about one minute), and the recently discovered repetitive behaviour with a period of three to five minutes. In this paper, we perform MHD numerical simulations of magnetic reconnection, where the effect of five-minute solar p-mode oscillations is examined. UV emission lines are synthesised on the basis of numerical results in order to compare with observations directly. It is found that several typical and puzzling features of the TREEs with impulsive bursty behaviour can only be explained if there exist p-mode oscillations and the reconnection site is located in the upper chromosphere at a height range of around 1900 km < h < 2150 km above the solar surface. Furthermore, the lack of proper motions of the high-velocity ejection may be due to a rapid change of temperature along the reconnection ejecta. Title: Coronal Magnetic Topologies in a Spherical Geometry II. Four Balanced Flux Sources Authors: Maclean, R. C.; Beveridge, C.; Priest, E. R. Bibcode: 2006SoPh..238...13M Altcode: 2006SoPh..tmp...32M The Sun's magnetic field is the primary factor determining the structure and evolution of the solar corona. Here, magnetic topology is used in combination with a Green's function method to model the global coronal magnetic field with a spherical photosphere. We focus on the case of three negative flux sources and one positive source, completing our previous categorisation of the topological states and bifurcations that are present in quadrupolar configurations in a spherical geometry. Three fundamental varieties of topological state are found, with three types of bifurcation taking one to the other. A comparison to the equivalent results for a planar photosphere is then carried out, and the differences between the two cases are explained. Title: Coronal Magnetic Topologies in a Spherical Geometry I. Two Bipolar Flux Sources Authors: Maclean, R. C.; Beveridge, C.; Hornig, G.; Priest, E. R. Bibcode: 2006SoPh..237..227M Altcode: No abstract at ADS Title: Our Enigmatic Sun Authors: Priest, E. R. Bibcode: 2006AIPC..848....3P Altcode: Many major puzzles in Solar Physics have not yet been answered and are of wide importance for astrophysics in general, such as: How is the magnetic field generated? How is the corona heated? How do solar flares occur? What is the effect of solar variations on the Earth's climate? How is the solar wind accelerated? In each case, the questions have multiple parts, some of which have been recently answered with the help of spectacular space observations, while others are being refined in ways that will be described. Title: Understanding Magnetic Structures in the Solar Corona Through Topological Analysis Authors: Maclean, R. C.; Parnell, C. E.; De Moortel, I.; Büchner, J.; Priest, E. R. Bibcode: 2006ESASP.617E.156M Altcode: 2006soho...17E.156M No abstract at ADS Title: Solar coronal heating by magnetic cancellation - II. Disconnected and unequal bipoles Authors: von Rekowski, B.; Parnell, C. E.; Priest, E. R. Bibcode: 2006MNRAS.369...43V Altcode: 2006MNRAS.tmp..503V Two-dimensional numerical magnetohydrodynamic simulations of a cancelling magnetic feature (CMF) and the associated coronal X-ray bright point (XBP) are presented. Coronal magnetic reconnection is found to produce the Ohmic heating required for a coronal XBP. During the BP phase where reconnection occurs above the base, about 90-95 per cent of the magnetic flux of the converging magnetic bipole cancels at the base. The last ~5 to 10 per cent of the base magnetic flux is cancelled when reconnection occurs at the base. Reconnection happens in a time-dependent way in response to the imposed converging footpoint motions. A potential field model gives a good first approximation to the qualitative behaviour of the system, but the magnetohydrodynamics (MHD) experiments reveal several quantitative differences: for example, the effects of plasma inertia and a pressure build-up in-between the converging bipole are to delay the onset of coronal reconnection above the base and to lower the maximum X-point height. Title: Coronal Magnetic Topologies in a Spherical Geometry I. Two Bipolar Flux Sources Authors: Maclean, R. C.; Hornig, G.; Priest, E. R.; Beveridge, C. Bibcode: 2006SoPh..235..259M Altcode: The evolution of the solar corona is dominated to a large extent by the hugely complicated magnetic field which threads it. Magnetic topology provides a tool to decipher the structure of this field and thus help to understand its behaviour. Usually, the magnetic topology of a potential field is calculated due to flux sources on a locally planar photospheric surface. We use a Green's function method to extend this theory to sources on a global spherical surface. The case of two bipolar flux-balanced source regions is studied in detail, with an emphasis on how the distribution and relative strengths of the source regions affect the resulting topological states. A new state with two spatially distinct separators connecting the same two magnetic null points, called the "dual intersecting" state, is discovered. Title: Solar coronal heating by magnetic cancellation - I. Connected equal bipoles Authors: von Rekowski, B.; Parnell, C. E.; Priest, E. R. Bibcode: 2006MNRAS.366..125V Altcode: 2006MNRAS.tmp....9V We present two-dimensional numerical magnetohydrodynamic simulations of a cancelling magnetic feature and the associated coronal X-ray bright point. Coronal reconnection is found to produce significant Ohmic heating, and at the same time about 90 per cent of the magnetic flux is cancelled. The presence of downflows accelerates the process of flux cancellation in the early phase. The last 10 per cent of the cancellation takes place by reconnection at the base. Reconnection occurs in a time-dependent way in response to the footpoint motions, and the resulting sequence of magnetic configurations is close to potential. Title: Book Review: THE SOLAR-B MISSION AND THE FOREFRONT OF SOLAR PHYSICS / Astronomical Society of the Pacific, 2005 Authors: Priest, Eric Bibcode: 2006Obs...126..215P Altcode: No abstract at ADS Title: Our Magnetic Sun Authors: Priest, E. R. Bibcode: 2006msu..conf..197P Altcode: No abstract at ADS Title: MHD simulations of photospheric cancelling magnetic features causing coronal X-ray bright points Authors: von Rekowski, B.; Parnell, C. E.; Priest, E. R. Bibcode: 2006cosp...36.2936V Altcode: 2006cosp.meet.2936V begin document Discovering the mechanisms for heating the solar corona represents one of the major challenges in astronomy at the present time Long-period MHD waves have now been ruled out as a mechanism and so the main focus is on various ways in which magnetic reconnection can heat the three main elements of the Sun s corona namely X-ray bright points coronal loops and coronal holes Coronal X-ray bright points XBPs have been observed to account for about 20 to 30 percent of the heating of the quiet-Sun corona releasing energies ranging from 10 27 to 10 29 erg About two thirds of XBPs are located above sites of cancelling magnetic bipoles so-called cancelling magnetic features CMFs The analytical converging flux model of Priest et al 1994 ApJ 427 459 is now recognised as a likely explanation of the heating of these XBPs where the heating takes place in response to the approach and cancellation of underlying photospheric magnetic fragments of opposite polarity to which the coronal magnetic loops are linked The CMFs trigger coronal magnetic reconnection and the associated coronal heating in form of XBPs Magnetic cancellation itself is driven by converging photospheric footpoint motions of the bipolar sources and involves flux submergence Building upon this model von Rekowski et al 2006 MNRAS 366 125 and 2006 MNRAS in press have recently begun to develop a greatly improved numerical MHD model that investigates the dynamical behaviour of CMFs and the associated reconnection and coronal heating Title: Solar Coronal Heating by Magnetic Cancellation Authors: von Rekowski, B.; Parnell, C. E.; Priest, E. R. Bibcode: 2005ESASP.600E..95V Altcode: 2005dysu.confE..95V; 2005ESPM...11...95V No abstract at ADS Title: Chromospheric and Coronal Magnetic Fields Authors: Priest, E. Bibcode: 2005ESASP.596E..47P Altcode: 2005ccmf.confE..47P No abstract at ADS Title: Low-order stellar dynamo models Authors: Wilmot-Smith, A. L.; Martens, P. C. H.; Nandy, D.; Priest, E. R.; Tobias, S. M. Bibcode: 2005MNRAS.363.1167W Altcode: 2005MNRAS.tmp..855W Stellar magnetic activity - which has been observed in a diverse set of stars including the Sun - originates via a magnetohydrodynamic dynamo mechanism working in stellar interiors. The full set of magnetohydrodynamic equations governing stellar dynamos is highly complex, and so direct numerical simulation is currently out of reach computationally. An understanding of the bifurcation structure, likely to be found in the partial differential equations governing such dynamos, is vital if we are to understand the activity of solar-like stars and its evolution with varying stellar parameters such as rotation rate. Low-order models are an important aid to this understanding, and can be derived either as approximations of the governing equations themselves or by using bifurcation theory to obtain systems with the desired structure. We use normal-form theory to derive a third-order model with robust behaviour. The model is able to reproduce many of the basic types of behaviour found in observations of solar-type stars. In the appropriate parameter regime, a chaotic modulation of the basic cycle is present, together with varying periods of low activity such as that observed during the solar Maunder minima. Title: Coronal Flux Recycling Times Authors: Close, R. M.; Parnell, C. E.; Longcope, D. W.; Priest, E. R. Bibcode: 2005SoPh..231...45C Altcode: High-cadence, high-resolution magnetograms have shown that the quiet-Sun photosphere is very dynamic in nature. It is comprised of discrete magnetic fragments which are characterized by four key processes - emergence, coalescence, fragmentation and cancellation. All of this will have consequences for the magnetic field in the corona above. Title: A topological analysis of the magnetic breakout model for an eruptive solar flare Authors: Maclean, Rhona; Beveridge, Colin; Longcope, Dana; Brown, D. S.; Priest, E. R. Bibcode: 2005RSPSA.461.2099M Altcode: The magnetic breakout model gives an elegant explanation for the onset of an eruptive solar flare, involving magnetic reconnection at a coronal null point which leads to the initially enclosed flux ‘breaking out’ to large distances. In this paper we take a topological approach to the study of the conditions required for this breakout phenomenon to occur. The evolution of a simple delta sunspot model, up to the point of breakout, is analysed through several sequences of potential and linear force-free quasi-static equilibria. We show that any new class of field lines, such as those connecting to large distances, must be created through a global topological bifurcation and derive rules to predict the topological reconfiguration due to various types of bifurcation. Title: Coronal Heating at Separators and Separatrices Authors: Priest, E. R.; Longcope, D. W.; Heyvaerts, J. Bibcode: 2005ApJ...624.1057P Altcode: Several ways have been proposed for heating the solar corona by magnetic reconnection in current sheets, depending on the nature of both the coronal magnetic field and the photospheric driving. Two ways that have recently been considered involve the formation of such current sheets either along separatrices (surfaces that separate topologically distinct regions) or along separators (intersections of separatrices linking one null point to another). The effect of slow photospheric motions on complex coronal magnetic configurations will in general be to generate three forms of electric current, namely, nonsingular distributed currents, singular currents on separatrices and singular currents on separators. These currents are not mutually exclusive but will in general coexist in the same configuration. The aim of this paper is to compare energy storage and heating that occurs at separatrices and separators. We use reduced MHD to model coronal loops that are much longer than they are wide, and we construct a series of examples for the formation of current sheets along separatrices and separators. We deduce that coronal heating is of comparable importance at separatrices and separators. Separatrices are twice as effective for observed small footpoint motions, while separators are twice as effective in the initial build-up of a new flux domain. Title: Forced magnetic reconnection Authors: Birn, J.; Galsgaard, K.; Hesse, M.; Hoshino, M.; Huba, J.; Lapenta, G.; Pritchett, P. L.; Schindler, K.; Yin, L.; Büchner, J.; Neukirch, T.; Priest, E. R. Bibcode: 2005GeoRL..32.6105B Altcode: 2005GeoRL..3206105B Using a multi-code approach, we investigate current sheet thinning and the onset and progress of fast magnetic reconnection, initiated by temporally limited, spatially varying, inflow of magnetic flux. The present study extends an earlier collaborative effort into the transition regime from thick to thin current sheets. Again we find that full particle, hybrid, and Hall-MHD simulations lead to the same fast reconnection rates, apparently independent of the dissipation mechanism. The reconnection rate in MHD simulations is considerably larger than in the earlier study, although still somewhat smaller than in the particle simulations. All simulations lead to surprisingly similar final states, despite differences in energy transfer and dissipation. These states are contrasted with equilibrium models derived for the same boundary perturbations. The similarity of the final states indicates that entropy conservation is satisfied similarly in fluid and kinetic approaches and that Joule dissipation plays only a minor role in the energy transfer. Title: Numerical Simulations of the Flux Tube Tectonics Model for Coronal Heating Authors: Mellor, C.; Gerrard, C. L.; Galsgaard, K.; Hood, A. W.; Priest, E. R. Bibcode: 2005SoPh..227...39M Altcode: In this paper we present results from 3D MHD numerical simulations based on the flux tube tectonics method of coronal heating proposed by Priest, Heyvaerts, and Title (2002). They suggested that individual coronal loops connect to the photosphere in many different magnetic flux fragments and that separatrix surfaces exist between the fingers connecting a loop to the photosphere and between individual loops. Simple lateral motions of the flux fragments could then cause currents to concentrate along the separatrices which may then drive reconnection contributing to coronal heating. Here we have taken a simple configuration with four flux patches on the top and bottom of the numerical domain and a small background axial field. Then we move two of the flux patches on the base between the other two using periodic boundary conditions such that when they leave the box they re-enter it at the other end. This simple motion soon causes current sheets to build up along the quasi-separatrix layers and subsequently magnetic diffusion/reconnection occurs. Title: Magnetic diffusion and the motion of field lines Authors: Wilmot-Smith, A. L.; Priest, E. R.; Hornig, G. Bibcode: 2005GApFD..99..177W Altcode: Diffusion of a magnetic field through a plasma is discussed in one-, two- and three-dimensional configurations, together with the possibility of describing such diffusion in terms of a magnetic flux velocity, which, when it exists, is in general non-unique. Physically useful definitions of such a velocity include doing so in terms of the energy flow or in such a way that it vanishes in a steady state. Straight field lines (or plane flux surfaces) diffuse as if flux is disappearing at a neutral sheet, whereas circular field lines (or cylindrical flux surfaces) do so as if flux is disappearing at an 0-type neutral line. In three dimensions it is not always possible to define a flux velocity, for example when the magnetic flux through a closed field line is changing in time. However, in at least some such cases it is possible to describe the behaviour of the magnetic field in terms of a pair of quasi-flux-velocities. Title: Kinematic reconnection at a magnetic null point: fan-aligned current Authors: Pontin, D. I.; Hornig, G.; Priest, E. R. Bibcode: 2005GApFD..99...77P Altcode: Magnetic reconnection at a three-dimensional null point is a natural extension of the familiar two-dimensional X-point reconnection. A model is set up here for reconnection at a null point with current directed parallel to the fan plane, by solving the kinematic, steady, resistive magnetohydrodynamic equations in its vicinity. The magnetic field is assumed to be steady, and a localised diffusion region surrounding the null point is also assumed, outside which the plasma is ideal. Particular attention is focussed on the way that the magnetic flux changes its connections as a result of the reconnection. The resultant plasma flow is found to cross the spine and fan of the null, and thus transfer magnetic flux between topologically distinct regions. Solutions are also found in which the flow crosses either the spine or fan only. Title: Domain structures in complex 3D magnetic fields Authors: Close, R. M.; Parnell, C. E.; Priest, E. R. Bibcode: 2005GApFD..99..513C Altcode: The numerous magnetic fragments that populate the mixed-polarity, quiet-Sun photosphere give rise to many interesting topological features in the corona. In light of this, much recent work has gone into classifying the configurations that arise from simple, point-source potential-field models in efforts to determine the nature of the quiet-Sun magnetic field. These studies have ranged from systematic and detailed examinations of magnetic fields arising from only a handful of sources, involving classifying the configurations that arise (and how some states may bifurcate into other states), to statistical studies of the overall properties of fields arising from hundreds of magnetic sources. Such studies have greatly increased our understanding of what we might expect the magnetic field over the quiet Sun to behave like; the purpose of the study presented here is to extend this understanding further by examining the structure of the individual domains (the regions in space through which pairs of opposite-polarity sources are connected). In particular, the features of lesser-known domain structures that are absent from fields arising from only a few sources and overlooked by sweeping statistical studies are documented. In spite of the incredible complexity of the coronal field, previous studies have shown that there are only two types of building block in a potential field arising from coplanar point sources: namely, an isolated dome, bounded by a single unbroken separatrix surface, and a separator-ring domain, engirdled by a ring of separators. However, it is demonstrated here how both isolated domains and separator-ring domains may be categorised further depending upon their particular geometrical and topological traits. As many models predict coronal heating at topologically distinct features in magnetic fields such as null points, separators and separatrices, for any such models to be applied to general fields would require a scheme for identifying which topological features are related to a given domain. The study here explores some of the issues that would need to be taken into account by such a scheme, and in particular the problems associated with trying to deduce the properties of a general magnetic field from knowledge of domain footprints alone. Animated 3D-rotational views of some of the figures in this manuscript may be viewed in AVI, MPEG and animated-GIF formats by visiting http://www-solar.mcs.st-and.ac.uk/robertc/animations/blocks.html and following the desired link. Title: Effects of Complexity on the Flux-Tube Tectonics Model Authors: Close, R. M.; Heyvaerts, J. F.; Priest, E. R. Bibcode: 2004SoPh..225..267C Altcode: The quiet-Sun magnetic field emerges through the solar photosphere in a multitude of mixed-polarity magnetic concentrations and is subsequently tangled up into intricate regions of interconnecting flux. Moreover, since these discrete concentrations are likely to be extremely small in size, with fluxes of around only 1017 Mx, the number of such flux sources in, say, a supergranule, will be extremely large. The flux-tube tectonics model of Priest, Heyvaerts, and Title (2002) demonstrated how the formation and dissipation of current sheets along the separatrices that separate the regions of different connectivity are likely to make an important contribution to coronal heating. Since the full complexity of the magnetic field is below present observable scales, this study examines the effect of having the magnetic flux emerge through configurations structured on smaller and smaller scales. It is found that, by fixing the amount of flux emerging into a given 2D region, the main factors influencing the current build-up along the separatrices are the number of sources through which the flux emerges and the spatial distribution of the sources on the photosphere. The free energy (i.e., that above potential) is stored lower and lower in the atmosphere as the complexity of the system increases. A simple comparison is then made between coronal heating by separator currents and by separatrix currents. It is found that both result in comparable amounts of energy release, with separatrix heating being the more dominant. Title: A Topological Analysis of the Magnetic Breakout Model for an Eruptive Solar Flare Authors: Maclean, R.; Beveridge, C.; Longcope, D.; Brown, D.; Priest, E. Bibcode: 2004ESASP.575..485M Altcode: 2004soho...15..485M No abstract at ADS Title: Kinematic Magnetic Reconnection at 3d Null Points Authors: Pontin, D. I.; Hornig, G.; Priest, E. R. Bibcode: 2004ESASP.575..507P Altcode: 2004soho...15..507P No abstract at ADS Title: Simple Numerical Simulations of the Flux Tube Tectonics Model for Coronal Heating Authors: Mellor, C.; Gerrard, C. L.; Galsgaard, K.; Hood, A. W.; Priest, E. R. Bibcode: 2004ESASP.575...29M Altcode: 2004soho...15...29M No abstract at ADS Title: Separators in 3D Quiet-Sun Magnetic Fields Authors: Close, R. M.; Parnell, C. E.; Priest, E. R. Bibcode: 2004SoPh..225...21C Altcode: At the confluence of four regions of different magnetic connectivity lies a distinct topological candidate for coronal heating, namely the magnetic separator. In this study, a method for tracing separator curves is developed and the statistical properties of separators in coronal fields are subsequently explored by analysing a model field with an exponential source distribution, similar to that studied by Schrijver and Title (2002). Magnetic fields based on data from an observed sequence of MDI magnetograms are also considered as a case study. The picture that emerges is one in which there are many more magnetic separators than previously thought, since many separators arise from each null point. For an exponential source distribution, an average of 10.1±0.13 separators per null are found, of which 1.04±0.04 "multiply link" pairs of nulls (i.e., there is more than one separator linking such pairs of nulls). For the observed sequence of magnetograms, these figures are 7.63±0.2 and 0.99± 0.059, respectively. The results obtained here show that separators have a tendency to group together into trunks about a null. In the case of prone nulls, these trunks lie either normal to the photospheric surface or on it. It is also established that pairs of coronal nulls are frequently interconnected, suggesting that they may have been created by purely coronal bifurcations. Title: Magnetic Reconnection Authors: Priest, E. R.; Pontin, D. I. Bibcode: 2004ASSL..317..397P Altcode: 2004shis.conf..397P No abstract at ADS Title: Recycling of the Solar Corona's Magnetic Field Authors: Close, R. M.; Parnell, C. E.; Longcope, D. W.; Priest, E. R. Bibcode: 2004ApJ...612L..81C Altcode: Magnetic fields play a dominant role in the atmospheres of the Sun and other Sun-like stars. Outside sunspot regions, the photosphere of the so-called quiet Sun contains myriads of small-scale magnetic concentrations, with strengths ranging from the detection limit of ~1016 Mx up to ~3×1020 Mx. The tireless motion of these magnetic flux concentrations, along with the continual appearance and disappearance of opposite-polarity pairs of fluxes, releases a substantial amount of energy that may be associated with a whole host of physical processes in the solar corona, not least the enigma of coronal heating. We find here that the timescale for magnetic flux to be remapped in the quiet-Sun corona is, surprisingly, only 1.4 hr (around 1/10 of the photospheric flux recycling time), implying that the quiet-Sun corona is far more dynamic than previously thought. Besides leading to a fuller understanding of the origins of magnetically driven phenomena in our Sun's corona, such a process may also be crucial for the understanding of stellar atmospheres in general. Title: The Dynamics of Reconnection in a Three Dimensional Current Sheet Authors: Linton, M. G.; Priest, E. R.; Longcope, D. W. Bibcode: 2004AAS...204.9509L Altcode: 2004BAAS...36R.827L Many models for solar flares and coronal heating rely on magnetic reconnection in three dimensional current sheets. Yet the topology and evolution of reconnection in such current sheets is not well known. We will present a numerical MHD study of such reconnection. We will show how the tearing mode evolves in a finite sized, 3D current sheet, and how this affects the dynamics of the magnetic field reconnecting in the sheet. We will show how the flux tubes formed in isolated reconnection regions slingshot away from the the reconnection site, how they interact with the unreconnected field surrounding them, and how this differs from the 2D reconnection limit. Finally we will discuss the dynamics of flux tubes reconnecting in a patchy reconnection scenario, where many isolated reconnection regions occur simultaneously in a current sheet. We will show how this causes reconnected flux tubes to become topologically entangled with each other, and how this limits the level of energy release which can be achieved in reconnection.

This work has been supported by NASA, ONR, and PPARC. Title: Kinematic reconnection at a magnetic null point: spine-aligned current Authors: Pontin, D. I.; Hornig, G.; Priest, E. R. Bibcode: 2004GApFD..98..407P Altcode: Magnetic reconnection at a three-dimensional null point is the natural extension of the familiar two-dimensional X-point reconnection. A model is set up here for reconnection at a spiral null point, by solving the kinematic, steady, resistive magnetohydrodynamic equations in its vicinity. A steady magnetic field is assumed, as well as the existence of a localised diffusion region surrounding the null point. Outside the diffusion region the plasma and magnetic field move ideally. Particular attention is focussed on the way that the magnetic flux changes its connections as a result of the reconnection. The resultant plasma flows are found to be rotational in nature, as is the change in connections of the magnetic field lines. Title: Magnetic topologies in the solar corona due to four discrete photospheric flux regions Authors: Beveridge, C.; Priest, E. R.; Brown, D. S. Bibcode: 2004GApFD..98..429B Altcode: Many dynamic phenomena in the solar corona are driven by the complex and ever-changing magnetic field. It is helpful, in trying to model these phenomena, to understand the structure of the magnetic field, i.e. the magnetic topology. We study here the topological structure of the coronal magnetic field arising from four discrete photospheric flux patches, for which we find that seven distinct, topologically stable states are possible; the changes between these are caused by six types of bifurcation. Two bifurcation diagrams are produced, showing how the changes occur as the relative positions and strengths of the flux patches are varied. A method for extending the analysis to higher numbers of sources is discussed. Title: Our Enigmatic Sun Authors: Priest, Eric Bibcode: 2004IAUS..223..715P Altcode: 2005IAUS..223..715P No abstract at ADS Title: Binary Reconnection and the Heating of the Solar Corona Authors: Priest, E. R.; Longcope, D. W.; Titov, V. S. Bibcode: 2003ApJ...598..667P Altcode: The relative motions of myriads of magnetic fragments in the solar surface are likely to drive magnetic reconnection and therefore heating among the magnetic field lines that spread from these fragments into the solar corona. We suggest that the fundamental mechanism is one of ``binary reconnection'' due to the motion of a given magnetic source relative to its nearest neighbor. The heating is due to several effects: (1) the three-dimensional reconnection of field lines that start out joining the two sources and end up joining the largest source to other more distant sources (or vice versa), so that the field line footpoints are exchanged; (2) the viscous or resistive damping of the waves that are emitted by the sources as their relative orientation rotates; and (3) the relaxation of the nonlinear force-free fields that join the two sources and that are built up by the relative motion of the sources. Title: Three-dimensional Reconnection of Untwisted Magnetic Flux Tubes Authors: Linton, M. G.; Priest, E. R. Bibcode: 2003ApJ...595.1259L Altcode: Understanding the reconnection of magnetic fields in flux tubes is of key importance for modeling solar activity and space weather. We are therefore studying this process via three-dimensional MHD simulations. We report here on a simulation of the collision of a pair of perpendicular, untwisted magnetic flux tubes. We find that the collision proceeds in four stages. First, on contact, the tubes flatten out into wide sheets. Second, they begin to reconnect and the tearing mode instability is excited in the reconnection region. Third, the nonlinear evolution of the tearing mode creates a pair of reconnected flux tubes. Finally, these flux tubes reconnect with each other to coalesce into a single flux tube. We then report on a pair of simulations exploring how this behavior changes when the speed of flux tube collision is increased and when the magnetic resistivity is increased. Title: A model for elemental coronal flux loops Authors: Beveridge, C.; Longcope, D. W.; Priest, E. R. Bibcode: 2003SoPh..216...27B Altcode: The photosphere possesses many small, intense patches of magnetic flux. Each of these patches (or sources) is connected magnetically through the corona to several sources of opposite polarity. An elemental flux loop consists of all of the flux joining one such source to another. We find that each source is connected to twenty other sources, on average, and that the typical flux and diameter of elemental loops in the corona are 1016 Mx and 200 km; there are approximately 17 separators for each source. We also model a typical large-scale coronal loop consisting of many elemental loops and determine its complex internal topology. Each upright null lies at the end of about 22 separatrices, which tend to be clustered together in trunk-like structures, analogous to river-valleys in a geographical contour map. Prone nulls correspond to saddle points, while their spines are analogous to watersheds. Title: Theory of 3D reconnection and coronal heating heating Authors: Priest, E. R. Bibcode: 2003AdSpR..32.1021P Altcode: Magnetic reconnection is a prime candidate for heating coronae. We here summarise recent developments in the theory of 3D reconnection and the different ways in which it is thought to heat the solar corona. At 3D null points reconnection may occur by either spine, fan or separator reconnection. In absence of null points, reconnection of two flux tubes is completely different from 2D reconnection, since in general in 3D a flux-conserving velocity w does not exist. Instead two flux tubes split into four parts, which 'flip' via 'virtual flux tubes' to form four flux tubes. Heating in the corona has been proposed to occur by: driven reconnection at X-ray bright points; binary reconnection due to the coronal interaction of a pair of opposite-polarity magnetic sources; separator reconnection due to a higher-order interaction; braiding; and coronal tectonics due to the formation and dissipation of current sheets at myriads of separatix surfaces that thread the corona and separate the flux coming from the many different sources in the photosphere. Title: On the distribution of magnetic null points above the solar photosphere Authors: Longcope, D. W.; Brown, D. S.; Priest, E. R. Bibcode: 2003PhPl...10.3321L Altcode: Many theories predict magnetic energy dissipation at locations, called null points, where the magnetic field vanishes. In several astrophysical contexts, most notably the solar corona, energy is released within a low-β magnetic field anchored to a lower boundary, the photosphere. A general expression is derived for the distribution of magnetic null points in potential magnetic fields anchored to a random, homogeneous distribution of field on the lower boundary. For all such fields the null point density decreases with height and scales with the inverse cube of the field's characteristic length. For photospheric fields which appear unipolar at the largest scales the nulls are confined to a narrow layer. The results are applied to models of the quiet Sun whose photospheric field consists of discrete sources of mixed polarity. The number of coronal nulls depends on the degree of imbalance between positive and negative sources. Numerical experiments reveal that the greatest column density of null points occurs when ~20% of the sources are of the minority sign. Were the coronal energy dissipation to occur at magnetic null points this result predicts an observable relationship between flux imbalance and the amplitude and distribution of dissipation. Title: On the nature of three-dimensional magnetic reconnection Authors: Priest, E. R.; Hornig, G.; Pontin, D. I. Bibcode: 2003JGRA..108.1285P Altcode: Three-dimensional magnetohydrodynamic reconnection in a finite diffusion region is completely different in many respects from two-dimensional reconnection at an X-point. In two dimensions a magnetic flux velocity can always be defined: two flux tubes can break at a single point and rejoin to form two new flux tubes. In three dimensions we demonstrate that a flux tube velocity does not generally exist. The magnetic field lines continually change their connections throughout the diffusion region rather than just at one point. The effect of reconnection on two flux tubes is generally to split them into four flux tubes rather than to rejoin them perfectly. During the process of reconnection each of the four parts flips rapidly in a virtual flow that differs from the plasma velocity in the ideal region beyond the diffusion region. Title: Linear collapse of spatially linear, three-dimensional, potential null points Authors: Mellor, C.; Titov, V. S.; Priest, E. R. Bibcode: 2003GApFD..97..489M Altcode: The collapse of the magnetic field in the vicinity of a null point creates a large electrical current. Non-ideal effects in the surrounding plasma can then allow the onset of magnetic reconnection, which is important in many astrophysical phenomena. An elegant technique is used to show that spatially linear, initially potential, three-dimensional null points have a tendency to collapse with a growth of either the spine current or the fan current or a combination of both. The rate of collapse is determined for an incompressible plasma flow with open boundary conditions. An initial plasma flow affects the rate of collapse by speeding it up. Title: Three Dimensional Reconnection of Untwisted Magnetic Flux Tubes Authors: Linton, M.; Priest, E. Bibcode: 2003SPD....34.0512L Altcode: 2003BAAS...35R.816L Understanding the reconnection of magnetic fields in coronal flux tubes is of key importance for modeling solar coronal flares. We are therefore studying this process via 3D MHD simulations of the reconnection of magnetic flux tubes. Here we will report on a series of such simulations in which pairs of untwisted flux tubes collide and reconnect. We find that in general these collisions flatten the flux tubes into flux sheets and then excite the tearing mode instability. In addition to the tearing mode reconnection, at high collision speed reconnection is simultaneously initiated at a number of other locations, leading to patchy reconnection and a significant tangling of the reconnected fields. In contrast, at low collision speed we find the reconnection is much smoother, and that the coalescence instability follows the tearing mode, causing the reconnected field to merge into a single twisted flux tube. In addition to discussing the global dynamics of these reconnection processes, we will also address the behavior of individual fieldlines as they reconnect, in an effort to more clearly understand how such fieldline reconnection occurs in truly 3D configurations.

This work was supported by NASA, ONR, and PPARC grants. Title: Flare activity in solar active region 8421 observed by the TRACE satellite Authors: Zuccarello, F.; Contarino, L.; Romano, P.; Priest, E. R. Bibcode: 2003A&A...402.1085Z Altcode: Due to the wide range of wavelengths examined and to the high angular and temporal resolution, TRACE allows one to carry out a spatial and temporal analysis of active regions during highly transient phenomena such as flares. This provides new input to the study of the mechanisms involved in these phenomena. We have studied 3 flares that occurred in AR 8421 between 29 and 30 December 1998 by comparing white light, 1600 Å, and 171 Å images obtained by TRACE with BBSO Halpha images, Mitaka magnetograms and Yohkoh hard X-ray data. The flares, characterized by sudden intensity enhancements in EUV loops and by moss brightenings, have been interpreted in the framework of the two canonical flare models: i.e. simple loop and two ribbon flares. Our analysis has shown that flare No. 1 may be interpreted as a two-ribbon flare triggered by reconnection between a sheared arcade and a new emerging flux tube. The analysis of flare No. 2 strongly supports the model of two-ribbon flares characterized by reconnection occurring at higher and higher levels as time proceeds. Finally, the analysis of flare No. 3 has given the opportunity to relate moss brightening with a probable process of chromospheric evaporation. Title: A Framework for Understanding the Topology of Complex Coronal Structures Authors: Pontin, D. I.; Priest, E. R.; Longcope, D. W. Bibcode: 2003SoPh..212..319P Altcode: The Sun's coronal magnetic field is highly complex and provides the driving force for many dynamical processes. The topology of this complex field is made up mainly of discrete topological building blocks produced by small numbers of magnetic fragments. In this work we develop a method for predicting the possible topologies due to a potential field produced by three photospheric sources, and describe how this model accurately predicts the results of Brown and Priest (1999). We then sketch how this idea may be extended to more general non-symmetric configurations. It is found that, for the case of positive total flux, a local separator bifurcation may take place with three positive sources or with one positive and two negative sources, but not for two positive sources and one negative. Title: Statistical Flux Tube Properties of 3D Magnetic Carpet Fields Authors: Close, R. M.; Parnell, C. E.; Mackay, D. H.; Priest, E. R. Bibcode: 2003SoPh..212..251C Altcode: The quiet-Sun photosphere consists of numerous magnetic flux fragments of both polarities that evolve with granular and supergranular flow fields. These concentrations give rise to a web of intermingled magnetic flux tubes which characterise the coronal magnetic field. Here, the nature of these flux tubes is studied. The photosphere is taken to be the source plane and each photospheric fragment is represented by a series of point sources. By analysing the potential field produced by these sources, it is found that the distribution of flux tube lengths obtained by (i) integrating forward from positive sources and (ii) tracing back from negative sources is highly dependent on the total flux imbalance within the region of interest. It is established that the relation between the footpoint separation of a flux tube and its height cannot be assumed to be linear. Where there is a significant imbalance of flux within a region, it is found that fragments of the dominant polarity will have noticeably more connections, on average, than the minority polarity fragments. Despite this difference, the flux from a single fragment of either polarity is typically divided such that (i) 60-70% connects to one opposite-polarity fragment, (ii) 25-30% goes to a further 1 to 2 opposite-polarity fragments, and (iii) any remaining flux may connect to as many as another 50 or more other opposite-polarity fragments. This is true regardless of any flux imbalance within the region. It is found that fragments connect preferentially to their nearest neighbours, with, on average, around 60-70% of flux closing down within 10 Mm of a typical fragment. Only 50% of the flux in a quiet region extends higher than 2.5 Mm above the solar surface and 5-10% extends higher than 25 Mm. The fragments that contribute to the field above this height cover a range of sizes, with even the smallest of fragments contributing to the field at heights of over 50 Mm. Title: Numerical experiments on wave propagation towards a 3D null point due to rotational motions Authors: Galsgaard, K.; Priest, E. R.; Titov, V. S. Bibcode: 2003JGRA..108.1042G Altcode: We describe 3D resistive magnetohydrodynamic (MHD) numerical experiments at a null point driven by the rotation of magnetic field lines near the spine of the null. When field lines around the spine are rotated, a twist wave propagates toward the null along field lines, satisfying a Klein-Gordon equation. While the helical Alfvén wave spreads out as the null is approached, a fast-mode wave focuses on the null and wraps around it. Only a weak diffusion of the twisted field line structure is found to take place. Title: Solar magnetohydrodynamics Authors: Priest, E. R. Bibcode: 2003dysu.book..217P Altcode: The magnetic field exerts a force, stores energy, acts as a thermal blanket, channels plasma, drives instabilities, and supports waves. For many purposes the behaviour of the magnetic field and its interaction with plasma is governed by the equations of magnetohydrodynamics (MHD). This chapter gives a brief account of some of the basics of MHD, and summarises the simple properties of the different kinds of waves that are present in ideal MHD. Title: The Evolution of the Sun's Open Magnetic Flux - II. Full Solar Cycle Simulations Authors: Mackay, D. H.; Priest, E. R.; Lockwood, M. Bibcode: 2002SoPh..209..287M Altcode: In this paper the origin and evolution of the Sun's open magnetic flux is considered by conducting magnetic flux transport simulations over many solar cycles. The simulations include the effects of differential rotation, meridional flow and supergranular diffusion on the radial magnetic field at the surface of the Sun as new magnetic bipoles emerge and are transported poleward. In each cycle the emergence of roughly 2100 bipoles is considered. The net open flux produced by the surface distribution is calculated by constructing potential coronal fields with a source surface from the surface distribution at regular intervals. In the simulations the net open magnetic flux closely follows the total dipole component at the source surface and evolves independently from the surface flux. The behaviour of the open flux is highly dependent on meridional flow and many observed features are reproduced by the model. However, when meridional flow is present at observed values the maximum value of the open flux occurs at cycle minimum when the polar caps it helps produce are the strongest. This is inconsistent with observations by Lockwood, Stamper and Wild (1999) and Wang, Sheeley, and Lean (2000) who find the open flux peaking 1-2 years after cycle maximum. Only in unrealistic simulations where meridional flow is much smaller than diffusion does a maximum in open flux consistent with observations occur. It is therefore deduced that there is no realistic parameter range of the flux transport variables that can produce the correct magnitude variation in open flux under the present approximations. As a result the present standard model does not contain the correct physics to describe the evolution of the Sun's open magnetic flux over an entire solar cycle. Future possible improvements in modeling are suggested. Title: Magnetic topologies due to two bipolar regions Authors: Beveridge, C.; Priest, E. R.; Brown, D. S. Bibcode: 2002SoPh..209..333B Altcode: The Sun's atmosphere contains many diverse phenomena that are dominated by the coronal magnetic field. To understand these phenomena it is helpful to determine first the structure of the magnetic field, i.e., the magnetic topology. We study here the topological structure of the coronal magnetic field arising from the interaction of two bipolar regions, for which we find that four distinct, topologically stable states are possible. A bifurcation diagram is produced, showing how the magnetic configuration can change from one topology to another as the relative orientation and sizes of the bipolar regions are varied. The changes are produced either by a global separator bifurcation, a local double-separator bifurcation, a new, global separatrix quasi-bifurcation, or a new, global spine quasi-bifurcation. Title: A Flux-Tube Tectonics Model for Solar Coronal Heating Driven by the Magnetic Carpet Authors: Priest, Eric R.; Heyvaerts, Jean F.; Title, Alan M. Bibcode: 2002ApJ...576..533P Altcode: We explore some of the consequences of the magnetic carpet for coronal heating. Observations show that most of the magnetic flux in the quiet Sun emerges as ephemeral regions and then quickly migrates to supergranule boundaries. The original ephemeral concentrations fragment, merge, and cancel over a time period of 10-40 hr. Since the network photospheric flux is likely to be concentrated in units of 1017 Mx or smaller, there will be myriads of coronal separatrix surfaces caused by the highly fragmented photospheric magnetic configuration in the quiet network. We suggest that the formation and dissipation of current sheets along these separatrices are an important contribution to coronal heating. The dissipation of energy along sharp boundaries we call, by analogy with geophysical plate tectonics, the tectonics model of coronal heating. Similar to the case on Earth, the relative motions of the photospheric sources will drive the formation and dissipation of current sheets along a hierarchy of such separatrix surfaces at internal dislocations in the corona. In our preliminary assessment of such dissipation we find that the heating is fairly uniform along the separatrices, so that each elementary coronal flux tube is heated uniformly. However, 95% of the photospheric flux closes low down in the magnetic carpet and the remaining 5% forms large-scale connections, so the magnetic carpet will be heated more effectively than the large-scale corona. This suggests that unresolved observations of coronal loops should exhibit enhanced heating near their feet in the carpet, while the upper parts of large-scale loops should be heated rather uniformly but less strongly. Title: The Evolution of the Sun's Open Magnetic Flux - I. A Single Bipole Authors: Mackay, D. H.; Priest, E. R.; Lockwood, M. Bibcode: 2002SoPh..207..291M Altcode: In this paper the origin and evolution of the Sun's open magnetic flux are considered for single magnetic bipoles as they are transported across the Sun. The effects of magnetic flux transport on the radial field at the surface of the Sun are modeled numerically by developing earlier work by Wang, Sheeley, and Lean (2000). The paper considers how the initial tilt of the bipole axis (α) and its latitude of emergence affect the variation and magnitude of the surface and open magnetic flux. The amount of open magnetic flux is estimated by constructing potential coronal fields. It is found that the open flux may evolve independently from the surface field for certain ranges of the tilt angle. For a given tilt angle, the lower the latitude of emergence, the higher the magnitude of the surface and open flux at the end of the simulation. In addition, three types of behavior are found for the open flux depending on the initial tilt angle of the bipole axis. When the tilt is such that αge2° the open flux is independent of the surface flux and initially increases before decaying away. In contrast, for tilt angles in the range −16°<α<2° the open flux follows the surface flux and continually decays. Finally, for αle−16° the open flux first decays and then increases in magnitude towards a second maximum before decaying away. This behavior of the open flux can be explained in terms of two competing effects produced by differential rotation. Firstly, differential rotation may increase or decrease the open flux by rotating the centers of each polarity of the bipole at different rates when the axis has tilt. Secondly, it decreases the open flux by increasing the length of the polarity inversion line where flux cancellation occurs. The results suggest that, in order to reproduce a realistic model of the Sun's open magnetic flux over a solar cycle, it is important to have accurate input data on the latitude of emergence of bipoles along with the variation of their tilt angles as the cycle progresses. Title: Our Enigmatic Sun Authors: Priest, E. Bibcode: 2002AAS...200.6701P Altcode: 2002BAAS...34..755P The Sun remains of central importance for astronomy as a whole, especially since it provides the closest cosmic view of many fundamental plasma processes at work. In this review we summarise the basic properties of the Sun and describe the major progress that has recently been made on a set of key questions that have far-reaching implications for many other parts of the Universe, namely: 1. How is the magnetic field generated ? 2. How are winds accelerated ? 3. How do eruptions occur ? 4. How is magnetic energy converted to other forms ? 5. How are coronae heated ? Title: Exact Solutions for Spine Reconnective Magnetic Annihilation Authors: Mellor, C.; Priest, E. R.; Titov, V. S. Bibcode: 2002GApFD..96..153M Altcode: Solutions for spine reconnective annihilation are presented which satisfy exactly the three-dimensional equations of steady-state resistive incompressible magnetohydrodynamics (MHD). The magnetic flux function (A) and stream function have the form $A = A_{0}(R) sin phi + A_{1}(R)z, qquad Psi = Psi _{0}(R) sin phi + Psi _{1}(R)z,$ in terms of cylindrical polar coordinates (R,,z). First of all, two non-linear fourth-order equations for A1 and are solved by the method of matched asymptotic expansions when the magnetic Reynolds number is much larger than unity. The solution, for which a composite asymptotic expansion is given in closed form, possesses a weak boundary layer near the spine (R = 0). These solutions are used to solve the remaining two equations for A0 and . Physically, the magnetic field is advected across the fan separatrix surface and diffuses across the spine curve. Different members of a family of solutions are determined by values of a free parameter and the components (BRe, Bze) and (vRe, vze) of the magnetic field and plasma velocity at a fixed external point (R,,z) = (1,/2,0), say. Title: The Nature of Blinkers and the Solar Transition Region Authors: Priest, E. R.; Hood, A. W.; Bewsher, D. Bibcode: 2002SoPh..205..249P Altcode: Solar plasma that exists at around 105 K, which has traditionally been referred to as the solar transition region, is probably in a dynamic and fibril state with a small filling factor. Its origin is as yet unknown, but we suggest that it may be produced primarily by one of five different physical mechanisms, namely: the heating of cool spicular material; the containment of plasma in low-lying loops in the network; the thermal linking of cool and hot plasma at the feet of coronal loops; the heating and evaporating of chromospheric plasma in response to a coronal heating event; and the cooling and draining of hot coronal plasma when coronal heating is switched off. We suggest that, in each case, a blinker could be produced by the granular compression of a network junction, causing subtelescopic fibril flux tubes to spend more of their time at transition-region temperatures and so to increase the filling factor temporarily. Title: Magnetic Reconnection and Coronal Heating Authors: Priest, Eric Bibcode: 2002smra.progE..21P Altcode: No abstract at ADS Title: Theory of 3D Reconnection and Coronal Heating Authors: Priest, E. Bibcode: 2002cosp...34E.450P Altcode: 2002cosp.meetE.450P Magnetic reconnection is a prime candidate for heating coronae. We here summarise recent developments in the theory of 3D reconnection and the different ways in which it is thought to heat the solar corona. Reconnection may occur at null points by either spine, fan or separator reconnection and in the absence of null points by magnetic flipping. Heating in the corona has been proposed to occur by: driven reconnection at X-ray bright points; binary reconnection due to the coronal interaction of a pair of opposite-polarity magnetic sources; separator reconnection due to a higher-order interaction; braiding; and coronal tectonics due to the formation and dissipation of current sheets at myriads of separatrix surfaces that thread the corona and separate the flux coming from the many different sources in the photosphere. Title: Magnetic structure and reconnection of x-ray bright points in the solar corona Authors: Brown, D. S.; Parnell, C. E.; DeLuca, E. E.; McMullen, R. A.; Golub, L.; Priest, E. R. Bibcode: 2002AdSpR..29.1093B Altcode: The three-dimensional magnetic topology of the solar corona is incredibly complex and its effect on the nature of 3D reconnection is profound. We study the supposedly simple topology of a small scale X-ray bright point observed by TRACE and SOHO/MDI, and how it is driven by reconnection when it forms and during the early stages of its lifetime. Title: The magnetic nature of solar flares Authors: Priest, E. R.; Forbes, T. G. Bibcode: 2002A&ARv..10..313P Altcode: The main challenge for the theory of solar eruptions has been to understand two basic aspects of large flares. These are the cause of the flare itself and the nature of the morphological features which form during its evolution. Such features include separating ribbons of Hα emission joined by a rising arcade of soft x-ray loops, with hard x-ray emission at their summits and at their feet. Two major advances in our understanding of the theory of solar flares have recently occurred. The first is the realisation that a magnetohydrodynamic (MHD) catastrophe is probably responsible for the basic eruption and the second is that the eruption is likely to drive a reconnection process in the field lines stretched out by the eruption. The reconnection is responsible for the ribbons and the set of rising soft x-ray loops, and such a process is well supported by numerical experiments and detailed observations from the Japanese satellite Yohkoh. Magnetic energy conversion by reconnection in two dimensions is relatively well understood, but in three dimensions we are only starting to understand the complexity of the magnetic topology and the MHD dynamics which are involved. How the dynamics lead to particle acceleration is even less well understood. Particle acceleration in flares may in principle occur in a variety of ways, such as stochastic acceleration by MHD turbulence, acceleration by direct electric fields at the reconnection site, or diffusive shock acceleration at the different kinds of MHD shock waves that are produced during the flare. However, which of these processes is most important for producing the energetic particles that strike the solar surface remains a mystery. Title: Solar Orbiter science Authors: Priest, E. R. Bibcode: 2001ESASP.493..127P Altcode: 2001sefs.work..127P A summary is given of the scientific advances that are expected from the Solar Orbiter. There will be unexpected discoveries from exploring new regions of the Sun for the first time - namely, the polar regions, the inner solar wind and increasing the current special resolution by an order of magnitude. However, it is also likely to make substantial advances or to provide definitive answers to several basic physics questions that are of substantial importance for our understanding of the wider universe. These include: the effect of the Sun on the Earth's climate; the structure of the solar interior and the nature of the solar dynamos; the nature and behaviour of the fundamental magnetic structures of the solar surface; the nature of the transition region; the drivers for the solar wind; and the mechanisms for heating the corona. Title: Application of an analytical MHD wind model with latitudinal dependences to the solar wind Authors: Lima, J. J. G.; Sauty, C.; Iro, N.; Tsinganos, K.; Priest, E. R. Bibcode: 2001ESASP.493..269L Altcode: 2001sefs.work..269L No abstract at ADS Title: Solar and stellar magnetic activity Authors: Schrijver, Carollus J.; Zwaan, Cornelis; Priest, Eric R. Bibcode: 2001PhT....54i..54S Altcode: No abstract at ADS Title: Meeting report : News from PPARC's Astronomy Committee Authors: Priest, Eric Bibcode: 2001A&G....42c..23P Altcode: Eric Priest, Chair of the Astronomy Committee, reports on the March meeting, which considered targets for future science and spending, particularly in view of the decision to join the European Southern Observatory. Title: Three-dimensional reconnection on the Sun Authors: Priest, Eric R. Bibcode: 2001EP&S...53..483P Altcode: A brief review is given of the theory of magnetic reconnection in three dimensions. The key elements of a three-dimensional null point are its spine and its fan, which consist, respectively, of a field line and a surface of field lines that pass through the null. The fans of two nulls intersect in general in a field line called a separator that joins the nulls. Several different types of reconnection have been proposed, namely: spine reconnection, fan reconnection, separator reconnection and quasi-separatrix layer reconnection. In addition, a new exact solution for reconnective annihilation has been recently discovered. A summary is also given of the impressive evidence of reconnection at work on the Sun provided by a range of observations from the Yohkoh and SOHO satellites, both of solar flares and of coronal heating events. Title: An analytical MHD wind model with latitudinal dependences obtained using separation of the variables Authors: Lima, J. J. G.; Priest, E. R.; Tsinganos, K. Bibcode: 2001A&A...371..240L Altcode: 2001astro.ph..3289L A new class of analytical 2-D solutions of the full set of the steady magnetohydrodynamic (MHD) equations, describing an axisymmetric helicoidal magnetized outflow originating from a rotating central object, is presented. The solutions are systematically obtained via a nonlinear separation of the variables in the momentum equation. The analysis yields three parameters which measure the anisotropy in the latitudinal distribution of various flow quantities. Topologically, the wind speed is controlled by an X-type critical point that acts to filter out a single wind-type branch and the Alfvén singularity. The solutions can be regarded as an extension outside the equatorial plane of the Weber & Davis (\cite{Weber67}) model of magnetized winds but with a variable polytropic index. Title: The topological behaviour of 3D null points in the Sun's corona Authors: Brown, D. S.; Priest, E. R. Bibcode: 2001A&A...367..339B Altcode: Many traditional two-dimensional models of flares and other reconnective events rely on an X-point in the corona which collapses to form a current sheet where reconnection takes place. However, the Sun's corona is three-dimensional and the X-point is only a two-dimensional artifact. Three-dimensional models can instead make use of 3D null points in the corona, and \cite{priest96} have studied how reconnection may take place at such locations. This paper aims to study possible conditions for coronal nulls to occur, and how they can be born. It starts with three negative sources and a positive source that is weaker than the sum of the negative sources. As the positive source moves inwards towards the negative sources, there is a local double-separator bifurcation of the topology to a new state, referred to as a Coronal Null state, which contains a null point above the photosphere. Title: Surprises from Our Sun Authors: Priest, Eric R. Bibcode: 2001RvMA...14..133P Altcode: No abstract at ADS Title: The Role of the Sun's Magnetic Field Authors: Priest, E. R. Bibcode: 2001ASPC..248...25P Altcode: 2001mfah.conf...25P No abstract at ADS Title: A review of: "Transport and energy conversion in the heliosphere" Authors: Priest, Eric Bibcode: 2001GApFD..95..333P Altcode: Lectures given at the CNRS Summer School on Solar Astrophysics, Oleron, France, 25-29 May 1998, edited by P.-P. Rozelot, L. Klein and J.-C. Vial, Lecture Notes in Physics: Vol. 553, Springer-Verlag Berlin Heidelberg New York, 2000. VIII+214 pp., DM 104.00, hardbound (ISBN 3-540-67595-7) Title: Magnetohydrodynamics Authors: Priest, E.; Forbes, T. Bibcode: 2000eaa..bookE1983P Altcode: Magnetohydrodynamics (or MHD for short) is the study of the interaction between a magnetic field and a plasma treated as a continuous medium (e.g. Cowling 1957, Roberts 1967, Priest 1982, 1994). Most of the universe is not a normal gas but is instead a plasma. We are all familiar on Earth with the three states of matter (solid, liquid and gas). You change from one state to another (such as ice to... Title: Sun and Solar-terrestrial Physics Authors: Priest, E. Bibcode: 2000eaa..bookE5397P Altcode: The Sun is of central importance in astronomy. On the one hand, many basic processes that occur throughout the cosmos may be well observed in the Sun and, on the other hand, the Sun acts as a source of the radiation and plasma emissions that affect the Earth in many ways. The study of the interaction of the Sun and its solar wind with the Earth is the burgeoning field of solar-terrestrial physics... Title: Simulations of Three-Dimensional Reconnection in the Solar Corona Authors: Birn, Joachim; Gosling, John T.; Hesse, Michael; Forbes, Terry G.; Priest, Eric R. Bibcode: 2000ApJ...541.1078B Altcode: Using ideal and resistive MHD, we investigate the stability and dynamic evolution of three-dimensional magnetic field configurations, representing stretched arcade structures above a dipolar ``photospheric'' magnetic field. Two types of configurations are studied that differ by the amount of divergence (``fanning'') of the initial field lines as viewed in the horizontal direction perpendicular to the photospheric magnetic neutral line and, correspondingly, by the radial decrease of magnetic field strength and current density. The two sets of configurations are found to differ in their stability behavior. The strongly fanning fields, associated with a rapid radial decrease of the field strength, current density, and plasma pressure, are more stable. A stability difference is found also when the configurations are first subjected to a converging motion of photospheric footpoints toward the neutral line, which leads to the buildup of thin current sheets in the region above. This current sheet formation is more pronounced for the weakly fanning fields. For similar current density enhancements, the occurrence of anomalous dissipation (resistivity) initiates magnetic reconnection in either configuration. However, the effects are much more drastic in magnitude and spread in the weakly diverging field structure. In the unstable cases, a strongly localized electric field parallel to the magnetic field develops, which results in integrated voltages with maximum values of the order of a few hundred MeV, both on open and closed field lines. For comparison, we studied both low-beta, force-free, and high-beta initial states. The weakly fanning high-beta configurations tend to show more drastic instability effects than the corresponding low-beta fields, but the stabilization of the strongly fanning fields pertains to both low-beta and high-beta fields. The three-dimensional reconnection in the unstable cases generates a region of intertwined magnetic flux tubes with different topologies that lie below a region of closed flux ropes not affected by reconnection. The topological changes could be the source of open flux tubes that are occasionally observed within coronal mass ejections, as recently discussed by Gosling et al. The fast outward flow generated in these simulations affects only the regions of changing topology but does not cause the above-lying closed flux ropes to move (within the times considered). This may be seen as an indication that reconnection may be associated with the onset of a flare, initiated after the eruption of a coronal mass ejection, but is not the driver of the coronal mass ejection itself. Title: A Method to Determine the Heating Mechanisms of the Solar Corona Authors: Priest, E. R.; Foley, C. R.; Heyvaerts, J.; Arber, T. D.; Mackay, D.; Culhane, J. L.; Acton, L. W. Bibcode: 2000ApJ...539.1002P Altcode: One of the paradigms about coronal heating has been the belief that the mean or summit temperature of a coronal loop is completely insensitive to the nature of the heating mechanisms. However, we point out that the temperature profile along a coronal loop is highly sensitive to the form of the heating. For example, when a steady state heating is balanced by thermal conduction, a uniform heating function makes the heat flux a linear function of distance along the loop, while T7/2 increases quadratically from the coronal footpoints; when the heating is concentrated near the coronal base, the heat flux is small and the T7/2 profile is flat above the base; when the heat is focused near the summit of a loop, the heat flux is constant and T7/2 is a linear function of distance below the summit. It is therefore important to determine how the heat deposition from particular heating mechanisms varies spatially within coronal structures such as loops or arcades and to compare it to high-quality measurements of the temperature profiles. We propose a new two-part approach to try and solve the coronal heating problem, namely, first of all to use observed temperature profiles to deduce the form of the heating, and second to use that heating form to deduce the likely heating mechanism. In particular, we apply this philosophy to a preliminary analysis of Yohkoh observations of the large-scale solar corona. This gives strong evidence against heating concentrated near the loop base for such loops and suggests that heating uniformly distributed along the loop is slightly more likely than heating concentrated at the summit. The implication is that large-scale loops are heated in situ throughout their length, rather than being a steady response to low-lying heating near their feet or at their summits. Unless waves can be shown to produce a heating close enough to uniform, the evidence is therefore at present for these large loops more in favor of turbulent reconnection at many small randomly distributed current sheets, which is likely to be able to do so. In addition, we suggest that the decline in coronal intensity by a factor of 100 from solar maximum to solar minimum is a natural consequence of the observed ratio of magnetic field strength in active regions and the quiet Sun; the altitude of the maximum temperature in coronal holes may represent the dissipation height of Alfvén waves by turbulent phase mixing; and the difference in maximum temperature in closed and open regimes may be understood in terms of the roles of the conductive flux there. Title: Mean Field Model for the Formation of Filament Channels on the Sun Authors: van Ballegooijen, A. A.; Priest, E. R.; Mackay, D. H. Bibcode: 2000ApJ...539..983V Altcode: The coronal magnetic field is subject to random footpoint motions that cause small-scale twisting and braiding of field lines. We present a mean field theory describing the effects of such small-scale twists on the large-scale coronal field. This theory assumes that the coronal field is force free, with electric currents flowing parallel or antiparallel to magnetic field lines. Random footpoint motions are described in terms of diffusion of the mean magnetic field at the photosphere. The appropriate mean field equations are derived, and a numerical method for solving these equations in three dimensions is presented. Preliminary results obtained with this method are also presented. In particular the formation of filament channels is studied. Filament channels are regions where the coronal magnetic field is strongly aligned with the underlying polarity inversion line in the photosphere. It is found that magnetic flux cancellation plays an important role in the formation of such channels. Various models of the coronal field are presented, including some in which the axial field is assumed to originate from below the photosphere. The models reproduce many of the observed features of filament channels, but the observed hemisphere pattern of dextral and sinistral channels remains a mystery. Title: Magnetic Reconnection Authors: Priest, Eric; Forbes, Terry Bibcode: 2000mare.book.....P Altcode: Magnetic reconnection is at the core of many dynamic phenomena in the universe, such as solar flares, geomagnetic substorms and tokamak disruptions. Written by two world leaders on the subject, this volume provides a comprehensive overview of this fundamental process. Coverage gives both a pedagogical account of the basic theory and a wide-ranging review of the physical phenomena created by reconnection--from laboratory machines, the Earth's magnetosphere, and the Sun's atmosphere to flare stars and astrophysical accretion disks. It also includes a succinct account of particle acceleration by electric fields, stochastic fields and shock waves, and how reconnection can be important in these mechanisms. Clearly written and highly accessible, this volume serves as an essential introduction for graduate students in solar physics, astrophysics, plasma physics and space science. Researchers in these fields also will find Magnetic Reconnection an authoritative reference. Title: Topological differences and similarities between force-free and potential models of coronal magnetic fields Authors: Brown, D. S.; Priest, E. R. Bibcode: 2000SoPh..194..197B Altcode: Potential fields and linear force-free fields are often used as models for the magnetic field of the Sun's corona. They can be written as analytical expressions in terms of boundary values at the photosphere. Because of their relative simplicity compared with nonlinear force-free fields, these two models are of particular importance in topological analysis of solar phenomena. However, it has been suggested by Hudson and Wheatland (1999) that the topologies of potential and force-free models are in general not even qualitatively equivalent. In this paper, their example is re-examined and it is found that the opposite conclusions hold. In general, potential and force-free fields are topologically similar sufficiently close to localized sources. The exception to this are structurally unstable states, such as bifurcation states, where a small change of current can produce a significant change of topology. Title: Three-dimensional Separator Reconnection - How Does It Occur? Authors: Galsgaard, K.; Priest, E. R.; Nordlund, Å. Bibcode: 2000SoPh..193....1G Altcode: In two dimensions magnetic energy release takes place at locations where the magnetic field strength becomes zero and has an x-point topology. The x-point topology can collapse into two y-points connected by a current sheet when the advection of magnetic flux into the x-point is larger than the dissipation of magnetic flux at the x-point. In three dimensions magnetic fields may also contain singularities in the form of three-dimensional null points. Three-dimensional nulls are created in pairs and are therefore, at least in the initial stages, always connected by at least one field line - the separator. The separator line is defined by the intersection of the fan planes of the two nulls. In the plane perpendicular to a single separator the field line topology locally has a two dimensional x-point structure. Using a numerical approach we find that the collapse of the separator can be initiated at the two nulls by a velocity shear across the fan plane. It is found that for a current concentration to connect the two nulls along the separator, the current sheet can only obtain two different orientations relative to the field line structure of the nulls. The sheet has to have an orientation midway between the fan plane and the spine axis of each null. As part of this process the spine axes are found to lose their identity by transforming into an integrated part of the separator surfaces that divide space into four magnetically independent regions around the current sheet. Title: How Accurately Can We Determine the Coronal Heating Mechanism in the Large-Scale Solar Corona? Authors: Mackay, D. H.; Galsgaard, K.; Priest, E. R.; Foley, C. R. Bibcode: 2000SoPh..193...93M Altcode: In recent papers by Priest et al., the nature of the coronal heating mechanism in the large-scale solar corona was considered. The authors compared observations of the temperature profile along large coronal loops with simple theoretical models and found that uniform heating along the loop gave the best fit to the observed data. This then led them to speculate that turbulent reconnection is a likely method to heat the large-scale solar corona. Here we reconsider their data and their suggestion about the nature of the coronal heating mechanism. Two distinct models are compared with the observations of temperature profiles. This is done to determine the most likely form of heating under different theoretical constraints. From this, more accurate judgments on the nature of the coronal heating mechanism are made. It is found that, due to the size of the error estimates in the observed temperatures, it is extremely difficult to distinguish between some of the different heat forms. In the initial comparison the limited range of observed temperatures (T>1.5 MK) in the data sets suggests that heat deposited in the upper portions of the loop, fits the data more accurately than heat deposited in the lower portions. However if a fuller model temperature range (T<1.0 MK) is used results in contridiction to this are found. In light of this several improvements are required from the observations in order to produce theoretically meaningful results. This gives serious bounds on the accuracy of the observations of the large-scale solar corona in future satellite missions such a Solar-B or Stereo. Title: Reconnection Theory and the MHD of Solar Flares Authors: Priest, Eric Bibcode: 2000IAUJD...7E...5P Altcode: A review is given of the recent developments in the theory of magnetic reconnection, including new exact solutions and the different regimes of three-dimensional reconnection that have been proposed. In addition, two key issues about the magnetohydrodynamics of solar flares are assessed, namely: why do eruptions of magnetic arcades occur that can produce coronal mass ejections, and what is the nature of the energy release process in a solar flare ? Title: Magnetic reconnection : MHD theory and applications Authors: Priest, Eric; Forbes, Terry Bibcode: 2000mrmt.conf.....P Altcode: No abstract at ADS Title: Solar Flare Theory and the Status of Flare Understanding Authors: Priest, E. R. Bibcode: 2000ASPC..206...13P Altcode: 2000hesp.conf...13P No abstract at ADS Title: Aspects of Three-Dimensional Magnetic Reconnection - (Invited Review) Authors: Priest, E. R.; Schrijver, C. J. Bibcode: 1999SoPh..190....1P Altcode: 1999SoPh..190....1S In this review paper we discuss several aspects of magnetic reconnection theory, focusing on the field-line motions that are associated with reconnection. A new exact solution of the nonlinear MHD equations for reconnective annihilation is presented which represents a two-fold generalization of the previous solutions. Magnetic reconnection at null points by several mechanisms is summarized, including spine reconnection, fan reconnection and separator reconnection, where it is pointed out that two common features of separator reconnection are the rapid flipping of magnetic field lines and the collapse of the separator to a current sheet. In addition, a formula for the rate of reconnection between two flux tubes is derived. The magnetic field of the corona is highly complex, since the magnetic carpet consists of a multitude of sources in the photosphere. Progress in understanding this complexity may, however, be made by constructing the skeleton of the field and developing a theory for the local and global bifurcations between the different topologies. The eruption of flux from the Sun may even sometimes be due to a change of topology caused by emerging flux break-out. A CD-ROM attached to this paper presents the results of a toy model of vacuum reconnection, which suggests that rapid flipping of field lines in fan and separator reconnection is an essential ingredient also in real non-vacuum conditions. In addition, it gives an example of binary reconnection between a pair of unbalanced sources as they move around, which may contribute significantly to coronal heating. Finally, we present examples in TRACE movies of geometrical changes of the coronal magnetic field that are a likely result of large-scale magnetic reconnection. Title: The Topological Behaviour of Stable Magnetic Separators Authors: Brown, D. S.; Priest, E. R. Bibcode: 1999SoPh..190...25B Altcode: It is important to understand the complex topology of the magnetic field in the solar corona in order to be able to comprehend the mechanisms which give rise to phenomena such as coronal loop structures and x-ray bright points. A key feature of the magnetic topology is a separator. A magnetic separator is a field line which connects two magnetic null points, places where the magnetic field becomes zero. A stable magnetic separator is important as it is the intersection of two separatrix surfaces. These surfaces divide the magnetic field lines into regions of different connectivity, so a separator usually borders four regions of field-line connectivity. This work examines the topological behaviour of separators that appear in a magnetic field produced by a system of magnetic sources lying in a plane (the photosphere). The questions of how separators arise and are destroyed, the topological conditions for which they exist, how they interact and their relevance to the coronal magnetic field are addressed. Title: Topological bifurcations in three-dimensional magnetic fields. Authors: Brown, D. S.; Priest, E. R. Bibcode: 1999RSPSA.455.3931B Altcode: Most of the dynamical processes that take place in the Sun's corona (its outer atmosphere) are dominated by the magnetic field. The sources of the coronal field are magnetic fragments scattered over the solar surface and mostly clustered around the edges of large convection cells called supergranules. These sources are not static but continually move about over the surface, coalescing, fragmenting and cancelling with one another. The resulting coronal magnetic field has an incredibly complex topology. In order to begin to understand this complexity it is important to consider, as building blocks, the field generated by a small number of discrete sources. Title: Wavelet Analysis Of Active Region Oscillations Authors: Ireland, J.; Walsh, R. W.; Priest, E. R.; Harrison, R. A. Bibcode: 1999ESASP.446..363I Altcode: 1999soho....8..363I The wavelet transform is applied to the analysis of active region oscillations. The localised (in time) nature of the wavelet transform allows us to study both the duration of any statistically significant oscillations as well as their period. Time series arising from SOHO (Solar and Heliospheric Observatory) CDS-NIS (Coronal Diagnostic Spectrometer Normal Incidence Spectrometer) active region observations on 14th-15th November 1996 are used to demonstrate the applicability of wavelet methods. High cadence (approximately 14 seconds) observations were made in He I 584.33 Angstroms (log T = 4.3, T being the electron temperature), O V 629.73 Angstroms(log T = 5.3), Mg IX 368.06 Angstroms (log T = 6.0), Fe XVI 360.76 Angstroms (log T = 6.4) provide detailed intensity information on the active region over a wide range of temperatures. The distribution of statistically significant periods found varies from line to line, as does their duration. Title: On the location of energy release and temperature profiles along coronal loops Authors: Galsgaard, K.; Mackay, D. H.; Priest, E. R.; Nordlund, Å. Bibcode: 1999SoPh..189...95G Altcode: Several mechanisms have been suggested to contribute to the heating of the solar corona, each of which deposits energy along coronal loops in a characteristic way. To compare the theoretical models with observations one has to derive observable quantities from the models. One such parameter is the temperature profile along a loop. Here numerical experiments of flux braiding are used to provide the spatial distribution of energy deposition along a loop. It is found that braiding produces a heat distribution along the loop which has slight peaks near the footpoints and summit and whose magnitude depends on the driving time. Using different examples of the heat deposition, the temperature profiles along the loop are determined assuming a steady state. Along with this, different methods for providing average temperature profiles from the time-series have been investigated. These give summit temperatures within approximately 10% of each other. The distribution of the heating has a significant impact on both the summit temperature and the temperature distribution along the loop. In each case the ratio between the heat deposited and radiation provides a scaling for the summit temperature. Title: A wavelet analysis of active region oscillations Authors: Ireland, J.; Walsh, R. W.; Harrison, R. A.; Priest, E. R. Bibcode: 1999A&A...347..355I Altcode: The wavelet transform is applied to the analysis of active region oscillations. The localised (in time) nature of the wavelet transform allows us to study both the duration of any statistically significant oscillations as well as their period. Time series arising from SOHO (Solar and Heliospheric Observatory) CDS-NIS (Coronal Diagnostic Spectrometer Normal Incidence Spectrometer) active region observations on 14th-15th November 1996 are used to demonstrate the applicability of wavelet methods. High cadence (approximately 14 seconds) observations were made in {He I} 584.33 Ä (log Te=4.3), {O V} 629.73 Ä (log Te=5.3), {Mg IX} 368.06 Ä (log Te=6.0), {Fe XVI} 360.76 Ä (log Te=6.4) provide detailed intensity information on the active region over a wide range of temperatures. The distribution of statistically significant periods found varies from line to line, as does their duration. Title: Magnetic Null Points due to Multiple Sources of Solar Photospheric Flux Authors: Inverarity, G. W.; Priest, E. R. Bibcode: 1999SoPh..186...99I Altcode: How common are magnetic null points in the highly complex magnetic field of the solar atmosphere? In this work we seek to model the magnetic structure of quiet regions by placing magnetic sources and sinks on a hexagonal network of supergranule cells to represent the intense magnetic fields that occur at the boundaries of these cells. The resulting potential coronal magnetic field is then computed analytically and searched numerically for magnetic null points, which are classified according to their types and spine directions. Two relations from the theory of vector fields relate the numbers of null points to the numbers of sources and sinks and these are used to check the numerical results. Previous results relating these quantities for monopolar and dipolar magnetic fields are described and a new one for a particular class of quadrupolar fields arising in this study is derived. We model a three-cell configuration and study the effects of increasing the strength of a central sink and of moving the central sink. A twelve-cell configuration is studied in lesser detail. Title: A spectacular new corona Authors: Walsh, Robert; Priest, Eric Bibcode: 1999A&G....40b..29W Altcode: No abstract at ADS Title: Dipped Magnetic Field Configurations Associated with Filaments and Barbs Authors: Mackay, D. H.; Longbottom, A. W.; Priest, E. R. Bibcode: 1999SoPh..185...87M Altcode: In this paper, three-dimensional linear force-free field configurations that can be associated with filaments are considered. It is assumed that the field configurations are suitable to represent filaments if they contain magnetic dips. With the photospheric flux distribution chosen to be an arcade with a dextral/sinistral axial component, it is found that dipped configurations exist only for large values of alpha (where, ∇×B=αB). The dips always lie above the polarity inversion line in the centre of the channel between the flux regions. When the dips are viewed from above to a depth of 1 Mm they resemble closely the shape of filaments viewed in absorption on the solar disk. As the magnitude of alpha increases, the horizontal and vertical extent of the dips also increases, giving active-region filaments for low values of alpha and quiescient filaments for high values of alpha. Dextral filaments only form for negative values of alpha and sinistral filaments for positive values of alpha. The portion of the field line that is dipped is always of inverse polarity and the magnitude of the field in the dipped region increases with height, both of which are consistent with Leroy, Bommier, and Sahal-Bréchot (1983). Overlying the region of dips there are arcades of normal polarity which have the correct left-bearing/right-bearing orientation for dextral/sinistral filaments. When the hypothesis of barbs occurring in dipped field lines is used, barbs that branch out of the main axis and to the right/left for dextral/sinistral filaments can be formed around minority polarity elements on either side of the polarity inversion line. No barbs are found around normal polarity elements. The model reproduces many of the observed features of filament channels, filaments and their barbs. Title: Heating the Solar Corona by Magnetic Reconnection Authors: Priest, E. R. Bibcode: 1999Ap&SS.264...77P Altcode: 1998Ap&SS.264...77P Here I review briefly the theory of magnetohydrodynamic reconnection and ask what observational evidence is there that it is heating the corona. In particular, the new directions in which three-dimensional theory for reconnection is heading are outlined. Part of the coronal heating problem has been solved with the identification of reconnection driven by converging flux motions as the key for x-ray bright points. Furthermore, it has been shown that the large-scale diffuse corona is heated rather uniformly, so that turbulent reconnection by braiding or ion-cyclotron waves driven by network micro-flares are prime candidates. Finally, reconnection is the natural explanation for a wide variety of phenomena discovered by SOHO including explosive events, blinkers, the magnetic carpet and even possibly tornadoes. Title: How is the Solar Corona Heated? Authors: Priest, E. R. Bibcode: 1999ASPC..158..321P Altcode: 1999ssa..conf..321P No abstract at ADS Title: Our New View of the Sun According to SOHO Authors: Priest, E. R. Bibcode: 1998ESASP.431..133P Altcode: 1998sslt.conf..133P No abstract at ADS Title: Magnetic Flux Transport and the Formation of Filament Channels on the Sun Authors: van Ballegooijen, A. A.; Cartledge, N. P.; Priest, E. R. Bibcode: 1998ApJ...501..866V Altcode: Observations of filaments and filament channels on the Sun indicate that the magnetic fields in these structures exhibit a large-scale organization: filament channels in the northern hemisphere predominantly have axial fields directed to the right when viewed from the positive polarity side of the channel (dextral orientation), while those in the south have axial fields directed to the left (sinistral orientation). In this paper we attempt to explain this pattern in terms of the most natural mechanism, namely, solar differential rotation acting on already emerged magnetic fields. We develop a model of global magnetic flux transport that includes the effects of differential rotation, meridional flow, and magnetic diffusion on photospheric and coronal fields. The model is applied to National Solar Observatory/Kitt Peak data1 on the photospheric magnetic flux distribution. We also present results from a simulation of solar activity over a period of two solar cycles, which gives a buildup of flux at the poles of a magnitude, in agreement with observations. We find that differential rotation acting on initially north-south oriented polarity inversion lines (PILs) does produce axial fields consistent with the observed hemispheric pattern. The fields associated with switchbacks in the PILs are predicted to have a definite orientation: the high-latitude ``lead'' arms of the switchbacks are preferentially sinistral (dextral) in the north (south), while the lower latitude ``return'' arms are, in agreement with observations, preferentially dextral (sinistral). The predicted orientation of fields at the polar crown, however, appear to be in conflict with observations. Further observational studies are needed to determine whether the model can explain the observed hemispheric pattern. Title: Role of Helicity in the Formation of Intermediate Filaments Authors: Mackay, D. H.; Priest, E. R.; Gaizauskas, V.; van Ballegooijen, A. A. Bibcode: 1998SoPh..180..299M Altcode: In the last few years new observations have shown that solar filaments and filament channels have a surprising hemispheric pattern. To explain this pattern, a new theory for filament channel and filament formation is put forward. The theory describes the formation of a specific type of filament, namely the `intermediate filament' which forms either between active regions or at the boundary of an active region. It describes the formation in terms of the emergence of a sheared activity complex. The complex then interacts with remnant flux and, after convergence and flux cancellation, the filament forms in the channel. A key feature of the model is the net magnetic helicity of the complex. With the correct sign a filament channel can form, but with the opposite sign no filament channel forms after convergence. It is shown how the hemispheric pattern of helicity in emerging flux regions produces the observed hemispheric pattern for filaments. Title: Nature of the heating mechanism for the diffuse solar corona Authors: Priest, E. R.; Foley, C. R.; Heyvaerts, J.; Arber, T. D.; Culhane, J. L.; Acton, L. W. Bibcode: 1998Natur.393..545P Altcode: The temperature of the Sun's outer atmosphere (the corona) exceeds that of the solar surface by about two orders of magnitude, but the nature of the coronal heating mechanisms has long been a mystery. The corona is a magnetically dominated environment, consisting of a variety of plasma structures including X-ray bright points, coronal holes and coronal loops. The latter are closed magnetic structures that occur over a range of scales and are anchored at each end in the solar surface. Large-scale regions of diffuse emission are made up of many long coronal loops. Here we present X-ray observations of the diffuse corona from which we deduce its likely heating mechanism. We find that the observed variation in temperature along a loop is highly sensitive to the spatial distribution of the heating. From a comparison of the observations and models we conclude that uniform heating gives the best fit to the loop temperature distribution, enabling us to eliminate previously suggested mechanisms of low-lying heating near the footpoints of a loop. Our findings favour turbulent breaking and reconnection of magnetic field lines as the heating mechanism of the diffuse solar corona. Title: A startling new Sun from SOHO Authors: Priest, Eric Bibcode: 1998A&G....39c..10P Altcode: No abstract at ADS Title: A crossroads for European solar and heliospheric physics. Recent achievements and future mission possibilities. Proceedings. Authors: Priest, E. R.; Moreno-Insertis, F.; Harris, R. A. Bibcode: 1998cesh.conf.....P Altcode: The following topics were dealt with: the solar interior, photosphere, solar corona, the solar wind, SOHO spacecraft mission results, the Ulysses mission, the Yohkoh mission, scientific objectives and future missions, the RAMSES proposal, INTERHELIOS, SOLARNET, the solar STEREO mission, HIREX, Solar-B mission, SOLAR LITE, UV coronagraphs. Title: Our new Sun Authors: Priest, Eric Bibcode: 1998A&G....39b..25P Altcode: No abstract at ADS Title: Solar flare MHD processes Authors: Priest, E. R. Bibcode: 1998PAICz..88...95P Altcode: No abstract at ADS Title: Crossroads for European Solar and Heliospheric Physics Authors: Priest, E. R. Bibcode: 1998ESASP.417.....P Altcode: No abstract at ADS Title: Force-Free Models of a Filament Channel in Which a Filament Forms Authors: Mackay, D. H.; Gaizauskas, V.; Priest, E. R. Bibcode: 1998ASPC..150..286M Altcode: 1998npsp.conf..286M; 1998IAUCo.167..286M No abstract at ADS Title: A Dynamic Dextral-Sinistral Model for the Structure and Evolution of Prominence Magnetic Fields Authors: Priest, E. R. Bibcode: 1998ASPC..150..453P Altcode: 1998npsp.conf..453P; 1998IAUCo.167..453P No abstract at ADS Title: Magnetic Flux Transport and Formation of Filament Channels Authors: van Ballegooijen, A. A.; Cartledge, N. P.; Priest, E. R. Bibcode: 1998ASPC..150..265V Altcode: 1998npsp.conf..265V; 1998IAUCo.167..265V No abstract at ADS Title: The Topology of Coronal Magnetic Fields in Active Regions Authors: Brown, D. S.; Priest, E. R. Bibcode: 1998ASPC..155...90B Altcode: 1998sasp.conf...90B No abstract at ADS Title: The roles of advection and diffusion in planar magnetic merging solutions Authors: Watson, P. G.; Priest, E. R.; Craig, I. J. D. Bibcode: 1998GApFD..88..165W Altcode: Since cosmic plasmas are highly conducting, large-scale magnetic fields are tied almost completely to the velocity field of the fluid. Only in localized regions of strong current density can the magnetic field slip through the plasma, allowing magnetic energy to be converted into ohmic heating or the kinetic energy of mass motion. Here we contrast the roles of advection and resistive diffusion in three different steady-state two-dimensional models for magnetic energy conversion: magnetic annihilation, reconnective diffusion and a kinematic model based on the classical magnetic reconnection picture. First we examine the diagnostic of 'field-line slippage' and show that it provides a useful indicator of the relative importance of advection and diffusion in each solution. We then quantify the energy release characteristics of the different models by examining the ratio of ohmic heat to kinetic energy generation. Title: Magnetic mechanisms for heating the corona Authors: Priest, E. R. Bibcode: 1998PAICz..88..142P Altcode: No abstract at ADS Title: The Skew of Polar Crown X-ray Arcades Authors: McAllister, A. H.; Hundhausen, A. J.; Mackay, D.; Priest, E. Bibcode: 1998ASPC..150..430M Altcode: 1998npsp.conf..430M; 1998IAUCo.167..430M No abstract at ADS Title: Alfven wave support of a dwarf molecular cloud. I. an isothermal model. Authors: Martin, C. E.; Heyvaerts, J.; Priest, E. R. Bibcode: 1997A&A...326.1176M Altcode: Dwarf (or dark) molecular clouds and molecular clumps have a lifetime which is greater than their dynamical time and must therefore be, in an average sense, in mechanical equilibrium. Equilibrium perpendicular to a global magnetic field is by magnetic forces and it is proposed that along the field the gas is supported by an Alfven wave pressure force. A self-consistent analytical model, utilising a WKB approximation, is developed for such support. It is found that Alfven waves are indeed a good candidate for this support, generating model cloud thicknesses consistent with observations. The effect of damping by the linear process of ion-neutral friction is considered. It is found that the damping of the waves is not a necessary condition for the support of the cloud although weak damping is an advantage. The possible sources of these waves are discussed. Title: Force-free and Potential Models of a Filament Channel in Which a Filament Forms Authors: Mackay, D. H.; Gaizauskas, V.; Rickard, G. J.; Priest, E. R. Bibcode: 1997ApJ...486..534M Altcode: Few examples of the creation of a filament channel or filament have ever been documented. In a recent paper, Gaizauskas and coworkers observed the early stages of creation of such a channel and then the formation of a filament in it. The filament channel was born when a new activity complex emerged near an old, decaying bipolar active region. The filament itself then formed after convergence of flux in the channel.

In this paper, force-free models are constructed for two phases of the channel's development. For the early days, the models show that the formation of the filament channel seen in Hα is due to the emerging activity complex. The field lines that give the best comparison to the fibril observations are low-lying and have a strong horizontal component. Later, when the activity complex has matured and a filament has formed between it and the adjacent decaying bipolar region, the models give a good representation of the path of the filament in the channel. It is found that the presence of flat or dipped field lines and of converging flux are necessary but not sufficient conditions for filament formation. Furthermore, the magnetic field lines of the filament itself form a narrow, vertical, sheetlike flux-tube corridor that is flat and low-lying. It connects one particular magnetic source to a sink and is bounded by separatrix surfaces that separate the filament from the old remnant region and most of the newly emerged flux. Title: The Importance of Photospheric Intense Flux Tubes for Coronal Heating Authors: Démoulin, P.; Priest, E. R. Bibcode: 1997SoPh..175..123D Altcode: Dissipation of magnetic energy in the corona requires the creation of very fine scale-lengths because of the high magnetic Reynolds number of the plasma. The formation of current sheets is a natural possible solution to this problem and it is now known that a magnetic field that is stressed by continous photospheric motions through a series of equilibria can easily form such sheets. Furthermore, in a large class of 3D magnetic fields without null points there are locations, called `quasi-separatrix layers' (QSLs), where the field-line linkage changes drastically. They are the relevant generalisation of normal separatrices to configurations without nulls: along them concentrated electric currents are formed by smooth boundary motions and 3D magnetic reconnection takes place when the layers are thin enough. With a homogenous normal magnetic field component at the boundaries, the existence of thin enough QSL to dissipate magnetic energy rapidly requires that the field is formed by flux tubes that are twisted by a few turns. However, the photospheric field is not homogeneous but is fragmented into a large number of thin flux tubes. We show that such thin tubes imply the presence of a large number of very thin QSLs in the corona. The main parameter on which their presence depends is the ratio between the magnetic flux located outside the flux tubes to the flux inside. The thickness of the QSLs is approximately given by the distance between neighbouring flux tubes multiplied by the ratio of fluxes to a power between two and three (depending on the density of flux tubes). Because most of the photospheric magnetic flux is confined in thin flux tubes, very thin QSLs are present in the corona with a thickness much smaller than the flux tube size. We suggest that a turbulent resistivity is triggered in a QSL, which then rapidly evolves into a dynamic current sheet that releases energy by fast reconnection at a rate that we estimate to be sufficient to heat the corona. We conclude that the fragmentation of the photospheric magnetic field stimulates the dissipation of magnetic energy in the corona. Title: Can we Extrapolate a Magnetic Field when its Topology is Complex? Authors: DÉmoulin, P.; HÉnoux, J. C.; Mandrini, C. H.; Priest, E. R. Bibcode: 1997SoPh..174...73D Altcode: In order to understand various solar phenomena controlled by the magnetic field, such as X-ray bright points, flares and prominence eruptions, the structure of the coronal magnetic field must be known. This requires a precise extrapolation of the photospheric magnetic field. Presently, only potential or linear force-free field approximations can be used easily. A more realistic modelling of the field is still an active research area because of well-known difficulties related to the nonlinear mixed elliptic-hyperbolic nature of the equations. An additional difficulty arises due to the complexity of the magnetic field structure which is caused by a discrete partition of the photospheric magnetic field. This complexity is not limited to magnetic regions having magnetic nulls (and so separatrices) but also occurs in those containing thin elongated volumes (called Quasi-Separatrix Layers) where the photospheric field-line linkage changes rapidly. There is a wide range for the thickness of such layers, which is determined by the character (bipolar or quadrupolar) of the magnetic region, by the sizes of the photospheric field concentrations and by the intensity of the electric currents. The aim of this paper is to analyse the recent nonlinear force-free field extrapolation techniques for complex coronal magnetic fields. Title: Reconnection in the solar corona and magnetospheric substorms. Proceedings. D0.4 Symposium of COSPAR Scientific Commission D which was held during the Thirty-first COSPAR Scientific Assembly, Birmingham (UK), 14 - 21 Jul 1996. Authors: Priest, E. R.; Baker, D. N. Bibcode: 1997AdSpR..19.1749P Altcode: 1997AdSpR..19R....P The following topics were dealt with: basic MHD theory; collisionless reconnection; solar reconnection; magnetospheric reconnection. Title: Phase-mixing in Dissipative Alfvén Waves Authors: Ireland, Jack; Priest, Eric R. Bibcode: 1997SoPh..173...31I Altcode: The phase-mixing mechanism first proposed as a coronal heating mechanism by Heyvaerts and Priest (1983) is examined using a length-scale analysis adapted from Cally (1991). This allows parameter ranges other than those studied by Heyvaerts and Priest (1983) to be described, together with a detailed examination of the transfer of energy to both longer and shorter length-scales as the Alfvén wave front evolves in the solar corona. The results of Heyvaerts and Priest (1983) are largely confirmed, but with some notable differences. Energy initially at smaller length-scales decays faster than their rate, because the plasma is more strongly dissipative at smaller length-scales. The full inclusion of diffusion across field lines also leads to smoother Alfvén wavefronts. Title: Three-dimensional magnetic reconnection in the solar corona Authors: Priest, E. R. Bibcode: 1997PhPl....4.1945P Altcode: In two dimensions the notions of magnetic topology and null-point bifurcations are straightforward. In addition, the nature of magnetic reconnection is fairly well understood and can be described by a new generation of fast reconnection mechanisms known as almost-uniform reconnection and nonuniform reconnection. However, in complex three-dimensional (3-D) magnetic fields, such as exist in the solar corona, these phenomena are only just beginning to be explored and are considerably more complex. The structural properties of the magnetic field created in turn by two, three and more magnetic sources at the photosphere have been recently studied. Passing through each 3-D magnetic null there is an isolated spine field line and a flux surface known as a fan. The fans form separatrix surfaces that separate the volume into topologically distinct regions, and the fan of one null can terminate at the spine of another null, while the spine terminates either at a source or at infinity. The skeleton of complex 3-D fields in the corona, therefore, comprises the magnetic-null points and a network of spine curves and separatrix fan surfaces. Magnetic reconnection can occur in these fields by a variety of mechanisms, including spine reconnection, fan reconnection, separator reconnection, and quasiseparatrix layer reconnection. These types of reconnection and the bifurcations of null points are described and found to be much richer than in the relatively simple two-dimensional fields. Title: How is the Solar Corona Heated ? Authors: Priest, Eric R. Bibcode: 1997SPD....28.0701P Altcode: 1997BAAS...29..911P Trying to determine which mechanisms are heating the corona is one of the main aims of the SOHO mission. A summary is given of the mechanisms that have been proposed together with the observational properties that have so far been determined. A new technique for determining the heating mechanisms is presented together with the results from applying it to Yohkoh data and SOHO data - it gives powerful evidence in favour of one particular mechanism for most of the corona. The technique provides a strong implication as to what observations could be most usefully made from SOHO and what theoretical developments of the different mechanisms are required in future. Title: The Skew of Polar Crown X-ray Arcades Authors: McAllister, A. H.; Mackay, D.; Hundhausen, A. J.; Priest, E. Bibcode: 1997SPD....28.0255M Altcode: 1997BAAS...29..903M A one-to-one relationship between the chirality of filament channels and the skew (relative orientation) of the overlying coronal arcades, as seen with the Yohkoh Soft X-ray Telescope (SXT) was found by Martin and McAllister [1997]. The basis of the relationship is a sample of over 30 mid-and low-latitude filaments during a 6 month period in early 1992. This relationship can be coupled with the predictions for the axial component of polar crown filaments based on the work of Leroy et al. [1983] to predict the skew of polar crown arcades in the recent cycle 22. Thus the axial component of the filament fields along the southern polar crown is predicted to point to the west and a similar component in the corona will lead to right skewed arcades. As has been pointed out in the past, this orientation is inconsistent with the action of photospheric differential rotation on an east-west arcade [Ballegooijen and Martens, 1990]. In this poster we report on the results of a recent survey of the SXT images over the whole declining phase of cycle 22 (Oct. 1991 to June 1995). These results are not in general agreement with those expected based on the past filament observations. They show highly left skewed polar arcades rather than the predicted right skew. The observations are, however, in general agreement with the effects of differential rotation and with recent numerical simulations of polar crown structures, which we will also briefly present. This posses an unexpected and challenging problem and we will discuss some possible ways of reconciling the different observational results. Leroy, Bommier, and Sahal-Brechot, The Magnetic Field in Prominences of the Polar Crown, Solar Physics, 83, 135-142, 1983. Martin and McAllister, The Chirality of X-ray Coronal Arcades Overlying Quiescent Filaments, Astrophys. Journ., submitted, 1997. Ballegooijen and Martens, Magnetic Fields in Quiescent Prominences, ApJ, 361, 283-289, 1990. Title: Heating of coronal holes by phase mixing. Authors: Hood, A. W.; Ireland, J.; Priest, E. R. Bibcode: 1997A&A...318..957H Altcode: A two-dimensional, analytical, self-similar solution to the Alfven wave phase mixing equations is presented for a coronal hole model. The solution shows clearly that the damping of the waves with height follows the scaling predicted by Heyvaerts & Priest at low heights, before switching to an algebraic decay at large heights. The ohmic dissipation is calculated and it is shown that the maximum dissipation occurs at a height that scales with η^1/3^. However, the total Ohmic dissipation is, of course, independent of the resistivity. Using realistic solar parameters it appears that phase mixing is a viable mechanism for heating the lower corona provided either the frequency of photospheric motions is sufficiently large or the background Alfven velocity is sufficiently small. Title: Active Region Blinkers: Transient Events in the Solar Atmosphere Authors: Walsh, R. W.; Ireland, J.; Harrison, R. A.; Priest, E. R. Bibcode: 1997ESASP.404..717W Altcode: 1997cswn.conf..717W No abstract at ADS Title: An Analytical MHD Model for Solar/Stellar Winds Authors: Lima, J. J. G.; Priest, E. R.; Tsinganos, K. Bibcode: 1997ESASP.404..521L Altcode: 1997cswn.conf..521L No abstract at ADS Title: Periodicities in Active Regions Authors: Ireland, J.; Walsh, R. W.; Harrison, R. A.; Priest, E. R. Bibcode: 1997ESASP.404..433I Altcode: 1997cswn.conf..433I No abstract at ADS Title: Magnetic Fields and Coronal Structures Authors: Priest, E. R. Bibcode: 1997ESASP.404...93P Altcode: 1997cswn.conf...93P; 1997soho....5...93P No abstract at ADS Title: Linear theory of steady X-point magnetic reconnection Authors: Titov, V. S.; Priest, E. R. Bibcode: 1997AdSpR..19.1777T Altcode: Slow magnetic reconnection at a neutral X-point of a two-dimensional magnetic field is studied in an incompressible viscous resistive fluid. It is shown analytically that the combined effect of viscosity and resistivity resolves the current singularity appearing in both the ideal and resistive magnetohydrodynamic approximations at the X-point and along the separatrices when the flow is allowed to cross them. A previous attempt had retained a weak singularity at third order. A two-parameter family of exact solutions describing the structure of the flow and current density distribution is found for the corresponding basic equations. Title: Basic magnetic field configurations for filament channels and filaments Authors: Mackay, D. H.; Priest, E. R. Bibcode: 1997A&AT...13..111M Altcode: Recent observations of Martin et al. have revealed two new magnetic and structural classes for solar filaments and filament channels. The magnetic classes are called sinistral and dextral while the structural classes are left-bearing and right-bearing. A potential model of the magnetic field in a filament channel consistent with the observations is developed, including the magnetic sources of network flux on both sides of the channel and concentrations of flux along the channel. A particular filament channel is also modelled by a set of discrete magnetic sources and sinks approximating the observed flux of the channel. In addition, the bending of a filament as it passes between opposite polarity sources is modelled. Title: The 3D topology and interaction of complex magnetic flux systems Authors: Priest, E. R.; Bungey, T. N.; Titov, V. S. Bibcode: 1997GApFD..84..127P Altcode: In order to understand the topology of complex flux systems we analyse in detail the rich structural properties of the magnetic field created in turn by two or three balanced or unbalanced flux sources. Passing through each three-dimensional magnetic null point (where the field vanishes) is an isolated spine field line and a flux surface known as a fan. The fans form separatrix surfaces which separate the volume into topologically distinct regions and generally intersect each other in separator field lines linking pairs of null points. Furthermore, the fan of one null can terminate at the spine of another null, whilst the spine terminates either at a source or at infinity. The skeleton of complex three-dimensional magnetic fields therefore comprises the magnetic null points and a network of spine curves and separatrix fan surfaces. The skeletons due to three sources are classified and found to be surprisingly complex. For example, a new discovery is that a configuration with a separator may be produced by only three sources. Title: Structure and collapse of three-dimensional magnetic neutral points Authors: Parnell, C. E.; Neukirch, T.; Smith, J. M.; Priest, E. R. Bibcode: 1997GApFD..84..245P Altcode: The structure and collapse of linear three-dimensional magnetic neutral points is studied by varying the four parameters (p, q,j|,j) that define, in general, the linear field of a neutral point. The effect of these parameters on both the skeleton structure (i.e. the fan and spine) and the actual field line structure of the null is considered. It is found that one current component (j) causes the skeleton structure of the null to fold up from its potential state, whereas the other current component (j|;) causes the field lines to bend. The two other parameters (p,q) determine the potential structure of the null and cause the null to transform from a three-dimensional null to a two-dimensional null and from a positive (type B) null to a negative (type A) null.

To investigate the collapse of three-dimensional nulls, solutions to the linear, low-β ideal magnetohydrodynamic equations are found. It is found that three-dimensional null points can collapse if the field line foot-points are free and energy can propagate into the system. Title: Bifurcations of magnetic topology by the creation or annihilation of null points Authors: Priest, E. R.; Lonie, D. P.; Titov, V. S. Bibcode: 1996JPlPh..56..507P Altcode: Linear null points of a magnetic field may come together and coalesce at a secondorder null, or vice versa a second-order null may form and split, giving birth to a pair of linear nulls. Such local bifurcations lead to global changes of magnetic topology and in some cases release of magnetic energy. In two dimensions the null points are of X or O type and the flux function is a Hamiltonian; the magnetic field may undergo addle-centre, pitchfork or degenerate resonant bifurcations. In three dimensions the null points and their creation or annihilation by bifurcations are considerably more complex. The nulls possess a skeleton consisting of a spine curve and a fan surface and are of radial-type (proper or improper) or spiral-type; the type of null and the inclination of spine and fan depend on the magnitudes of the current components along and normal to the spine. In cylindrically symmetric fields a comprehensive treatment is given of the various types of saddle-node, Hopf and saddle-node—Hopfbifurcations. In fully three-dimensional situations examples are given of saddle-node and degenerate bifurcations, in which generically two nulls are created or destroyed and are joined by a separator field line, which is the intersection of the two fans. Furthermore, global bifurcations can create chaotic field lines that could perhaps trigger energy release in, for example, solar flares. Title: Magnetic Reconnection at Three-Dimensional Null Points Authors: Priest, E. R.; Titov, V. S. Bibcode: 1996RSPSA.354.2951P Altcode: The skeleton of an isolated null point in three dimensions consists of a `spine curve' and a `fan surface'. Two isolated magnetic field lines approach (or recede from) the null point from both directions along the spine, and a continuum of field lines recedes from (or approaches) the null in the plane of the fan surface. Two bundles of field lines approach the null point around the spine (one from each direction) and spread out near the fan. The kinematics of steady reconnection at such a null point is considered, depending on the nature of the imposed boundary conditions on the surface that encloses the null, in particular on a cylindrical surface with its axis along the spine. Three kinds of reconnection are discovered. In `spine reconnection' continuous footpoint motions are imposed on the curved cylindrical surface, crossing the fan and driving singular jetting flow along the spine. In `fan reconnection' continuous footpoint motions are prescribed on the ends of the cylinder, crossing the spine and driving a singular swirling motion at the fan. An antireconnection theorem is proved, which states that steady MHD reconnection in three dimensions with plasma flow across the spine or fan is impossible in an inviscid plasma with a highly subAlfvenic flow and uniform magnetic diffusivity. One implication of this is that reconnection tends to be an inherently nonlinear phenomenon. A linear theory for slow steady reconnection is developed which demonstrates explicitly the nature of the spine singularity in spine reconnection. Finally, the properties of `separator reconnection' in complex configurations containing two null points are discussed by means of analytical examples. Title: Magnetic Reconnection at Three-Dimensional Null Points Authors: Priest, E. R.; Titov, V. S. Bibcode: 1996RSPTA.354.2951P Altcode: No abstract at ADS Title: Magnetic Field Diffusion in Self-consistently Turbulent Accretion Disks Authors: Heyvaerts, J.; Priest, E. R.; Bardou, A. Bibcode: 1996ApJ...473..403H Altcode: We show how the level of turbulence in accretion disks can be derived from a self-consistency requirement that the associated effective viscosity should match the instantaneous accretion rate. This method is applicable when turbulence has a direct energy cascade. Only limited information on the origin and properties of the turbulence, such as its injection scale and anisotropy, is needed. The method is illustrated by considering the case of turbulence originating from the magnetic shearing instability. The corresponding effective kinematic viscosity coefficient is shown to scale as the 1/3 power of surface mass density at a given radius in optically thick disks, and to be describable by a Shakura-Sunyaev law with α≍0.04. Mass flow in disks fed at a localized hot spot is calculated for accretion regimes driven by such turbulence, as well as passive magnetic field diffusion and dragging. An important result of this analysis is that thin disks supported by turbulence driven by the magnetic shearing instability, and more generally any turbulence with injection scale of order of the disk thickness, are very low magnetic Reynolds number systems. Turbulent viscosity-driven solutions with negligible field dragging and no emission of cold winds or jets are natural consequences of such regimes. Disks of accreting objects that are magnetized enough to be shielded by a magnetopause, however, may not operate in their innermost regions in the magnetic shearing instability regime. The possibility therefore remains to be explored of centrifugally driven winds emanating from such regions. Title: Quasi-Separatrix Layers in Simple Magnetic Configurations Authors: Mandrini, C. H.; Demoulin, P.; Henoux, J. C.; Priest, E. Bibcode: 1996RMxAC...4Q.104M Altcode: No abstract at ADS Title: A Strong Limitation on the Rapidity of Flux-Pile-Up Reconnection Authors: Litvinenko, Y. E.; Forbes, T. G.; Priest, E. R. Bibcode: 1996SoPh..167..445L Altcode: The reconnection rate which can be achieved in the steady-state flux-pile-up regime is severely limited by the gas pressure of the plasma. Using the family of solutions obtained previously by Priest and Forbes, we show that the Alfvén Mach number of the plasma flowing towards the reconnection site cannot exceed πβe/(8 ln Rme), where βe and Rme are the plasma β and magnetic Reynolds numbers at large distance. This limit corresponds to a very weak flux-pile-up, and it is a factor of βe slower than the maximum Petschek rate. Thus the maximum flux-pile-up reconnection rate in the corona is at least two orders of magnitude smaller than the rate implied by flare observations. Title: A Potential-Field Model for Dextral and Sinistral Filament Channels Authors: Mackay, D. H.; Priest, E. R. Bibcode: 1996SoPh..167..281M Altcode: Recent observations of Martin, Bilimoria, and Tracadas (1995) have revealed two new magnetic and structural classes for solar filaments and filament channels. The magnetic classes are called sinistral and dextral, while the structural classes are left-bearing and right-bearing. Dextral filaments dominate in the northern hemisphere and sinistral in the southern. A model consistent with the observations is developed with magnetic sources that represent the network flux on both sides of the channel and extra concentrations of flux that produce the strong field component along the channel. We suggest that it is the imbalance of flux locations along the channel that creates the field of a filament channel. The resulting separatrix surfaces have distinct upper and lower boundaries that may produce the upper boundary of the filament cavity or filament and the lower boundary of the filament. The model is applied to a specific filament channel, with discrete sources and sinks that represent the flux observed in a photospheric magnetogram. The resulting three-dimensional field lines near the filament location are low-lying and possess dips. Title: A 2-D model for the support of a polar-crown solar prominence Authors: Cartledge, N. P.; Titov, V. S.; Priest, E. R. Bibcode: 1996SoPh..166..287C Altcode: 1996SoPh..166..287G We present a 2-D potential-field model for the magnetic structure in the environment of a typical quiescent polar-crown prominence. The field is computed using the general method of Titov (1992) in which a curved current sheet, representing the prominence, is supported in equilibrium by upwardly directed Lorentz forces to balance the prominence weight. The mass density of the prominence sheet is computed in this solution using a simple force balance and observed values of the photospheric and prominence magnetic field. This calculation gives a mass density of the correct order of magnitude. The prominence sheet is surrounded by an inverse-polarity field configuration adjacent to a region of vertical, open polar field in agreement with observations. Title: Magnetohydrodynamic Waves in Solar Coronal Arcades Authors: Oliver, R.; Hood, A. W.; Priest, E. R. Bibcode: 1996ApJ...461..424O Altcode: The propagation of magnetohydrodynamic (MRD) disturbances in a solar coronal arcade is investigated. The equations of magnetoacoustic fast and slow waves are presented in a very general form: a pair of second-order, two-dimensional partial differential equations in which the two dependent variables are the components of the velocity perturbation parallel and normal to the magnetic field. In deriving these equations, a general two-dimensional equilibrium structure with no longitudinal magnetic field component has been assumed. Thus, the equations are valid for rather general configurations. Alfvén waves are decoupled from the magnetoacoustic modes and give rise to an Alfvén continuous spectrum.

The solutions to the wave equations have been obtained numerically, and the perturbed restoring forces (plasma pressure gradient, magnetic pressure gradient, and magnetic tension), responsible for the oscillatory modes, have also been computed. These forces give rise to the propagation of MRD waves, and their interaction determines the physical properties of the various modes. Therefore, the spatial structure of the forces and their interplay are basic in characterizing fast and slow modes.

Pure fast and pure slow waves do not exist in the present configuration, although for the considered parameter values, all modes possess either fast-mode or slow-mode properties. "Slow" modes in these two-dimensional equilibria can propagate across the magnetic field only with difficulty and so display a structure of bands, centred about certain field lines, of alternate positive and negative parallel velocity component. On the other hand, "fast" modes are isotropic in nature, and their spatial structure is not so intimately linked to the shape of field lines. In addition, as a consequence of the distinct characteristic propagation speeds of fast and slow modes, their frequencies typically differ by an order of magnitude. Title: Basic topological elements of coronal magnetic fields. Authors: Bungey, T. N.; Titov, V. S.; Priest, E. R. Bibcode: 1996A&A...308..233B Altcode: We model the magnetic field of a coronal active region using discrete magnetic sources and look for regions of the photospheric inversion line which are tangentially touched by coronal field lines. These locations are called `Bald Patches'. Field lines threading these bald patch regions, together with those threading any coronal null points, determine the `Topological Skeleton' of the field. We examine the properties of these null points and bald patch regions for two, three and four magnetic sources, and study the evolution of the coronal topological skeleton as a result of moving and varying the sources. In particular, for a four-source magnetic configuration, we establish the existence of a well-defined `separator' field line in the absence of any coronal null points. We conclude that bald patches as well as coronal nulls constitute an elemental topological feature of the coronal field: they may be significant as possible regions for coronal current sheet formation and for prominence formation. Title: Three-dimensional magnetic reconnection without null points 2. Application to twisted flux tubes Authors: Démoulin, P.; Priest, E. R.; Lonie, D. P. Bibcode: 1996JGR...101.7631D Altcode: Magnetic reconnection has traditionally been associated exclusively with the presence of magnetic null points or field lines tangential to a boundary. However, in many cases introducing a three-dimensional perturbation in a two-and-half-dimensional magnetic configuration implies the disappearance of separatrices. Faced with this structural instability of separatrices when going from two-and-half to three-dimensional configurations, several approaches have been investigated to replace the topological ideas familiar in two-dimensional, but no unanimity has yet emerged on the way reconnection should be defined. While it is true that the field line linkage is continuous in three-dimensional, we show here that extremely thin layers (called quasi-separatrix layers (QSLs)) are present. In these layers the gradient of the mapping of field lines from one part of a boundary to another is very much larger than normal (by many orders of magnitude). Even for highly conductive media these extremely thin layers behave physically like separatrices. Thus reconnection without null points can occur in QSLs with a breakdown of ideal MHD and a change in connectivity of plasma elements. We have analyzed several twisted flux tube configurations, going progressively from two-and-half to three-dimensional, showing that QSLs are structurally stable features (in contrast to separatrices). The relative thickness w of QSLs depends mainly on the maximum twist; typically, with two turns, w~10-6, while with four turns, w~10-12. In these twisted configurations the shape of the QSLs, at the intersection with the lower planar boundary, is typical of the two ribbons observed in two-ribbon solar flares, confirming that the accompanying prominence eruption involves the reconnection of twisted magnetic structures. We conclude that reconnection occurs in three-dimensional in thin layers or QSLs, which generalise the traditional separatrices (related only to magnetic null points or field lines tangential to the boundary). Title: Quasi-Separatrix layers in solar flares. I. Method. Authors: Demoulin, P.; Henoux, J. C.; Priest, E. R.; Mandrini, C. H. Bibcode: 1996A&A...308..643D Altcode: Magnetic reconnection is usually thought to be linked to the presence of magnetic null points and to be accompanied by the transport of magnetic field lines across separatrices, the set of field lines where the mapping of field lines is discontinuous. In view of the variety of observed flaring configurations, we show that this view is too restrictive. Instead, Priest and Demoulin (1995) have explored a way of generalising the concept of separatrices to magnetic configurations without field-line linkage discontinuities. They propose that magnetic reconnection may also occur in 3D in the absence of null points at "quasi-separatrix layers" (QSLs), which are regions where there is drastic change in field-line linkage. In previous studies we have shown that solar flare kernels are linked to the topology of the active-region magnetic field. The observed photospheric field was extrapolated to the corona using subphotospheric magnetic sources and the topology was defined by the magnetic linkage between these sources, the method being called SM (for Source Method). In this paper we define a new method, called QSLM (for Quasi-Separatrix Layers Method), which finds the location of QSLs above the photosphere. It is designed to be applied to any kind of magnetic field representation, while, in the present paper, we apply it only to simple theoretical magnetic configurations in order to compare it with the SM. It generalises the concept of separatrices to magnetic configurations without field-line linkage discontinuities. The QSLM determines elongated regions that are in general located along small portions of the separatrices defined by the SM, and in the limit of very concentrated photospheric fields both methods give the same result. In bipolar magnetic configurations two QSLs are found at both sides of the inversion line, while in quadrupolar configurations four appear. We find that there is a wide range for the thickness of the QSLs, which is determined by the character (bipolar or quadrupolar) of the magnetic region and by the sizes of the photospheric field concentrations. We then show that smooth photospheric motions induce concentrated currents at the locations defined by the QSLM. We prove this only for initially potential configurations but, due to the form of the equations, we conjecture that it is also valid for any kind of initial magnetic equilibrium. We conclude that, even in bipolar configurations, there are localized places where current build-up can be induced by photospheric motions, leading to ideal MHD breakdown with strong flows and magnetic energy release. Title: A Model for Dextral and Sinistral Prominences Authors: Priest, E. R.; van Ballegooijen, A. A.; Mackay, D. H. Bibcode: 1996ApJ...460..530P Altcode: In a recent paper Martin and coworkers have discussed several striking facts about the structure of solar prominences and the filament channels in which they lie. They form two classes, called dextral and sinistral. In a dextral (sinistral) prominence, an observer viewing a prominence or filament channel from the positive-polarity side would see the magnetic field point to the right (left) along the axis of the filament channel, whereas an observer viewing from above would see the prominence feet bear off the axis to the right (left). Furthermore, dextral prominences dominate the northern hemisphere and sinistral the southern hemisphere, regardless of the cycle. Fibrils in the filament channels do not cross the prominence but usually stream from or to plagettes parallel to the prominence axis.

These pioneering observations suggest that there is a coherent organizational principle orchestrating the global nature of prominences, and they have led us to reexamine the standard paradigms of contemporary prominence theory, such as that (1) prominences form in a sheared force-free arcade, (2) formation is by radiative instability, (3) the prominence material is static, and (4) eruption occurs when the shear or twist is too great. We propose a new model which accounts for the above new observational features in a natural way, replaces many of the above paradigms, and explains the previously puzzling feet of a prominence. It is a dynamic model in which a prominence is maintained by the continual input of mass and magnetic flux. The correct global dextral and sinistral patterns for high-latitude east-west prominences (such as those in the polar crown) are created by an organizational principle that includes the combined effects of differential rotation on subphotospheric flux, its subsequent emergence by magnetic buoyancy, and its rearrangement by flux reconnection to form a filament channel with magnetic flux oriented along its axis. Continual emergence and reconnection creates a prominence as a flux tube along the filament channel axis and filled with cool plasma which is lifted up from the photosphere and chromosphere by the reconnection process. Prominences at low latitudes are in this model formed in a similar way, except that it is a general subphotospheric flow (rather than differential rotation) which acts and so may produce either dextral or sinistral structures, depending on the sense of the flow. The effect of neighboring plagettes in avoiding the prominence and making it snake its way along the filament channel is modeled. It is suggested that feet are short-lived structures caused by the interaction of nearby magnetic fragments with the prominence field and may represent either the addition or the extraction of mass from the prominence. Title: Coronal Heating by Magnetic Reconnection Authors: Priest, Eric R. Bibcode: 1996Ap&SS.237...49P Altcode: The theory of magnetic reconnection has advanced substantially over the past few years. There now exists a new generation of fast two-dimensional models known as almost-uniform reconnection and nonuniform reconnection, depending on the boundary conditions. Also, we are beginning to explore the uncharted region of three-dimensional reconnection, where regimes of “spine reconnection” and “fan reconnection” have been discovered. Furthermore, part of the coronal heating problem appears to have been solved with recent observational support for the Converging Flux Model in which heating is produced by coronal reconnection driven by footpoint motions. Title: A Model for Polar-Crown Prominences Authors: Cartledge, N. P.; Titov, V. S.; Priest, E. R. Bibcode: 1996ApL&C..34...89C Altcode: No abstract at ADS Title: 3D Reconnection in Complex Topologies (Invited) Authors: Priest, E. R. Bibcode: 1996ASPC..111..331P Altcode: 1997ASPC..111..331P In order to understand the topology of complex flux systems such as occur in the solar corona, the author studies the structural properties of the magnetic field created in turn by 2, 3 and 4 magnetic sources at the photosphere. Passing through each 3D magnetic null there is an isolated spine field line and a flux surface known as a fan. The fans form separatrix surfaces which separate the volume into topologically distinct regions, and the fan of one null can terminate at the spine of another null, while the spine terminates either at a source or at infinity. Magnetic reconnection can occur in these fields by a variety of mechanisms, including spine reconnection, fan reconnection, separator reconnection and quasi-separatrix layer reconnection. The skeleton of complex 3D fields in the corona therefore comprises the magnetic null points and a network of spine curves and separatrix fan surfaces. The types of reconnection in these fields and the bifurcations of null points are described in some detail and found to be much richer than in the relatively simple 2D fields that have been the main object of study up to now. Title: Separatrix Characteristics in Steady MHD Flows Authors: Surlantzis, G.; Tsinganos, K.; Priest, E. Bibcode: 1996ApL&C..34..251S Altcode: No abstract at ADS Title: New developments in magnetic reconnection theory. Authors: Priest, E. R. Bibcode: 1996ASIC..481..171P Altcode: Although two-dimensional reconnection is now fairly well understood, there have recently been some interesting new developments. Four distinct types of reconnection are possible, namely: viscous (or kinematic) reconnection; extra-slow (or linear) reconnection; slow (or Sweet-Parker) reconnection; and fast (Almost-uniform or Nonuniform) reconnection. An antireconnection theorem has been discovered which states that steady two-dimensional reconnection (with flow across the separatrices) is impossible for slow inviscid flow (and it has also been generalised to three dimensions). Solutions for linear reconnection have been presented and a new theory for the self-consistent time-dependent collapse of an X-point to form a reconnecting current sheet has been developed. The new field of three-dimensional reconnection is only just beginning. Reconnection at null points is discussed. Title: Two-Dimensional MHD Models for Stellar Winds Authors: Lima, J. J. G.; Tsinganos, K.; Priest, E. R. Bibcode: 1996ApL&C..34..281L Altcode: No abstract at ADS Title: Plasma Beta Limitations for Magnetic Annihilation Models Authors: Inverarity, G. W.; Priest, E. R. Bibcode: 1996ASPC..111..296I Altcode: 1997ASPC..111..296I The need to keep the plasma pressure positive in fast reconnection solutions introduces a minimum plasma beta (ratio of plasma pressure to magnetic pressure) at the edge of the region in which annihilation or reconnection is occurring. Such constraints are presented for the models of Sonnerup and Priest (1975) and Craig and Henton (1995). It is found that in astrophysical contexts the models are only applicable at very slow reconnection rates. Title: New Paradigms for Solar Prominences Authors: Priest, E. R. Bibcode: 1996ASPC...95..229P Altcode: 1996sdit.conf..229P No abstract at ADS Title: Interaction of turbulent accretion disks with embedded magnetic fields. Authors: Heyvaerts, J. F.; Bardou, A.; Priest, E. R. Bibcode: 1996ASIC..481..659H Altcode: The authors show that the level of turbulence in accretion disks can be derived from a self-consistency requirement that the associated effective viscosity should match the instantaneous accretion rate. When turbulence originates in the magnetic shearing instability, the effective kinematic viscosity coefficient is shown to be describable by a Shakura-Sunyaev law with α ≍ 0.04. It is shown that thin disks suported by any turbulence with injection scale of order of the disk thickness, are very low magnetic Reynolds number systems. Turbulent viscosity-driven solutions with negligible field dragging and no emission of cold winds or jets are natural consequences of such regimes. Such disks are shown to expell the magnetic field of the accreting object from their Keplerian regions radially outwards, resulting in a flux distribution in the disk which differs very much from a dipolar one. Title: Reconnection of magnetic lines of force. Authors: Priest, E. R. Bibcode: 1996ASIC..481..151P Altcode: Parker laid the foundation for the subject of magnetic reconnection in his fundamental early papers. The author summarises his contributions and gives a new generalisation of the Sweet-Parker relations for a current sheet in which the outflow pressure is an extra parameter. Then he reviews the models for fast reconnection that have since been proposed, beginning with the Petschek mechanism and continuing to the more general Almost-Uniform and Nonuniform families. A comparison with numerical experiments is also made and the conditions under which fast reconnection exists are elucidated. Title: 3D Magnetic Reconnection: Example of an X-Ray Bright Point Authors: Demoulin, P.; Mandrini, C. H.; van Driel-Gesztelyi, L.; Priest, E. R.; Henoux, J. C.; Schmieder, B. Bibcode: 1996ASPC..111...49D Altcode: 1997ASPC..111...49D In the classical view magnetic reconnection occurs at neutral points and implies transport of magnetic field-lines across separatrices. The authors show that reconnection may also occur in the absence of neutral points at so-called "quasi-separatrix layers" (QSLs), where there is a steep gradient in field-line linkage at the boundaries. Reconnection occurs in QSLs where the field-line velocity becomes larger than the allowed maximal plasma velocity or where the electric-current density becomes too great. The authors describe both a theoretical and an observed configuration. In the case of a simple sheared X-field they show that even a smooth continuous shear flow, imposed at the boundary, gives strong plasma jetting inside and parallel to the QSLs. Applying the QSL method to an X-ray bright point observed by Yohkoh, they find field lines in the extrapolated field which are on both sides of QSLs and which are in good agreement with loops observed in Hα and X-rays related to emerging flux. The evolution of the QSL width may explain the brightness evolution of the XBP. Title: Book-Review - Lectures on Solar and Planetary Dynamos Authors: Proctor, M. R. E.; Gilbert, A. D.; Priest, E. R. Bibcode: 1995Obs...115..338P Altcode: No abstract at ADS Title: Three-dimensional magnetic reconnection without null points. 1. Basic theory of magnetic flipping Authors: Priest, E. R.; Démoulin, P. Bibcode: 1995JGR...10023443P Altcode: In two or three dimensions, magnetic reconnection may occur at neutral points and is accompanied by the transport of magnetic field lines across separatrices, the field lines (or flux surfaces in three dimensions) at which the mapping of field lines is discontinuous. Here we show that reconnection may also occur in three dimensions in the absence of neutral points at so-called ``quasi-separatrix layers,'' where there is a steep gradient in field line linkage. Reconnection is a global property, and so, in order to determine where it can occur, the first step is to enclose the volume being considered by a boundary (such as a spherical surface). Then the mapping of field lines from one part of the boundary to another is determined, and quasi-separatrix layers may be identified as regions where the gradient of the mapping or its inverse is very much larger than normal. The most effective measure of the presence of such layers is the norm of the displacement gradient tensor; their qualitative location is robust and insensitive to the particular surface that is chosen. Reconnection itself occurs when there is a breakdown of ideal MHD and a change of connectivity of plasma elements, where the field line velocity becomes larger than the plasma velocity, so that the field lines slip through the plasma.

This breakdown can occur in the quasi-separatrix layers with an electric field component parallel to the magnetic field. In three dimensions the electric field E (and therefore the field line velocity v⊥) depends partly on the imposed values of E (or v⊥) at the boundary and partly on the gradients of the inverse mapping function. We show that the inverse mapping determines the location of the narrow layers where the breakdown of ideal MHD can occur, while the imposed boundary values of v⊥ determine mainly the detailed flow pattern inside the layers. Thus, in general, E (and therefore v⊥) becomes much larger than its boundary values at locations where the gradients of the inverse mapping function are large. An example is given of a sheared X field, where a slow smooth continuous shear flow imposed on the boundary across one quasi-separatrix produces a flipping of magnetic field lines as they slip rapidly through the plasma in the other quasi-separatrix layer. It results in a strong plasma jetting localized in, and parallel to, the separatrix layers. Title: Disques d'accrétion turbulents auto-cohérents. Authors: Bardou, A.; Heyvaerts, J.; Priest, E. Bibcode: 1995JAF....49...51B Altcode: No abstract at ADS Title: Turbulent coronal heating. III. Wave heating in coronal loops. Authors: Inverarity, G. W.; Priest, E. R. Bibcode: 1995A&A...302..567I Altcode: The heating which results from damped oscillations of a uniform solar coronal loop driven by photospheric motions is considered for an incompressible, visco-resistive, turbulent medium. Photospheric disturbances on a time-scale faster than the time for an Alfven wave to cross the loop drive damped standing waves in the loop. Including turbulent effects permits the generation of gradients sufficiently intense to allow dissipation of the kinetic and magnetic energy of the waves to balance the rate of injection of energy from the photosphere, thus maintaining a steady state. Assuming a single global driving frequency, levels of heating approaching 10^4^Wm^-2^ (10^7^erg cm^-2^/s) are attainable for the fundamental resonance and first few harmonics, which could account for the heating of short (10^4^km) loops with fields of order 100G if sufficiently rapid photospheric oscillations occur. Also, for fields of about 10G, which occur in the longer loops (10^5^km) found outside active regions, levels approaching 100Wm^-2^ (10^5^ergcm^-2^/s) are obtained -- sufficient to heat the quiet corona. Title: Models for the Motions of Flare Loops and Ribbons Authors: Lin, J.; Forbes, T. G.; Priest, E. R.; Bungey, T. N. Bibcode: 1995SoPh..159..275L Altcode: We have found a conformal mapping which is valid for any magnetic boundary condition at the photosphere and which can be used to determine the evolution of an open, two-dimensional magnetic field configuration as it relaxes to a closed one. Solutions obtained with this mapping are in quasi-static equilibrium, and they contain a vertical current sheet and have line-tied boundary conditions. As a specific example, we determine the solution for a boundary condition corresponding to a submerged, two-dimensional dipole below the photosphere. We assume that the outer edges of the hottest X-ray loops correspond to field lines mapping from the outer edges of the Hα ribbon to the lower tip of the current sheet where field lines reconnect at aY-type neutral line which rises with time. The cooler Hα loops are assumed to lie along the field lines mapping to the inner edges of the flare ribbons. With this correspondence between the plasma structures and the magnetic field we determine the shrinkage that field lines are observed to undergo as they are disconnected from the neutral line. During the early phase of the flare, we predict that shrinkage inferred from the height of the Hα and X-ray loops is close to 100% of the loop height. However, the shrinkage should rapidly decrease with time to values on the order of 20% by the late phase. We also predict that the shrinkage in very large loops obeys a universal scaling law which is independent of the boundary condition, provided that the field becomes self-similar (i.e., all field lines have the same shape) at large distances. Specifically, for any self-similar field containing aY-type neutral line, the observed shrinkage at large distances should decrease as (ΔX/XR)−2/3, where ΔX is the ribbon width andXRis the ribbon separation. Finally, we discuss the relation between the electric field at the neutral line and the motions of the flare loops and ribbons. Title: Erratum - Turbulent Coronal Heating Authors: Inverarity, G. W.; Priest, E. R.; Heyvaerts, J. Bibcode: 1995A&A...299..640I Altcode: No abstract at ADS Title: Book Review: Fundamentals of cosmic electrodynamics / Kluwer, 1994 Authors: Priest, E. R. Bibcode: 1995Obs...115..142P Altcode: 1995Obs...115..142S No abstract at ADS Title: Photospheric Magnetic Field Evolution and Eruptive Flares Authors: Forbes, T. G.; Priest, E. R. Bibcode: 1995ApJ...446..377F Altcode: Using an eruptive flare model based on a loss of equilibrium in a coronal flux rope, we show that the average horizontal component of the photospheric field does not necessarily become more like a potential (current-free) field immediately after the eruption begins. Therefore, recent observations showing that the average horizontal field becomes less potential during the impulsive phase of a flare do not necessarily imply that the magnetic energy in the corona has increased as has sometimes been assumed. The flux-rope model which we use also has relevance to coronal mass ejections. It differs from previous models because eruption is triggered solely by the converging motion of two photospheric field sources that lie below the coronal flux rope. Because this boundary condition is much simpler than that used in previous formulations, this particular version of the model is especially well-suited for two-dimensional numerical simulations with translational symmetry. Title: Book Review: Solar surface magnetism / Kluwer, 1994 Authors: Priest, E. Bibcode: 1995Obs...115..103P Altcode: 1995Obs...115..103R No abstract at ADS Title: Turbulent coronal heating. II. Twisted flux tube. Authors: Inverarity, G. W.; Priest, E. R. Bibcode: 1995A&A...296..395I Altcode: Inverarity et al. extended the model of Hevyaerts & Priest for turbulent coronal heating in a sheared arcade, again achieving the observed levels of heating but with improved mathematical consistency. A similar model for heating in a flux tube twisted by vortical photospheric motions is here developed. Two models for the turbulence are investigated: three-dimensional, helically isotropic turbulence and two-dimensional turbulence, isotropic in the plane perpendicular to the background field. It is found that the three-dimensional turbulence model can reproduce the observed levels of coronal heating. However, the purely two-dimensional model cannot be used when modelling steady-state heating. Title: On the Nature of 3D Reconnection Authors: Priest, E. R. Bibcode: 1995LNP...462..303P Altcode: 1995ssst.conf..303P In two dimensions the theory of magnetic reconnection is now highly developed and fairly well understood. A general configuration will contain X-type neutral points and separatrix field lines which link to it. Reconnection occurs by the breaking and rejoining of field lines at the X-point and the transfer of flux across the separatrices from one topological region to another. Title: Current sheet configurations in potential and force-free fields. Authors: Bungey, T. N.; Priest, E. R. Bibcode: 1995A&A...293..215B Altcode: Using complex variables and the method of conformal mappings, an analytical expression is produced for the possible configurations of constant-current, force-free or magnetostatic magnetic fields in the neighbourhood of a linear current sheet. The configurations obtained include the well-known potential solutions of Green and Syrovatskii as special cases. New potential and force-free solutions possess asymmetry along the current sheet and a closing over of the field lines for the force-free case. Title: A converging flux model for the formation of an X-ray bright point above a supergranule cell Authors: Parnell, C. E.; Priest, E. R. Bibcode: 1995GApFD..80..255P Altcode: The many complex regions of positive and negative flux that thread the surface of the Sun are mainly grouped around the edges of supergranule cells. These cells have large concentrations of magnetic flux on their boundaries and very little flux inside, with the magnetic fragments that appear in the centre of the cells swept to the boundaries by convective motions. Thus, a small bipolar pair of magnetic fragments (such as an ephemeral region) emerges inside a cell and moves towards the cell boundary as it grows. On reaching the boundary the fragments encounter unipolar regions of network flux with which they may merge or cancel. When cancellation takes place there is often an associated X-ray bright point in the overlying corona. Here, the emergence and interaction of an ephemeral region in a quiet-region or active-region super-granule cell is considered. It is found that there are three possible scenarios for the evolution of an ephemeral region in a supergranule cell and these are all investigated. The magnetic fields for the supergranule cell and ephemeral region are modelled by finite sources of flux and are studied as the ephemeral region moves through a series of quasi-static states. It is found that the ratio of the cancelling fragment widths (strengths) is important in determining the lifetime and path of the bright point, while the actual sizes of the fragments is important for determining the intensity of the bright point, the lifetime of the cancelling magnetic feature and the relative times of the bright point completion and cancelling magnetic feature onset. From this we suggest that transient brightenings in active regions and bright points on the quiet Sun may both be created by the converging flux mechanism detailed here. Title: Turbulent coronal heating. I. Sheared arcade. Authors: Inverarity, G. W.; Priest, E. R.; Heyvaerts, J. Bibcode: 1995A&A...293..913I Altcode: The model of Heyvaerts & Priest for heating the solar corona by turbulent processes in a sheared arcade is examined in more detail by numerically solving their basic equations for the turbulent viscosity, magnetic diffusivity, velocity and energy flux density. A weighted spectrum for the mean square velocity in the photosphere and a scale-dependent turbulent viscosity and magnetic diffusivity for local eddy relaxation are introduced which improve the self-consistency of the model. Estimates are made of the turbulent variables listed above which are found to accord well with the requirements for heating a solar active region (=~10^7^erg/cm^2^/s). Title: Magnetic Reconnection in the Sun's Atmosphere Authors: Priest, E. R. Bibcode: 1995fras.conf..191P Altcode: No abstract at ADS Title: Solar Flares Authors: Priest, Eric R. Bibcode: 1995LNP...454....3P Altcode: 1995flfl.conf....3P; 1995IAUCo.151....3P; 1995LNP...454....1P There are many types of solar flare, but the classic type is a two-ribbon flare with three phases — a preflare phase, a rise phase and a main phase. The properties of these phases are described, together with some recent observational advances in understanding the conditions for solar flares. Such flares are thought to be caused by an eruptive MHD instability which drives reconnection and therefore energy conversion. A review is given of our current understanding of the nature of this instability and the resulting reconnection process, including a recent attempt to describe its three-dimensional nature. Title: Thermal equilibria in solar coronal magnetic loops: gravitational considerations. Authors: Steele, C. D. C.; Priest, E. R. Bibcode: 1994A&A...292..291S Altcode: Equations for thermal equilibria along coronal magnetic loops (with constant cross-sectional area) are solved in the absence and the presence of gravity. When the effect of gravity is negligible, loops may exist with cool summits; these loops consist of two portions, an isothermal portion at the summit and a non-isothermal portion near the footpoint. In the presence of gravity, the two-component structure no longer exists and there is a restriction (dependent on the heating) on the lengths of loops with cool summits. Loops with hot summits are cooled slightly by the incorporation of gravity. A model of a cylindrical arcade is set up where the heating and the magnetic field vary with position. Hot arcades exist as do arcades with a vertical cool sheet surrounded by hotter plasma - a situation that occurs for a prominence. It is anticipated that loops with cool summits may exist for higher values of gravity when the loop area is allowed to vary with position. Title: Book-Review - Solar Magnetic Fields Authors: Schussler, M.; Schmidt, W.; Priest, E. R. Bibcode: 1994Ap&SS.222..266S Altcode: No abstract at ADS Title: Book reviews Authors: Burgess, D.; Kahn, F. D.; Dyson, John; Roche, Patrick; Priest, E. R.; Budding, Edwin; Keenan, F. P. Bibcode: 1994Ap&SS.222..263B Altcode: No abstract at ADS Title: Steady linear X-point magnetic reconnection Authors: Priest, E. R.; Titov, V. S.; Vekestein, G. E.; Rikard, G. J. Bibcode: 1994JGR....9921467P Altcode: In the main part of this paper a model for linear reconnection is developed with a current spike around the X-point and vortex current sheets along the separatrices, which are resolved by the effects of viscosity and magnetic diffusivity. The model contains three regions. In the external ideal region, diffusion effects are negligible, and the flow is purely radial but becomes singular both along the separatrices and at the X-point. Near the separatrix there is a self-similar boundary layer with strong electric current and vorticity, where resistivity and viscosity resolve the singularity and allow the flow to cross the separatrix. A composit solution is set up that matches the external and separatrix solutions. Near the origin diffusion also resolves the singularity and is described approximately by a biharmonic solution. A classification of steady two-dimensional reconnection regimes is proposed into viscous reconnection (Me greater than Re,) extra slow (linear) reconnection (Me less than Rme-1), slow reconnection (Rme-1/2 Me less than or = Rme-1/2), and fast reconnection (Rme-1/2 less than Me is the dimensionless reconnection rate, Rme the magnetic Reynolds number, and Re the Reynolds number, all based on the Alfven speed far from the reconnection point. Also, an anti-reconnection theorem is proved, which has profound effects on the nature of linear reconnection. It states that steady two-dimensional magnetohydrodynamcis (MHD) reconnection with plasma flow across the separatrices is impossible in a plasma which is inviscid, highly sub-Alfvenic, and has uniform magnetic diffusivity. Title: Coronal magnetic field evolution under reconnective relaxation Authors: Vekstein, G. E.; Priest, E. R.; Wolfson, R. Bibcode: 1994SSRv...70..303V Altcode: The nonlinear evolution of a partially open coronal magnetic configuration is considered, assuming that corona responds to photospheric footpoint motions by small-scale reconnection events that produce a relaxed lower-energy state while conserving the global magnetic helicity of the system. The results of numerical calculations for such a relaxed equilibrium show an essential role of the amount of helicity injected to the closed-field region. If photospheric perturbations are incoherent (small-scale shearing with inefficient helicity injection), the relaxed state becomes close to an initial potential field. In this case reconnective relaxation does not result in a substantial global evolution, just providing heating of the corona (Vekstein et al, 1993). On the contrary, sufficient injection of the magnetic helicity can lead to a considerable restructuring of the coronal magnetic configuration, with possible change of its topology (formation of magnetic islands), and even catastrophic loss of equilibrium (Wolfson et al, 1994) Title: Working group 2: Loops and prominences Authors: Priest, E. R. Bibcode: 1994SSRv...70..221P Altcode: No abstract at ADS Title: A Model for X-Ray Bright Points due to Unequal Cancelling Flux Sources Authors: Parnell, C. E.; Priest, Eric R.; Titov, V. S. Bibcode: 1994SoPh..153..217P Altcode: A recent discovery from the Big Bear Solar Observatory has linked the cancellation of opposite polarity magnetic fragments in the photosphere (i.e., so-called cancelling magnetic features) to X-ray bright points and has stimulated the setting up of a converging flux model for the process. Cancelling magnetic features can occur between magnetic fragments of differing strengths in many different situations. Here, therefore, we model two opposite polarity fragments of different strengths in the photosphere by two unequal sources in an overlying uniform field. Initially in thepre-interaction phase these sources are assumed to be unconnected, but as they move closer together theinteraction phase starts with an X-type neutral point forming, initially on the photosphere, then rising up into the chromosphere and corona before lowering back down to the photosphere. Thecapture phase then follows with the sources fully connected as they move together. Finally, after they come in to contact, during thecancellation phase the weaker source is cancelled by part of the stronger source. The height of the X-type neutral point varies with the separation of the sources and the ratio of the source strengths, as do the positions of the neutral points before connection and after complete reconnection of the two sources. The neutral point is the location of magnetic reconnection and therefore energy release which is believed to power the X-ray bright point in the corona. By using a current sheet approximation, where it is assumed no reconnection takes place as the two sources move together, the total amount of energy released during reconnection may be estimated. The typical total free magnetic energy is found to be of the order of 1020-1021 J, which is as required for an X-ray bright point. It is also found that, as the ratio of the source strengths increases, the height of the X-type neutral point decreases, as do the total energy released, and the lifetime of the bright point. Title: Preflare State Authors: Rust, David M.; Sakurai, Takashi; Gaizauskas, Victor; Hofmann, Axel; Martin, Sara F.; Priest, Eric R.; Wang, Jing-Xiu Bibcode: 1994SoPh..153....1R Altcode: Discussion on the preflare state held at the Ottawa Flares 22 Workshop focused on the interpretation of solar magnetograms and of Hα filament activity. Magnetograms from several observatories provided evidence of significant build up of electric currents in flaring regions. Images of X-ray emitting structures provided a clear example of magnetic relaxation in the course of a flare. Emerging and cancelling magnetic fields appear to be important for triggering flares and for the formation of filaments, which are associated with eruptive flares. Filaments may become unstable by the build up of electric current helicity. Examples of heliform eruptive filaments were presented at the Workshop. Theoretical models linking filaments and flares are briefly reviewed. Title: Energy Release in Solar Flares Authors: Brown, John C.; Correia, Emilia; Farnik, Frantisek; Garcia, Howard; Henoux, Jean-Claude; Larosa, Ted N.; Machado, Marcos E.; Nakajima, Hiroshi; Priest, Eric R. Bibcode: 1994SoPh..153...19B Altcode: Team 2 of the Ottawa FLARES 22 Workshop dealt with observational and theoretical aspects of the characteristics and processes of energy release in flares. Main results summarized in this article stress the global character of the flaring phenomenon in active regions, the importance of discontinuities in magnetic connectivity, the role of field-aligned currents in free energy storage, and the fragmentation of energy release in time and space. Title: Dynamic Coronal Heating by Magnetic Flux Interaction Authors: Priest, E. R. Bibcode: 1994kofu.symp...93P Altcode: The elements of a Converging Flux Model for heating X-ray bright points are here put forward which also accounts for the cancelling magnetic features that are usually observed to be present in the photosphere below bright points and the jets that are observed with Yohkoh. The model has three phases: a preinteraction phase in which two opposite polarity photospheric fragments are unconnected magnetically; an interaction phase when the fragments reconnect in the corona and create the bright point and x-ray jet; a cancellation phase when reconnection in the photosphere produces the cancelling magnetic feature. An analytical model is presented together with preliminary results of a numerical experiment and a three-dimensional modelling of particular bright points observed by the NIXT telescope. Furthermore, dynamic reconnection driven by footpoint motions in a bright point may represent an elementary heating event that could be heating coronal loops and coronal holes and not just bright points. Title: Nonlinear Evolution of the Coronal Magnetic Field under Reconnective Relaxation Authors: Wolfson, R.; Vekstein, G. E.; Priest, E. R. Bibcode: 1994ApJ...428..345W Altcode: Recently, Vekstein et al. (Vekstein, Priest, & Steele 1993) have developed a model for coronal heating in which the corona responds to photospheric footpoint motions by small-scale reconnection events that bring about a relaxed state while conserving magnetic helicity but not field-line connectivity. Vekstein et al. consider a partially open field configuration in which magnetic helicity is ejected to infinity on open field lines but retained in the closed-field region. Under this scheme, they describe the evolution of an initially potential field, in response to helicity injection, in the linear regime. The present work uses numerical calculations to extend the model of Vekstein et al. into the fully nonlinear regime. The results show a rise and bulging of the field lines of the closed-field region with increasing magnetic helicity, to a point where further solutions are impossible. We interpret these solution-sequence endpoints as indicating a possible loss of equilibrium, in the sense that a relaxed equilibrium state may no longer be available to the corona when sufficient helicity has been injected. The rise and bulging behavior is reminiscent of what is observed in a helmet streamer just before the start of a coronal mass ejection (CME), and so our model suggests that a catastrophic loss of magnetic equilibrium might be the initiation mechanism for CMEs. We also find that some choices of boundary conditions can result in qualitative changes in the magnetic topology, with the appearance of magnetic islands. Whether or not this behavior occurs depends on the relative strengths of the fields in the closed- and open-field regions; in particular, island formation is most likely when the open field (which is potential) is strong and thus acts to confine the force-free closed field. Finally, we show that the energy released through reconnective relaxation can be a substantial fraction of the magnetic energy injected into the corona through footpoint motions and may be sufficient for heating the corona above active regions. Title: A Converging Flux Model of an X-Ray Bright Point and an Associated Canceling Magnetic Feature Authors: Priest, E. R.; Parnell, C. E.; Martin, S. F. Bibcode: 1994ApJ...427..459P Altcode: X-ray bright points are an important part of the solar corona and therefore of the coronal heating problem. When it was first realized that bright points are always situated above opposite polarity magnetic fragments in the photosphere, it was natural to suggest that such fragments represent emerging flux and that an X-ray bright point is caused by reconnection of the emerging flux with an overlying coronal magnetic field. However, a recent important discovery at the Big Bear Solar Observatory is that the magnetic fragments of opposite polarity are usually not emerging but are instead coming together and disappearing and so are referred to as canceling magnetic features. Sometimes a tiny filament is observed to form and erupt at the same time. A unified model is here proposed which explains these observational features and has several phases: (1) a preinteraction phase, in which two photospheric fragments are unconnected magnetically and begin to approach one another, until eventually oppositely directed fields from the fragments come into contact at a second-order null point; (2) an interaction phase, in which the null point becomes an X-point and rises into the corona; an X-ray bright point is created for typically 8 hr by coronal reconnection, driven by the continued approach of the photospheric sources; long hot loops and Yohkoh X-ray jets may be created by the reconnection, and rapid variability in bright point emission may be produced by an impulsive burst regime of reconnection; the explosive events seen with High Resolution Telescope and Spectrograph (HRTS) may be produced as the X-point passes through the upper chromosphere; (3) a cancellation phase, in which a canceling magnetic feature is produced by photospheric reconnection as the fragments come into contact and decrease in strength; above the canceling fragments a small filament may form and erupt over typically an hour. An important role is played by the interaction distance (d), which is proportional to the magnetic flux of the fragments and inversely proportional to the overlying magnetic field strength. It determines the fragment separation at which the interaction phase begins and the resulting maximum height of the reconnection point. It is suggested that coronal reconnection driven by footpoint motion represents an elementary heating event that may be heating normal coronal loops and may be at the root of the nanoflare/microflare process. Bright points may well be at the large-scale end of a broad spectrum of events of the type modeled in this paper, which are heating the solar corona. At very small scales, such events in 'furnaces' in the coronal hole network may even produce high-frequency waves that propagate out and drive the solar wind (Axford 1993). Title: Magnetic Energy Dissipation via Reconnective Relaxation in Astrophysical Jets Authors: Vekstein, G. E.; Priest, E. R.; Steele, D. C. Bibcode: 1994ApJS...92..111V Altcode: The magnetic energy release through field-line reconnection is considered for a force-free jet which expands (or contracts) radially in response to variations in the confining external pressure. The main new result obtained in comparison with previous publications on the subject, where this mechanism has been proposed, is that a self-consistent theory for the reconnective relaxation of the jet's magnetic configuration has been constructed. It enables us to calculate the magnetic energy dissipation rate inside a jet for an arbitrary value of the ratio T_r_/Tnu_ where T_r_ is a typical reconnection time and Tnu_, is the expansion time. Thus these results provide a well-grounded support to the conclusion that this magnetic energy dissipation mechanism could, in principle, power the observed radio emission in extragalactic jets. Moreover, knowing the observed radiation power (and, hence, the required energy supply) it is possible to obtain information about the value of T_r_, which enters in the theory as a phenomenological parameter. Title: The Three-Dimensional Structures of X-Ray Bright Points Authors: Parnell, C. E.; Priest, E. R.; Golub, L. Bibcode: 1994SoPh..151...57P Altcode: Recently, the Converging Flux Model has been proposed for X-ray bright points and cancelling magnetic features. The aim of this peice of work is to try and model theoretically specific X-ray bright points in the framework of the Converging Flux Model. The observational data used includes a magnetogram showing the normal component of the magnetic field at the photosphere and a high-resolution soft X-ray image from NIXT showing the brightenings in the lower solar corona. By approximating the flux concentrations in the magnetograms with poles of the appropriate sign and sense, the overlying three-dimensional potential field structure is calculated. Deduction of plausible motions of the flux sources are made which produce brightenings of the observed shape due to reconnection between neighbouring flux regions. Also the three-dimensional separarix and separator structure and the way the magnetic field lines reconnect in three dimensions is deduced. Title: The Dynamics of Driven Magnetic Reconnection in Coronal Arcades Authors: Rickard, G. J.; Priest, E. R. Bibcode: 1994SoPh..151..107R Altcode: The dynamics of interacting coronal loops and arcades have recently been highlighted by observations from theYohkoh satellite and may represent a viable mechanism for heating the solar corona. Here such an interaction is studied using two-dimensional resistive magnetohydrodynamic (MHD) simulations. Initial potential field structures evolve in response to imposed photospheric flows. In addition to the anticipated current sheet about theX-point separating the colliding flux systems, significant current layers are found to lie all the way along the separatrices that intersect at theX-point and divide the coronal magnetic field into topologically distinct regions. Shear flows across the separatrices are also observed. Both of these features are shown to be compatible with recent analytical studies of two-dimensional linear steady-state magnetic reconnection, even though the driven system that has been simulated is not strictly `open' in the sense implied by steady-state calculations. The implications for future steady-state models are also discussed. The presence of the neutral point also brings into question any constant-density approximations that have previously been used for such quasi-steady coronal evolution models. This results from the intimate coupling between the neutral point and its separatrices communicated via the gas pressure. Title: On the Maximum Energy Release in Flux Rope Models of Eruptive Flares Authors: Forbes, T. G.; Priest, E. R.; Isenberg, P. A. Bibcode: 1994SoPh..150..245F Altcode: We determine the photospheric boundary conditions which maximize the magnetic energy released by a loss of ideal-MHD equilibrium in two-dimensional flux-rope models. In these models a loss of equilibrium causes a transition of the flux rope to a lower magnetic energy state at a higher altitude. During the transition a vertical current sheet forms below the flux rope, and reconnection in this current sheet releases additional energy. Here we compute how much energy is released by the loss of equilibrium relative to the total energy release. When the flux-rope radius is small compared to its height, it is possible to obtain general solutions of the Grad-Shafranov equation for a wide range of boundary conditions. Variational principles can then be used to find the particular boundary condition which maximizes the magnetic energy released for a given class of conditions. We apply this procedure to a class of models known as cusp-type catastrophes, and we find that the maximum energy released by the loss of equilibrium is 20.8% of the total energy release for any model in this class. If the additional restriction is imposed that the photospheric magnetic field forms a simple arcade in the absence of coronal currents, then the maximum energy release reduces to 8.6%. Title: General family of nonuniform reconnection models with separatrix jets Authors: Strachan, N. R.; Priest, E. R. Bibcode: 1994GApFD..74..245S Altcode: The Nonuniform Magnetic Reconnection model presented by Priest and Lee (1990) was the first to incorporate several features observed in previous numerical models, in particular the highly curved field in the inflow region, which relaxes one of the key assumptions of the classical Almost-Uniform reconnection model of Petschek (1964). Also present is a strong jet of plasma emerging from the reconnection region along the separatrix and a negative current spike at the outflow from the central diffusion region. In this paper we present a generalization of the Priest-Lee model to include pressure gradients in the inflow region, so relaxing the other main assumption of the Petschek and Priest-Lee models, namely that the inflow is current-free or potential. This produces several reconnection regimes similar to those described by Priest and Forbes (1986) in their Unified Almost-Uniform solutions, where significant pressure gradients are included, but their inflow, like Petschek's, is almost-uniform with slightly curved field lines. We investigate the behaviour of the inflow magnetic field without linearizing about a uniform field. We study both a shockless, incompressible outflow and one containing weak shocks, where the type of reconnection is dictated by both the inflow and outflow boundary conditions. In order to introduce a pressure gradient into the Priest-Lee model an extra non-potential field in the x-direction is added. This field has a uniform current and does not alter the Y-point nature of the neutral points at the ends of the diffusion region but does alter the position of the separatrix, where the flow becomes singular, and hence the position of the Alfvenic discontinuity and the strength of the plasma jet. The maximum reconnection rate given by the model scales as (1 + c)(exp 3/2)R(sub me)(exp -1/2), where the parameter c is a measure of the current and is such that c greater than 0 gives fast- or slow-mode expansions and c less than 0 gives slow-mode compressions. These regimes are also found in the Unified Almost-Uniform model. Fast reconnection with a reconnection rate in excess of the pure Sweet-Parker scaling is therefore possible in the flux pile-up regimes with c greater than 0. For a given large magnetic Reynolds number, a fast reconnection rate of, say, 0.1 times the Alfven speed is possible provided c is large enough (e.g. c greater than 10 for R(sub me) = 10(exp 5)). Title: Magnetic Coronal Heating and Global Restructuring of the Coronal Magnetic Field by Reconnective Relaxation Authors: Vekstein, G.; Priest, E.; Steele, C.; Wolfson, R. Bibcode: 1994ASPC...68..194V Altcode: 1994sare.conf..194V No abstract at ADS Title: Book-Review - Advances in Solar System Magnetohydrodynamics Authors: Priest, E. R.; Hood, A. W.; Burlaga, L. F. Bibcode: 1994SSRv...67..225P Altcode: No abstract at ADS Title: Magnetohydrodynamics (With 87 figures) Authors: Priest, Eric R. Bibcode: 1994plas.conf....1P Altcode: 1994SAAS...24....1P Prelude The Sun Brief History Overall Properties The Atmosphere Solar Activity The Solar Revolution Magnetohydrodynamic Equations Flux Tubes Fundamental Equations Induction Equation The Lorentz Force Concluding Comment Magnetohydrostatics Introduction Potential Fields Force-Free Fields Magnetic Flux Tubes Magnetohydrodynamic Waves Sound Waves Alfven Waves Compressional Alfven Waves Magnetoacoustic Waves Effect of Magnetic Diffusion on Alfven Waves Shock Waves The Solar Wind Introduction Parker Solution Effect of the Magnetic Field Magnetic Reconnection Introduction Magnetic Annihilation (Sonnerup and Priest, 1975) Qualitative Effects of Reconnection Formation of a Current Sheet Linear Reconnection Fast Steady-State Reconnection Coronal Heating Introduction Magnetically Open Regions - Heating by Magnetic Waves Magnetically Closed Regions - Heating by Current Sheets Self-Consistent Model for Heating by MHD Turbulence Conclusion Prominences Observations Formation of a Prominence Internal Structure External Structure A Flux Tube Model Conclusion Solar Flares Introduction Energy Release by Magnetic Reconnection Conditions for Flare Occurrence Conclusion References Title: A Model of an X-Ray Bright Point Authors: Parnell, C. E.; Priest, E. R. Bibcode: 1994swms.conf....1P Altcode: No abstract at ADS Title: Solar Coronal Heating by Magnetic Flux Interaction Authors: Priest, E. R.; Parnell, C. E.; Rickard, G. J. Bibcode: 1994ASIC..422...11P Altcode: 1994coma.conf...11P No abstract at ADS Title: Plasma Astrophysics Authors: Kirk, J. G.; Melrose, D. B.; Priest, E. R.; Benz, A. O.; Courvoisier, T. J. -L. Bibcode: 1994plas.conf.....K Altcode: 1994QB462.7.K57....; 1994plas.conf.....B This volume presents the lecture notes of the 24th Advanced Course of the Swiss Society for Astrophysics and Astronomy in March 1994 at Les Diablerets. In three lectures on magnetohydrodynamics, on kinetic plasma physics and on particle acceleration leading experts describe the physical basis of their subjects and extend the discussion to several applications in modern problems of astrophysics. In style and presentation the texts are well-suited for graduate work in plasma astrophysics, one of the very important tools of modern astronomy. The themes developed in this book will be helpful in understanding many processes in the universe from the solar corona to active galaxies. Title: Motions of Loops and Ribbons of Two-Ribbon Flares Authors: Lin, J.; Forbes, T. G.; Priest, E. R. Bibcode: 1994ASPC...68..202L Altcode: 1994sare.conf..202L No abstract at ADS Title: Heating of X-ray bright points and other coronal structures. Authors: Priest, E. R. Bibcode: 1994GMS....84....1P Altcode: A brief summary is given of the observations of X-ray bright points in the solar corona and of their relation to cancelling magnetic features in the underlying photosphere. A new Converging Flux Model for bright points is proposed with three phases. In the Preinteraction Phase photospheric magnetic fragments of opposite polarity are unconnected and approach one another. In the Interaction Phase the X-ray bright points is created by coronal reconnection. Finally, in the Cancellation Phase the cancelling magnetic feature is produced by photospheric reconnection. It is suggested that coronal reconnection driven by footpoint motions may represent an elementary heating event that is heating all coronal loops and not just bright points. Title: Aspects of Filament Evolution Authors: Dumitrache, C.; Dinulescu, S.; Priest, E. R. Bibcode: 1994emsp.conf...65D Altcode: No abstract at ADS Title: A Comparison of Theories and Numerical Experiments on Fast Steady-State Reconnection Authors: Priest, E. R. Bibcode: 1994swms.conf...93P Altcode: No abstract at ADS Title: The Propagation of Sound Waves in a Randomly Magnetized Medium. II. The Interaction of an Unsteady Wave Packet with an Ensemble of Magnetic Flux Tubes Authors: Ryutova, M. P.; Priest, E. R. Bibcode: 1993ApJ...419..371R Altcode: The interaction of an unsteady wave packet of acoustic waves with plasma containing ensembles of random magnetic flux tubes and the physical mechanisms of energy transfer to the plasma are described. It is shown that the propagation of an acoustic wave-packet in the randomly magnetized solar atmosphere is accompanied by clear morphological effects which include the spreading of the energy absorption region over scales much larger than the size of the initial wave packet, and which, in principle, can be observed. The regions of an efficient energy input and their localization crucially depend on the distribution of magnetic flux tubes in space and over their physical parameters (including noncollinearity). The very existence of these effects is determined by the fact that the solar atmosphere is randomly magnetized, and magnetic flux tubes are essentially nonidentical. The results may be useful for the diagnostics of the visible layers of the solar atmosphere and magnetic helioseismology. Title: The Propagation of Sound Waves in a Randomly Magnetized Medium. I. General Considerations Authors: Ryutova, M. P.; Priest, E. R. Bibcode: 1993ApJ...419..349R Altcode: We study the time-dependent response of a randomly magnetized medium (such as the solar atmosphere) to the propagation of acoustic waves, including energy transfer to the medium due to different physical processes. It is shown that the details of the interaction of a sound wave with an ensemble of magnetic flux tubes, and, in particular, the maximum energy input, crucially depends on the magnetic filling factor of the medium as well as on the distribution of the random tubes in space. The interaction of acoustic waves and unsteady wave packets with an ensemble of magnetic flux tubes reveals some simple and important features, which, in principle, are observable. A most important role in these effects is played by resonant interaction both absorption and scattering of the sound wave by flux tubes. We focus on the case when the incident wavelength (λ) is much larger than the separation (d) between tubes, which is in turn much larger than the tube radii (R).

In the case of resonant absorption (an effect similar to Landau damping in the collisionless plasma) the energy of the incident acoustic wave is accumulated in the system of magnetic flux tubes and causes the acoustic wave (of frequency ω) to damp at a rate νL ∼ (R2/d2)ω. The energy remains for a long time in the form of flux-tube oscillations. Then, in a time ν-1rad which is much longer than the damping time of the sound wave, the resonant flux tubes radiate their energy as secondary acoustic (or MHD) waves, where νrad ∼ ωk2R2. The incident acoustic wave can also be resonantly scattered with the main contribution coming from the kink mode; it leads to a linear frequency shift and to the appearance of incoherent noise without a preliminary build up of wave energy in flux-tube oscillations. When the distribution of flux-tube natural frequencies is broader than νL the Landau-like resonant absorption process is more important than resonant scattering, but when the distribution is narrow the tubes are essentially identical and resonant absorption is generally absent so that resonant scattering dominates. A nonlinear analysis allows us to find the maximum energy input and the frequency shift and their dependence on the parameters of medium. Also, a detailed treatment is given of Landau-like damping due to excitation of sausage modes. Title: Time-dependent magnetic annihilation at a stagnation point Authors: Anderson, C.; Priest, E. R. Bibcode: 1993JGR....9819395A Altcode: Magnetic reconnection is a funcamental process that can take place in astrophysical or laboratory plasmas. It occurs within regions of large magnetic gradients where the magnetic field is no longer frozen to the plasma but instead diffuses through it, releasing magnetic energy and causing a change in the connectivity of the field lines. In particular, on the Sun, magnetic reconnection is believed to play an important role in coronal heating, X ray bright points, solar flares and cancelling magnetic features. Here, an exact time-dependent solution of the MHD equations for magnetic annihilation in response to a time-varying stagnation point flow is presented. The main assumptions in this model are that the magnetic field lines are straight (so that there is no magnetic tension acting on the plasma) and the flow that carries the field lines together is of stagnation point type. This a reasonable model for the resistive MHD behavior near the X point of a reconnecting field, especially when the central diffusion region is long, as in the flux pile up regime (Priest and Forbes 1986). The general solution is used to conduct a series of numerical experiments, namely, the evolution of different initial magnetic profiles in a steady flow; the effect of a sudden change in magnetic diffusivity on an initially steady state; the effects of a velocity that either increases linearly in time or ramps up from one steady value to another. The results exhibit the effects of subtle imbalances in diffusion and advection but have the following general features: (1) a diffusion layer is created, the thickness of which is determined by the nature of the plasma flow; (2) the magnetic field outside the diffusion region is determined by advection and will either exponentially increase, exponentially decay or remain in a steady state, depending on whether the initial magnetic profile By varies as y-n has n less than 1, n greater than 1, or n = 1, respectively; and (3) the magnetic field within the diffusion layer tends to respond to the advected magnetic field at its edge. Title: On the Problem of Magnetic Coronal Heating by Turbulent Relaxation Authors: Vekstein, G. E.; Priest, E. R.; Steele, C. D. C. Bibcode: 1993ApJ...417..781V Altcode: Three developments in the basic theory for heating the solar corona by Taylor-Heyvaerts relaxation are presented. First of all, a general expression is derived for coronal heating in response to small footpoint motions by intermediate relaxation to a state that lies between the ideal MHD state and the lowest energy linear force-free field. It depends on the ratio (ωτr) of the relaxation time (τr) to the timescale (ω-1) for footpoint motions: when this is much smaller than unity, there is complete relaxation to the linear force-free state, and when it is much larger the deviation from the ideal state is small but it is in practice still sufficient to provide the observed heating.

Second, a well-known difficulty with linear force-free fields, namely, that in a semi-infinite region such fields have infinite energy, is resolved: it is shown that the only possible relaxed state is a potential field, so that any excess magnetic helicity is ejected to infinity. Third, it is suggested that in practice the solar corona may be in a state not of complete relaxation but of partial relaxation, in which open fields continually relax to a potential state and eject magnetic helicity into the solar wind, while closed fields relax to a linear force-free state by means of small-scale reconnections. Title: Conditions for the appearance of "bald patches" at the solar surface Authors: Titov, V. S.; Priest, E. R.; Demoulin, P. Bibcode: 1993A&A...276..564T Altcode: A general criterion for the existence of sections of the photospheric polarity inversion line where the overlying magnetic field lines are parallel to the photosphere is presented. It is shown that such sections, called "bald patches", exist for a wide range of parameters in potential and constant-α force-free fields created by four concentrated sources of magnetic flux. Bald patches appear when the polarity inversion line is bent too much in an S-like manner. The appearance of bald patches may be important for the formation of prominences and possibly for solar flares. Title: MHD equilibria with flows in unifrom gravity. II. A class of exact 2-D loop-like solutions. Authors: Tsinganos, K.; Surlantzis, G.; Priest, E. R. Bibcode: 1993A&A...275..613T Altcode: We present a novel class of two-dimensional MHD equilibria which emerge as exact solutions of the coupled transfield and Bernoulli nonlinear equations governing the dynamics of steady flows along magnetic lines in an atmosphere that is horizontally compressible and vertically stratified in the presence of a uniform gravitational field. The topology of the solutions is analysed in detail and is found to be controlled by a classical sonic and a novel X-type critical point corresponding to a new characteristic speed for MHD wave propagation in an inhomogeneous medium. A subclass of low Alfvén numbers loop-like solutions is found for a mildly stratified atmosphere; for very strong stratification no solutions exist while for moderate stratification only periodic solutions are allowed. The results of the study are compared with those of models without flows and models with low Alfvén number flows while the approach followed here extends that of treating the flux tube as rigid, or slender. Among our conclusions is that an increase of the magnitude of the flow speed increases the height of the loops, while for stronger flows there are no equilibrium solutions and it is conjectured that the loop is disrupted. Thus, the general trends emerging from this analysis may be contrasted with solar observations wherein, for example, some solar loops extend over heights much higher than those predicted by models without flows. Then, in the quiet Sun and in chromospheric or coronal loops with plasma-β and Alfvén number not much smaller than unity, the above nonlinear effects of the flows should be taken into account. Title: Prominence Support in Helical Coronal Fields Formed by Photospheric Motions Authors: Ridgway, C.; Priest, E. R. Bibcode: 1993SoPh..146..277R Altcode: We consider the effect of converging photospheric motions acting upon a sheared cylindrically-symmetric line-tied arcade. The motions drive a reconnection process whereby a helical structure is formed, in which cool, dense plasma may accumulate at the lowest points of the helical windings thus creating a prominence. Title: Magnetostatic Equilibria and Current Sheets in an Sheared Magnetic Field with an X-Point Authors: Vekstein, G.; Priest, E. R. Bibcode: 1993SoPh..146..119V Altcode: When a two-dimensional magnetic field containing X-points is sheared, in general current sheets appear all along the separatrices and the X-points are structurally unstable. Their splitting into pairs of cusp points near which the magnetic field is of self-similar form is suggested. Solutions both inside and outside the cusps are obtained and are matched together by the conditions of continuity of the flux function and continuity of magnetic pressure. Title: Oscillations of a Quiescent Solar Prominence Embedded in a Hot Corona Authors: Oliver, R.; Ballester, J. L.; Hood, A. W.; Priest, E. R. Bibcode: 1993ApJ...409..809O Altcode: The magneto-acoustic-gravity modes of vibration of a Kippenhahn-Schlueter prominence model, surrounded by an external medium representing the solar corona, are investigated. Modes which do not disappear when the coronal region is removed are called internal modes, while modes which do not disappear when the prominence is removed are called external modes. Three modes were found which could be labeled as either internal or external modes, since they do not disappear when either region is removed. The results of this study suggest that short-period oscillations in limb prominences may be caused by the fundamental and first harmonics of the internal magneto-acoustic-gravity slow and Alfven modes, while the reported long-period oscillations in limb prominences may be the result of the hybrid slow mode. Short-period oscillations lasting a few minutes and detected in filaments may be related to internal fast modes, while the hybrid fast mode causes vertical oscillations with periods of approximately 20 min. Title: Upper Limits for Impulsive Energy Release in Flux-Rope Models of Eruptive Flares Authors: Forbes, T. G.; Isenberg, P. A.; Priest, E. R. Bibcode: 1993BAAS...25.1198F Altcode: No abstract at ADS Title: Magnetohydrodynamic waves in a potential coronal arcade Authors: Oliver, R.; Ballester, J. L.; Hood, A. W.; Priest, E. R. Bibcode: 1993A&A...273..647O Altcode: An important result obtained from solar observations made in coronal emission lines has been to establish the existence of periodic oscillations or waves in the corona. These are detected, although not always simultaneously, in line intensity, line-width or Doppler velocity with oscillation periods of several minutes. For this reason, we have studied the magnetohydrodynamic modes of oscillation of a coronal potential arcade under different boundary conditions, solving the wave equations for different density profiles. Our results show that only the Alfvén and the fast mode exist in such a structure and that the slow mode is absent, because of the assumed low-β limit. The Alfvén mode produces a continuous spectrum of frequencies with periods which can vary from zero to infinity, depending on the assumed density profile. Due to the polarization direction of the plasma motions, these waves could in principle be detected in front-view observations of coronal arcades at the limb. Concerning the fast mode, we have obtained several diagnostic diagrams using different density profiles and boundary conditions. These diagrams would be useful for comparing the predicted and observed periods. However, the observational identification of fast modes could be harder since we would need lateral observations of the coronal arcades. Title: Magnetic reconnection with large separatrix angles Authors: Yan, M.; Lee, L. C.; Priest, E. R. Bibcode: 1993JGR....98.7593Y Altcode: A two-dimensional incompressible MHD simulation model is developed to study magnetic reconnection with large magnetic separatrix angles. It is found that the normal magnetic field on the inflow boundary plays an important role in determining the reconnection configuration. When the normal magnetic field on the inflow boundary is large, steady state reconnection with large magnetic separatrix angles is obtained. When the normal magnetic field is small, a localized resistivity is required to maintain the steady state Petschek-like reconnection configuration, which has small magnetic separatrix angles. Field-aligned plasma jets are observed when the normal magnetic field and magnetic Reynolds number Rm are large. The plasma jets are located slightly downstream of the magnetic separatrices and each plasma jet consists of two parts: (1) a slow-mode shock and (2) a fast-mode compressional structure. The length and width of the diffusion region depend on the values of Me, Rm, and the normal magnetic field on the inflow boundary. For a fixed normal inflow magnetic field the diffusion region becomes longer and thinner as Me becomes larger; the width of the diffusion region decreases with an increasing Rm, while the length of the diffusion region has a minimum value at about Rm=500. The length of the diffusion region increases with a decreasing normal magnetic field, while the width does not change remarkably. It is also found that the multiple X line bursty reconnection tends to occur with the development of tearing-mode instability in cases with a large Me, a large Rm, or a small normal magnetic field on the inflow boundary. Title: A Model for an Inverse Polarity Prominence Supported in a Dip of a Quadrupolar Region Authors: Demoulin, P.; Priest, E. R. Bibcode: 1993SoPh..144..283D Altcode: We investigate the formation and support of solar prominences in a quadrupolar magnetic configuration. The prominence is modeled as a current sheet with mass in equilibrium in a two-dimensional field. The model possesses an important property which is now thought to be necessary, namely that the prominence forms within the dip, rather than the dip being created by the prominence. Title: Book Review: Physical processes in solar flares / Kluwer, 1991 Authors: Priest, E. R. Bibcode: 1993SoPh..144..203P Altcode: 1993SoPh..144..203S No abstract at ADS Title: Book Review: Solar interior and atmosphere / U Arizona Press, 1991 Authors: Heinzel, P.; Priest, E. R.; Heinzel, P. Bibcode: 1993SoPh..144..203H Altcode: 1993SoPh..144..203C No abstract at ADS Title: Two-dimensional models for solar and stellar winds - Hydrodynamic effects Authors: Lima, J. J. G.; Priest, E. R. Bibcode: 1993A&A...268..641L Altcode: . A new family of solutions of the system of steady hydrodynamic equations describing the axisymmetric outflow originating from a rotating central object, surrounded by a compressible, non-polytropic and inviscid fluid, is deduced. The system is solved self-consistently without any explicit assumption on the form of the velocity field and density; the solutions result purely from the assumed set of equations, the boundary conditions and the assumption of separation of variables. The analysis gives three dimensionless parameters that control the degree of collimation of the outflow as well as the anisotropy of the density distribution. The solution reproduces in a natural way the presence of jets around the polar axis and of disks around the equator that are observed in many astrophysical objects. Title: On the nonlinear theory of the radiation-driven thermal instability of a magnetized plasma Authors: Meerson, B.; Priest, E. R.; Steele, C. D. C. Bibcode: 1993GApFD..71..243M Altcode: The nonlinear evolution of perturbations in a magnetized plasma subject to the radiation-driven thermal instability (RDTI) is investigated analytically in a simplified model. The perturbed plasma motions are assumed to be one-dimensional and perpendicular to the magnetic field. The intermediate- and long-wavelength limits of the RDTI are considered. In the former limit, the force balance sets in rapidly, on the magneto-acoustic time scale and we assume the total (thermal-magnetic) pressure remains constant. By transforming to Lagrangian variables, the problem is reduced to a single generalized reaction-diffusion equation, which is employed to analyze the two following stages of the RDTI. The first develops on the radiative time scale, when the heat conduction is insignificant, while the second usually occurs on a much longer, heat conduction-related time scale. For the first stage, a simple analytical solution is found, which describes the development of a strong plasma stratification (coexisting hot rarefied phase and cool dense phase) across the magnetic field. Slow erosion of the stratification in the form of almost uniform motion, collision and "annihilation" of the inter-phase boundaries generally occurs at the second stage. Title: The collapse of an X-type neutral point to form a reconnecting time-dependent current sheet Authors: Titov, Vyacheslav S.; Priest, Eric R. Bibcode: 1993GApFD..72..249T Altcode: A general method for solving the two-dimensional time-dependent ideal MHD equations is developed when the Alfven-Mach number is small and the Mach number large in comparison with unity. The method is applied to the problem of the time-dependent nonlinear collapse of an X-type neutral point. A current sheet is formed which grows in a self-similar manner. Title: MHD Waves in a Solar Prominence Authors: Oliver, R.; Ballester, J. L.; Hood, A. W.; Priest, E. R. Bibcode: 1993ASSL..183..191O Altcode: 1993pssc.symp..191O No abstract at ADS Title: Implications of Rapid Footpoint Motions of Photospheric Flux Tubes for Coronal Heating Authors: Choudhuri, Arnab R.; Auffret, Herve; Priest, Eric R. Bibcode: 1993SoPh..143...49C Altcode: Some recent observations at Pic-du-Midi (Mulleret al., 1992a) suggest that the photospheric footpoints of coronal magnetic field lines occasionally move rapidly with typical velocities of the order 3 km s−1 for about 3 or 4 min. We argue that such occasional rapid footpoint motions could have a profound impact on the heating of the quiet corona. Qualitative estimates indicate that these occasional rapid motions can account for the entire energy flux needed to heat the quiet corona. We therefore carry out a mathematical analysis to study in detail the response of a vertical thin flux tube to photospheric footpoint motions in terms of a superposition of linear kink modes for an isothermal atmosphere. We find the resulting total energy that is asymptotically injected into an isothermal atmosphere (i.e., an atmosphere without any back reflection). By using typical parameter values for fast and slow footpoint motions, we show that, even if the footpoints spend only 2.5% of the time undergoing rapid motions, still these rapid motions could be more efficient in transporting energy to the corona than the slow motions that take place most of the time. Title: Coronal Heating Mechanisms Authors: Priest, E. R. Bibcode: 1993ASSL..183..515P Altcode: 1993pssc.symp..515P No abstract at ADS Title: Unsteady Wave-Packet in the Random Ensemble of Magnetic Flux Tubes: Acoustic Halos Authors: Ryutova, M.; Priest, E. Bibcode: 1993ASPC...46..554R Altcode: 1993mvfs.conf..554R; 1993IAUCo.141..554R No abstract at ADS Title: Steady MHD Flows in Uniform Gravity Authors: Tsinganos, K.; Surlantzis, G.; Priest, E. P. Bibcode: 1993ASSL..183..623T Altcode: 1993pssc.symp..623T No abstract at ADS Title: Quiescent Solar Prominences: A Two-Dimensional Model Authors: Oliver, R.; Ballester, J. L.; Priest, E. R. Bibcode: 1993ASSL..183..187O Altcode: 1993pssc.symp..187O No abstract at ADS Title: Does fast magnetic reconnection exist? Authors: Priest, E. R.; Forbes, T. G. Bibcode: 1992JGR....9716757P Altcode: The classical Petschek model of fast, steady state reconnection has been generalized in two families of reconnection regimes. The first family, which we refer to as ``almost uniform,'' models the reconnection of nearly uniform, antiparallel magnetic fields, and it includes Petschek's model as a special case. The second family, which we refer to as nonuniform, models the reconnection of strongly curved magnetic fields, and it includes separatrix jets and reversed current spikes at the ends of the diffusion region. In general, both families contain regimes having fast reconnection rates, but we show here that these fast reconnection regimes do not occur when the boundary conditions often used in numerical experiments are adopted. In 1986, D. Biskamp carried out a series of numerical experiments to check Petschek's prediction that the maximum reconnection rate should scale with the magnetic Reynolds number, Rme, as [ln(Rme)]-1. Biskamp found that the maximum reconnection rate in his experiments did not scale in this way but instead as Rme-1/2. Because this corresponds to the scaling predicted by the slow reconnection theory of Sweet (1958) and Parker (1957), Biskamp has argued that his numerical experiments show that fast reconnection does not exist at high magnetic Reynolds numbers. However, by applying boundary conditions similar to Biskamp's to the ``nonuniform'' family of reconnection regimes, we are able to explain Biskamp's scaling results and to explain why he did not achieve fast reconnection in his numerical experiments. Therefore, we conclude that numerical experiments with suitably designed boundary conditions are highly likely to exhibit fast reconnection and that such reconnection is a common process in astrophysical and space plasmas. Title: Magnetohydrodynamic Waves in a Solar Prominence Authors: Oliver, R.; Ballester, J. L.; Hood, A. W.; Priest, E. R. Bibcode: 1992ApJ...400..369O Altcode: The presence of oscillations in solar prominences has been known for a long time, and at first they were thought to be initiated by shock waves emitted by a flare. However, short- and long-period oscillations, not related to flares, have been abundantly reported during recent years. In limb prominences they have been detected mainly in the velocity field, whereas in filaments they are hardly detected at all. In this paper we try to provide a theoretical explanation for these oscillations by investigating the magneto-acoustic-gravity modes of vibration of a Kippenhahn-Schlueter prominence model. First of all, we obtain the magneto-acoustic modes for a very thin prominence with horizontal magnetic field, and later we solve the full problem numerically. Our results suggest that short-period oscillations detected in limb prominences could be due to the fundamental and first harmonic of the magneto-acoustic-gravity slow modes of the prominence itself, while the long-period oscillations could be due to global oscillations of the whole surrounding arcade. Title: Thermal profiles of coronal loops - gravitational considerations. Authors: Steele, Colin D. C.; Priest, E. R. Bibcode: 1992ESASP.348..193S Altcode: 1992cscl.work..193S Equations of thermal equilibrium along coronal magnetic loops are solved in the absence and presence of gravity. Without gravity, four categories of loop are found - hot, cool, hot-cool and warm. Which categories exist depends on two parameters involving the heating, the loop length and the footpoint pressure. Including gravity, the longer hot loops suffer a decrease in their summit temperatures. The hot-cool loops are restricted to a very small range of lengths. A hot-cool arcade can still exist if either the coronal heating or the loop footpoint pressure varies. When the cross-sectional area does not vary from footpoint to summit, hot-cool loops may exist only for unrealistically low gravity. However, causing the cross-sectional area to vary may allow hot-cool loops to exist for realistic gravity. Title: Book-Review - Dynamics and Structure of Quiescent Solar Prominences Authors: Priest, E. R.; Sakurai, T. Bibcode: 1992SSRv...61..430P Altcode: No abstract at ADS Title: Solar coronal magnetic structure. Authors: Priest, E. R. Bibcode: 1992ESASP.346...13P Altcode: 1992ssts.rept...13P The solar corona has a four-fold structure of coronal loops, coronal holes, X-ray bright points and prominences, which evolve usually slowly but often dramatically in response to photospheric footpoint motions and which are dominated by the magnetic field. A brief review is given of recent developments in the theory for heating the corona including a self-consistent MHD turbulence mechanism and new ways of creating current sheets by shearing force-free fields or collapsing X-points. Prominences may be formed in huge flux tubes in response to flux cancellations at the photosphere, and flares may result from a magnetic catastrophe. Title: A Model for the Fibril Structure of Normal Polarity Solar Prominences Authors: Steele, C. D. C.; Priest, E. R. Bibcode: 1992SoPh..140..289S Altcode: A normal-polarity prominence is modelled as a series of cool fibrils set in the hotter corona. Equations of magnetostatic equilibrium are solved and each fibril corresponds to a dip in the mgnetic field. The ratio of fibril width to interfibril spacing is dependent on the prominence-coronal temperature ratio and the ratio of plasma to magnetic pressure. The prominence mass is found to depend on the square of the magnetic field strength. When variations along the prominence are allowed in addition to those across the prominence, an apparently random pattern of fibrils results. Title: Fast magnetic reconnection with small shock angles Authors: Yan, M.; Lee, L. C.; Priest, E. R. Bibcode: 1992JGR....97.8277Y Altcode: The steady state fast magnetic reconnection process with small separatrix angles proposed by Pestchek (1964) and generalized by Priest and Forbes (1986) is studied by a two-dimensional incompressible magnetohydrodynamic (MHD) code. In the code a uniform tangential magnetic field and normal plasma speed are specified on the inflow boundary. On the outflow boundary the tangential flow speed and tangential magnetic field are specified to be those in the Priest-Forbes' model in order to obtain different reconnection regimes. In our simulations both a uniform and a nonuniform resistivity are used. For a nonuniform resistivity model in which the resistivity in the outflow region is highly reduced, our simulations are in many aspects consistent with those in the analytical results. A steady state magnetic reconnection configuration with small separatrix angle is obtained. The plasma is heated and accelerated by the current sheets associated with slow shocks. We also obtain various regimes predicted by Priest and Forbes for different boundary conditions on the outflow boundary which are characterized by a parameter b0. They are a weak fast-mode expansion (b0=0), slow-mode compression (b0<0), slow-mode expansion (b0>=0), and a hybrid regime of fast-mode and slow-mode expansion (0<b0<1). The width and length of the current sheet for different parameters obtained in the simulations are found to be consistent with theoretical values. When the magnetic Reynolds number or the reconnection rate given on the inflow boundary increases, the diffusion region becomes smaller. However, for cases with a uniform resistivity imposed in the simulation domain it is found that the diffusion region tends to lengthen indefinitely and no steady state configuration is obtained. Magnetic islands are usually formed at the later stage of the simulation. Title: Book-Review - Advances in Solar System Magnetohydrodynamics Authors: Priest, E. R.; Hood, A. W.; Hartquist, T. W. Bibcode: 1992Ap&SS.192..159P Altcode: No abstract at ADS Title: A Self-consistent Turbulent Model for Solar Coronal Heating Authors: Heyvaerts, J.; Priest, E. R. Bibcode: 1992ApJ...390..297H Altcode: The rate of solar coronal heating induced by the slow random motions of the dense photosphere is calculated in the framework of an essentially parameter-free model. This model assumes that these motions maintain the corona in a state of small-scale MHD turbulence. The associated dissipative effects then allow a large-scale stationary state to be established. The solution for the macroscopic coronal flow and the heating flux is first obtained assuming the effective (turbulent) dissipation coefficients to be known. In a second step these coefficients are calculated by the self-consistency argument that they should result from the level of turbulence associated with this very heating flux. For the sake of tractability the derivation is restricted to a two-dimensional situation where boundary flows are translationally symmetric. The resulting value of the heating rate and the predicted level of microturbulent velocity compare satisfactorily with the observational data. Title: The properties of sources and sinks of a linear force-free field Authors: Demoulin, P.; Priest, E. R. Bibcode: 1992A&A...258..535D Altcode: In a highly conducting plasma, the magnetic field topology determines where, for example, current sheets can form, which is of great importance as a potential coronal heating source. With the classical extrapolation of a continuous weak photospheric field, the determination of topology is in general a difficult challenge. Because of the concentration of the photospheric field at intense flux tubes in supergranulation boundaries a more realistic field representation may be a description in terms of magnetic singularities located just below the photosphere. In this paper we analyze in detail the generalization to linear force-free fields of the standard multipole expansion for singular potential fields. Solutions are presented in spherical coordinates with the constraint that all singularities are located in the half-space z is less than 0 below the solar photospheric plane (z = 0). A great variety of solutions is shown to exist depending on two continuous and one discrete parameter. The properties of monopole and dipole solutions in particular are discussed and it is shown that isolated magnetic charges exist only in the potential limit and not in a linear force-free field. Title: The Fibril Structure of Prominences Authors: Hood, A. W.; Priest, E. R.; Anzer, U. Bibcode: 1992SoPh..138..331H Altcode: In this paper we present several magneto-hydrostatic equilibrium models for prominences with fibril-like fine structure. For all the models ad hoc temperature profiles are used without discussing the energetics. For our models we assume fine structure to occur either across the prominence axis or along it. This approach is intended as a first step towards more realistic models based upon a series of vertical fibril structures. Title: A Family of Two-Dimensional Nonlinear Solutions for Magnetic Field Annihilation Authors: Jardine, M.; Allen, H. R.; Grundy, R. E.; Priest, E. R. Bibcode: 1992JGR....97.4199J Altcode: We present a family of nonlinear solutions for magnetic field annihilation in two dimensions. These solutions include fully the effects of viscosity and resistivity and are a generalization of the Sonnerup and Priest model, where an irrotational stagnation point flow carriers straight field lines toward a long, thin current sheet. Here, we allow for vorticity in the inflow. When this is low, there is a unique solution for the flow and magnetic field. The current sheet adjusts its dimensions to accommodate different inflows. It is widest for a negative imposed vorticity and increases in width as the resistivity or viscosity is increased. When the imposed vorticity is large and negative, however, the solutions become nonunique, the flow pattern becomes cellular, and current sheets develop at the cell boundaries. These results, then, show that it is possible to have many more different types of inflow matched to full solutions for the current sheet than have been considered hitherto. Title: Prominence Sheets Supported by Constant-Current Force-free Fields. II. Imposition of Normal Photospheric Field Component and Prominence Surface Current Authors: Ridgway, C.; Amari, T.; Priest, E. R. Bibcode: 1992ApJ...385..718R Altcode: Attention is given to a method of constructing longitudinally invariant magnetic field configurations in which a symmetric finite vertical current sheet is in magnetohydrostatic equilibrium between the combined forces exerted by a background constant-current force-free field and a uniform gravitational field. Both the normal magnetic field component along the photosphere and the current density along the prominence sheet are imposed as functions of position. The method is used to generate both N- and I-type configurations by selecting a convenient form for the imposed functions. Consideration is given to the evolution of these configurations as the strength of the current (and hence the mass) is increased while all other parameters are held fixed. It is shown that in general the sheet loses equilibrium near its upper extremity as I is increased beyond a certain value. Title: Magnetic Flipping: Reconnection in Three Dimensions Without Null Points Authors: Priest, E. R.; Forbes, T. G. Bibcode: 1992JGR....97.1521P Altcode: In three dimensions, magnetic reconnection may take place in a sheared magnetic field at any singular field line, where the nearby field has X-type topology in planes perpendicular to the field line and where an electric field is present parallel to the field line. In the ideal region around the singular line there will, in general, be singularities in the plasma flow and electric field, both at the singular line and at ``magnetic flipping layers,'' which are remnants of local magnetic separatrices. In the absence of a three-dimensional magnetic neutral point or null point, reconnection of field lines can still occur by a process of magnetic flipping, in which the plasma crosses the flipping layers but the field lines rapidly flip along them by magnetic diffusion. Depending on the boundary conditions, there may be two or four flipping layers which converge on the singular line. A boundary layer analysis of a flipping layer is given in which the magnetic field parallel to the layer decreases as one crosses it while the plasma pressure (or magnetic pressure associated with the field along the singular line) increases. The width of the flipping layer decreases with distance from the singular line. Title: Structural instability of nonlinear Alfven waves Authors: Nocera, L.; Priest, E. R. Bibcode: 1992MmSAI..63..773N Altcode: Results are presented of a study of the nonlinear dynamics of O(sq rt epsilon) amplitude Alfven waves forced into a solar coronal loop where they drive and interact with slow magnetosonic waves. The evolution of the loop is described as the solution of a simple forced dissipative dynamical system led to be a regular Galerkin analysis of the one-dimensional MHD equations. Title: Basic Magnetic Configuration and Energy Supply Processes for an Interacting Flux Model of Eruptive Solar Flares Authors: Priest, E. R. Bibcode: 1992LNP...399...15P Altcode: 1992esf..coll...15P; 1992IAUCo.133...15P No abstract at ADS Title: Book-Review - Advances in Solar System Magnetohydrodynamics Authors: Priest, E. R.; Hood, A. W.; Ghizaru, M. Bibcode: 1992RoAJ....2...95P Altcode: No abstract at ADS Title: Magnetohydrodynamic Equilibria and Cusp Formation at an X-Type Neutral Line by Footpoint Shearing Authors: Vekstein, G. E.; Priest, E. R. Bibcode: 1992ApJ...384..333V Altcode: Two-dimensional magnetohydrodynamic equilibria in the presence of an X-type natural line are investigated in the context of ideal magnetohydrodynamics. The poloidal field geometry with a neutral X-line is shown to be inconsistent with general sheared magnetostatic equilibria. Shearing of an initial potential poloidal magnetic field results in the splitting of an X-point into a current sheet with cusp-points (or Y-points in some particular cases) at its ends. The global geometry of the poloidal magnetic field produced by different types of footpoint shearing motions is discussed. Title: Steady flows in solar magnetic solutions structures-a class of exact MHD solutions Authors: Ville, De. A.; Priest, E. R. Bibcode: 1991GApFD..59..253V Altcode: A class of exact solutions to the steady, two-dimensional magnetohydrodynamic equations ina cylindrical geometry is presented. These may model both closed and open magnetic structures found in the solar atmosphere. For closed structures, it is found that increasing the flow speed causes the summit of the arcade of closed magnetic fieldlines to rise. Parameter ranges also exist where the solution has regions of open and closed field, and so the solutions may be relevant for modelling flows in solar magnetic structures such as coronal streamers, X-ray bright points coronal plumes and coronal holes. Title: Steady flows in solar magnetic structures - a class of exact MHD solutions. Authors: de Ville, A.; Priest, E. R. Bibcode: 1991GApFD..59..253D Altcode: A class of exact solutions to the steady, two-dimensional magnetohydrodynamic equations in a cylindrical geometry is presented. These may model both closed and open magnetic structures found in the solar atmosphere. For closed structures, it is found that increasing the flow speed causes the summit of the arcade of closed magnetic fieldlines to rise. Parameter ranges also exist where the solution has regions of open and closed field, and so the solutions may be relevant for modelling flows in solar magnetic structures such as coronal streamers, X-ray bright points, coronal plumes and coronal holes. Title: Book-Review - Advances in Solar System Magnetohydrodynamics Authors: Priest, E. R.; Hood, A. W. Bibcode: 1991JBAA..101..300P Altcode: No abstract at ADS Title: The Magnetohydrodynamics of Energy Release in Solar Flares: Discussion Authors: Phillips, K. J. H.; Priest, E. R.; Haines, M. G. Bibcode: 1991RSPTA.336..380P Altcode: No abstract at ADS Title: The Magnetohydrodynamics of Energy Release in Solar Flares Authors: Priest, E. R. Bibcode: 1991RSPTA.336..363P Altcode: A large solar flare is thought to occur when a sheared magnetic arcade loses equilibrium or goes unstable and erupts, and drives magnetic reconnection in the stretched-out magnetic field lines. These two key processes of magnetic eruption and magnetic energy conversion by reconnection are reviewed briefly, with an account of recent analytical and numerical models. When the height or length of a prominence in a sheared coronal arcade is too great it may erupt and drive the formation and reconnection of a current sheet below it. Recent progress in fast steady-state reconnection theory has explained many puzzling features of numerical experiments, and has shown how a new process of magnetic flipping can reconnect fields in three dimensions. Also numerical modelling of the formation of flare loops and ribbons by reconnection has accounted for many observational properties. Title: Prominence Sheets Supported by Constant-Current Force-free Fields. I. Imposition of Normal Magnetic Field Components at the Current Sheet and the Photosphere Authors: Ridgway, C.; Amari, T.; Priest, E. R. Bibcode: 1991ApJ...378..773R Altcode: We present an analytical model for the support of a prominence (represented by a sheet of mass and current) in a constant-current force-free field. The model allows us to produce both normal-type and inverse-type configurations which are in equilibrium everywhere along the sheet and for which the field is locally bounded. Title: Bistability of a forced hydromagnetic cavity Authors: Nocera, Luigi; Priest, Eric R. Bibcode: 1991JPlPh..46..153N Altcode: We study the nonlinear stability of a one-dimensional hydromagnetic cavity into which Alfvén waves are fed by harmonic shear motions of its boundaries and where they interact with slow magnetosonic waves. We use characteristic conditions for the outgoing and ingoing Alfven waves at the boundaries where the magnetosonic oscillations are required to vanish. Forcing of Alfven waves takes place at a frequency close to the eigenfrequency of the lowest-order mode of the cavity. We let the frequency detuning δω vary as a free parameter together with the amplitude of the forcing, the plasma β and the compressive Reynolds number Re0. Given these last three parameters and varying δω, we calculate the amplitude of the nonlinear equilibrium state of the cavity as the stationary solution of a simple forced, dissipative dynamical system that governs the evolution of the cavity over a slow time scale and to which we are led by multiple-scale and Galerkin analyses of the one-dimensional MHD equations. This amplitude is a multi-valued function of δω (bistability), and we discuss the possibility of nonlinear stabilization of the Alfven wave by locking it in one of the bistable states. This amplitude undergoes saddle-node bifurcations: we calculate the two values of δω at which this occurs and the lowest value of the Reynolds number (27/2) for this to happen. We show that the magnetic energy density released during a bistable transition scales as (Re0)2; it has a maximum at β = 1 - (⅔)½ and it may amount to a substantial part of the energy originally stored in the unperturbed cavity. The magnetic power density released scales as (Re0)3 and has a maximum at β = 1 ± (⅓)½5. We conclude that the cavity is a good site for plasma heating such as that of the solar corona. Title: Advances in solar system magnetohydrodynamics Authors: Priest, Eric R.; Hood, Alan W. Bibcode: 1991gamp.conf.....P Altcode: Most of the solar system is in the plasma state and its subtle non-linear interaction with the magnetic field is described for many purposes by the equations of magnetohydrodynamics (MHD). Over the past few years this important and complex field has become one of the most actively pursued areas of research, with increasingly diverse applications in geophysics, space physics and astrophysics. This book examines the basic MHD topics, such as equilibria, waves, instabilities and reconnection and examines each in the context of different areas that utilize MHD. Many of the world's leading experts have contributed to this volume, which has been edited by two of the key enthusiasts. It is hoped that it can help the reader to appreciate and understand the common threads between the different branches of magnetohydrodynamics. This book will be a timely exposition of recent advances made in the field. Title: A Two-Dimensional Model for a Solar Prominence - Effect of an External Magnetic Field Authors: Oliver, R.; Ballester, J. L.; Priest, E. R. Bibcode: 1991SoPh..134..123O Altcode: Using analytical approximations we study the effects of different external magnetic configurations on the half-width, mass, and internal magnetic structure of a quiescent solar prominence, modelled as a thin vertical sheet of cool plasma. Firstly, we build up a zeroth-order model and analyse the effects produced by a potential coronal field or a constant-α force-free field. This model allows us to obtain the half-width and mass of the prominence for different values of the external field, pressure and shear angle. Secondly, the effects of these external magnetic configurations on a two-dimensional model proposed by Ballester and Priest (1987) are studied. The main effects are a change of the half-width with height, an increase of the mass, a decrease of the magnetic field strength with height and a change in the shape of the magnetic field lines. Title: Thermal Equilibria of Isobaric Coronal Magnetic Arcades Authors: Steele, C. D. C.; Priest, E. R. Bibcode: 1991SoPh..134...73S Altcode: A coronal magnetic arcade can be thought of as consisting of an assembly of coronal loops. By solving equations of isobaric thermal equilibrium along each loop and assuming a base temperature of 2 × 104 K, the thermal structure of the arcade can be found. The possible thermal equilibria can be shown to depend on two parameters L*p* and h*/p* representing the ratios of cooling (radiation) to condu and heating to cooling, respectively. Arcades can contain four types of loops: hot loops with summits hotter than 400000 K; cool loops at temperatures less than 80000 K along their lengths; hot-cool loops with cool summits and cool footpoints but hotter intermediate portions; and warm loops, cooler than 80000 K along most of their lengths but with summits as hot as 400000 K. Two possibilities for coronal heating are considered, namely a heating that is independent of magnetic field and a heating that is proportional to the square of the local magnetic field. When the arcade is sheared the thermal structure of the arcade may change, leading in some cases to non-equilibrium or in other cases to the formation of a cool core. Title: Advances in Solar System Magnetohydrodynamics, 1991 Authors: Priest, Eric R.; Hood, Alan W. Bibcode: 1991assm.conf.....P Altcode: 1991QB460.A38...... Most of the solar system exists in the plasma state (the fourth state of matter). Its subtle nonlinear interaction with the magnetic field can be described by the equations of magnetohydrodynamics (MHD). Over the past few years this important and complex field of research has been actively pursued and increasingly diversely applied to the fields of geophysics, space physics, and astrophysics. It is, for instance, relevant to the study of many dynamic phenomena such as solar flares, and the origins of magnetic fields in the Sun and the Earth. This book examines basic MHD topics, such as equilibria, waves, instabilities, and reconnection, and examines each in the context of different areas that utilize MHD. Many of the world's leading experts have contributed to this volume, which has been edited by two of the key enthusiasts. It is hoped that it will help researchers to appreciate and understand the common threads among the different branches of magnetohydrodynamics. Title: Instability of a prominence supported in a linear force-free field. II - Effect of twist or flux conservation Authors: Demoulin, P.; Ferreira, J.; Priest, E. R. Bibcode: 1991A&A...245..289D Altcode: Ideal MHD equations are used to study the vertical stability of a prominence in a linear force-free field in two dimensions. The prominence is modeled by a line current in equilibrium at a height between the background magnetic force, the repulsion of image currents and gravity. Attention is given to boundary conditions, current evolution, parameters, stability results with boundary conditions, and the effects of lateral boundaries. Title: Thermal Equilibria of Coronal Magnetic Loops with Non Constant Cross-Secitonal Area Authors: Steele, C. D. C.; Priest, E. R. Bibcode: 1991SoPh..132..293S Altcode: Equations of thermal equilibrium along coronal loops are solved in the absence of gravity but where the cross-sectional area changes along the loop. The footpoint temperature is assumed to be 2 × 104 K. Several fundamental types of solution are found, namely hot loops, cool loops, hot-cool loops (where the footpoints and summits are cool but the intermediate parts are hotter) and warm loops (cool along most of their lengths except the summits). On increasing the cross-sectional area the summit temperature generally increases slightly except for warm loops where no increase in temperature is recorded and hot-cool loops where a dramatic increase in summit temperature may occur. The cool and hot-cool loops may model elementary fibril structures within prominences. Title: Formation of current sheets in force-free magnetic fields. Authors: Vekstein, G.; Priest, E. R.; Amari, T. Bibcode: 1991A&A...243..492V Altcode: It is shown that the evolution of coronal magnetic fields in response to slow photospheric footpoint motions in general produces states with current sheets rather than smooth force-free equilibria. When a separatrix surface is present, shearing motions of a two-dimensional double arcade in general produce a current sheet all along the separatrix, whether the motions are infinitesimal or of finite amplitude; local singularities in the horizontal field component occur at the footpoints of the separatrix where it becomes tangential to the solar surface although the flux function is regular there. The particular case of equal lobes and an antisymmetric shear gives a smooth field without current sheets. When there is an X-type neutral line (or separator) present, converging or divering motions create a current sheet with Y-points at its ends; shearing motions create a current sheet all along the separattrices, which coalesce at two cusp-points to give a single current sheet near the original separator. In general these current sheets could heat the corona as they dissipate, but when new flux emerges into a highly sheared field they could also trigger a solar flare. Title: The Fibril Structure of Prominences Authors: Priest, E. R.; Hood, A. W.; Anzer, U. Bibcode: 1991SoPh..132..199P Altcode: We suggest that the fibril structure of prominences may be caused by filamentation during its formation by radiative instability. We also discuss the effects of other types of instability and give a mechanism for the formation of vertical threads. The models indicate that highly inhomogeneous density structures can exist in the presence of smooth profiles for the plasma pressure and magnetic field. In our particular models the plasma pressure of a fibril prominence is higher and the vertical magnetical field is weaker than in a uniform prominence model, while the mass is substantially smaller. Title: Magnetic Reconnection and Energy Release in the Solar Corona by Taylor Relaxation Authors: Vekstein, G. E.; Priest, E. R.; Steele, C. D. C. Bibcode: 1991SoPh..131..297V Altcode: The heating of the solar corona by resistive turbulence of coronal magnetic fields is considered. The theory of this process, based on the Taylor-Heyvaerts-Priest hypothesis and a magnetic relaxation equation, is developed. Such an approach allows one to obtain the successive magnetic reconnection configurations and energy balance of the coronal magnetic field in response to prescribed motions of the photospheric footpoints. Two specific models of the coronal magnetic configuration are investigated, namely an array of closely packed flux tubes and a two-dimensional magnetic arcade. Title: Introduction to Solar System Magnetohydrodynamics Authors: Priest, E. R. Bibcode: 1991assm.conf....1P Altcode: No abstract at ADS Title: Current Sheet Formation in Force-Free Magnetic Fields (With 2 Figures) Authors: Vekstein, G.; Priest, E. R. Bibcode: 1991mcch.conf..536V Altcode: No abstract at ADS Title: The structure of magnetic neutral points in two dimensions Authors: Strachan, N. R.; Priest, E. R. Bibcode: 1991GApFD..61..199S Altcode: Magnetic neutral points are of central importance in many solar phenomena, such as flares, reconnection and coronal structures. Despite their importance, the mathematical nature of magnetic neutral points has not previously come under detailed mathematical scrutiny. We present here a series of models for different types of neutral points in two dimensions. X-points have four separatrix field lines meeting at the neutral point and are a particular class of star-point which have an even number of separatrices. Asymmetric star-points (with an odd number of separatrices, at least one of which is a current sheet or a neutral sheet) include: Y-points with three separatrices intersecting at angles of 2/3; cusp-points with two of the three separatrices touching at the neutral point; and T-points with two of the separatrices meeting the third at right angles. Title: Effect of Coronal Heating on Coronal Arcades (With 3 Figures) Authors: Steele, C. D. C.; Priest, E. R. Bibcode: 1991mcch.conf..544S Altcode: No abstract at ADS Title: Mechanisms of Chromospheric and Coronal Heating Authors: Ulmschneider, Peter; Priest, Eric R.; Rosner, Robert Bibcode: 1991mcch.conf.....U Altcode: 1991QB809.M43...... One of the great problems of astrophysics is the unanswered question about the origin and mechanism of chromospheric and coronal heating. Just how these outer stellar envelopes are heated is of fundamental importance, since all stars have hot chromospheric and coronal shells where the temperature rises to millions of degrees, comparable to the temperatures in the stars' cores. Here for the first time is a comprehensive inventory of the proposed chromospheric and coronal heating theories. The proposed heating processes are critically compared, and the observational evidence for the various mechanisms is reviewed. This is essential reading for all those working in such fields as stellar activity, radio and XUV emission, rotation, and mass loss, for whom a detailed and consistent presentation of our knowledge of chromospheric and coronal heating mechanisms is urgently needed. Title: Report of IAU Commission 10: Solar activity (Activité solaire). Authors: Priest, E. R. Bibcode: 1991IAUTA..21...53P Altcode: No abstract at ADS Title: Steady flows in magnetic arcades - a class of exact mhd solutions Authors: de Ville, A.; Priest, E. R. Bibcode: 1991GApFD..61..225D Altcode: A class of exact solutions to the steady, two-dimensional magnetohydrodynamic equations in a cartesian geometry is presented. The method developed by Tsinganos (1981, 1982) is employed. These solutions may mode! siphon flow in magnetic arcades, the flow being driven by pressure differences between the footpoints. The basic result is that the presence of inertial forces causes the arcade to rise in comparison to the static case. Eventually, the arcade may be caused to erupt by continuing to increase the magnitude of inertial forces. Title: A Twisted Flux-Tube Model for Solar Prominences. III. Magnetic Support Authors: Ridgway, C.; Priest, E. R.; Amari, T. Bibcode: 1991ApJ...367..321R Altcode: The model for the support of a solar prominence in a twisted flux tube by Priest et al. (1989) is here extended to consider large deviations of the tube from cylindrical symmetry. The prominence is modeled as a finite current sheet with mass which is locally free from singularities in the magnetic field. Analytical solutions are found to the nonlinear force-free equations for the structure around the prominence for two functional forms of the field component parallel to the prominence axis. An associated mixed boundary-value problem is also solved in which the prominence is connected at its base to the photosphere, and the normal magnetic field components along the prominence and the photosphere are imposed. Title: The magnetohydrodynamics of energy release in solar flares. Authors: Priest, E. R. Bibcode: 1991psf..conf..363P Altcode: A large solar flare is thought to occur when a sheared magnetic arcade loses equilibrium or goes unstable and erupts, and drives magnetic reconnection in the stretched-out magnetic field lines. These two key processes of magnetic eruption and magnetic energy conversion by reconnection are reviewed briefly, with an account of recent analytical and numerical models. When the height or length of a prominence in a sheared coronal arcade is too great it may erupt and drive the formation and reconnection of a current sheet below it. Title: Magnetic Field Annihilation Within a Stagnation Point Flow (With 2 Figures) Authors: Jardine, M.; Priest, E. R.; Allen, H. R. Bibcode: 1991mcch.conf..601J Altcode: No abstract at ADS Title: Introduction to solar system MHD. Authors: Priest, E. R. Bibcode: 1991gamp.conf....1P Altcode: Most of the solar systems are in the plasma state and its subtle non-linear interaction with the magnetic field is described for many purposes adequately by the equations of magnetohydrodynamics (MHD). These equations are also applicable to the electrically conducting liquid cores of planets, such as our Earth, where magnetic fields are being generated by dynamo action. Indeed, this realisation of the existence of a strong coupling between a magnetic field and a plasma has revolutionised our understanding of the solar system. Furthermore, the complementary remote sensing observations at high resolution of the Sun and in-situ spacecraft measurements of solar system plasmas have revealed a spectacular world of intriguing dynamic activity over a wide range of length- and time-scales. Title: Two-Dimensional Magnetic Neutral Points (With 1 Figure) Authors: Strachan, N. R.; Priest, E. R. Bibcode: 1991mcch.conf..539S Altcode: No abstract at ADS Title: The Formation of Current Sheets and Coronal Heating (With 12 Figures) Authors: Priest, E. R. Bibcode: 1991mcch.conf..520P Altcode: No abstract at ADS Title: The creation of the magnetic environment for prominence formation in a coronal arcade Authors: Amari, T.; Démoulin, P.; Browning, P.; Hood, A.; Priest, E. Bibcode: 1991A&A...241..604A Altcode: The possibility of prominence formation in sheared coronal arcades is investigated. The creation of a dip at the summit of field lines is a likely requirement before a prominence can form; then dense plasma can be supported against gravity by the Lorentz force. It is proved that, in fact, no shear profile can create a dip in a two-dimensional force-free arcade if the photospheric field is bipolar. However, numerical investigations show that shearing an arcade can induce very flat field lines. It is investigated, in order of magnitude, how this flattening of the field can increase the free fall time of a dense plasma. Also, the interaction between shear and twist is analyzed; the critical twist needed to have a dip is a decreasing function of shear. Title: The Evolution of Coronal Magnetic Fields Authors: Priest, E. R.; Forbes, T. G. Bibcode: 1990SoPh..130..399P Altcode: Slow photospheric motions can produce flow speeds in the corona which are fast enough to violate quasi-static evolution. Therefore, high-speed flows observed in the corona are not necessarily due to a loss of equilibrium or stability. In this letter we present an example where the flow speed increases indefinitely with, height, while the coronal magnetic energy increases quadratically with time. Title: Nonlinear magnetic reconnection models with separatrix jets Authors: Priest, E. R.; Lee, L. C. Bibcode: 1990JPlPh..44..337P Altcode: A new theory for fast steady-state magnetic reconnection is proposed that includes many features of recent numerical experiments. The inflow region differs from that in the classical model of Petschek (1964) and the unified linear solutions of Priest & Forbes (1986) in possessing highly curved magnetic field lines rather than ones that are almost straight. A separatrix jet of plasma is ejected from the central diffusion region along the magnetic separatrix. Two types of outflow are studied, the simplest possessing an outflow magnetic field that is potential. The other contains weak standing shock waves attached to the ends of the diffusion region and either slowing down the flow (fast-mode shock) after it crosses the separatrix jet or speeding it up (slow-mode), depending on the downstream boundary conditions. A spike of reversed current slows down the plasma that emerges rapidly from the diffusion region into the more slowly moving downstream region, and diverts most of it along the separatrix jets. In the simplest case the outflow possesses no vorticity over most of the downstream region. The models demonstrate that both upstream and downstream boundary conditions are important in determining which regime of reconnection is produced from a wide variety of possibilities. Title: Thermal Equilibria of Coronal Magnetic Loops Authors: Steele, C. D. C.; Priest, E. R. Bibcode: 1990SoPh..125..295S Altcode: Equations of thermal equilibrium along coronal loops with footpoint temperatures of 2 × 104 K are solved. Three fundamentally different categories of solution are found, namely hot loops with summit temperatures above about 4 × 105 K, cool loops which are cooler than 8 × 104 K along their whole length and hot-cool loops which have summit temperatures around 2 × 104 K but much hotter parts at intermediate points between the summit and the footpoints. Hot loops correspond to the hot corona of the Sun. The cool loops are of relevance for fibrils, for the cool cores observed by Foukal and also for active-region prominences where the magnetic field is directed mainly along the prominence. Quiescent prominences consist of many cool threads inclined to the prominence axis, and each thread may be modelled as a hot-cool loop. In addition, it is possible for warm loops at intermediate summit temperatures (8 × 104K to 4 × 105 K) to exist, but the observed differential emission measure suggests that most of the plasma in the solar atmosphere is in either the hot phase or the cool phase. Thermal catastrophe may occur when the length or pressure of a loop is so small that the hot solution ceases to exist and there are only cool loop solutions. Many loops can be superimposed to form a coronal arcade which contains loops of several different types. Title: The Nonuniform Magnetohydrodynamic Nature of the Solar Corona. IV. Effect of Magnetogravity Interactions Authors: de Ville, A.; Priest, E. R. Bibcode: 1990ApJ...359..560D Altcode: Magnetogravity interactions in the solar corona are considered by extending the method proposed by Priest for modeling standing magnetohydrodynamic disturbances. The effects of gravity on the basic solutions are to increase the maxima of the plasma and magnetic pressures and to decrease the curvature of the field lines. Also, the classification of the solutions is altered. When the transverse component of the magnetic field has a zero, more complex magnetic field structures are produced, reminiscent of coronal streamers, in which the type of interaction occurring in the plasma alters with height in the corona. Title: Relaxed states in a spheromak with inhomogeneous boundary fields Authors: Dixon, A. M.; Browning, P. K.; Bevir, M. K.; Gimblett, C. G.; Priest, E. R. Bibcode: 1990JPlPh..43..357D Altcode: In this paper we consider force-free equilibrium solutions of the MHD equations in a spherical geometry for the case in which magnetic flux crosses the boundary of the containing vessel. The main motivation is to model more faithfully actual spheromak experiments in the laboratory, for which boundaries are unlikely to be magnetic surfaces. We show how a general inhomogeneous boundary field may be constructed from individual components. In particular, we consider the cases of a boundary field of dipolar form and one of quadrupolar form. We then go on to discuss solutions for fields embedded in point or ring electrodes using the ‘general solution’, some of which can be used to model experiments such as the PS-1- or CTX-type spheromaks. Title: Thermal Equilibria of Coronal Magnetic Arcades Authors: Steele, C. D. C.; Priest, E. R. Bibcode: 1990SoPh..127...65S Altcode: A coronal magnetic arcade can be thought of as consisting of an assembly of coronal loops. By solving equations of thermal equilibrium along each loop and assuming a base temperature of 2 × 104 K, the thermal structure of the arcade can be found. By assuming a form for the plasma pressure in the arcade, the possible thermal structures can be shown to depend on three parameters. Arcades can contain hot loops with summits hotter than 400 000 K, cool loops at temperatures less than 80 000 K along their lengths, hot-cool loops with cool summits and cool footpoints but hotter intermediate portions, and warm loops, cooler than 80 000 K along most of their lengths but with summits as hot as 400 000 K. For certain arcades, there exist regions where more than one kind of loop is possible. If the parameters describing the arcade are varied, it is possible for non-equilibrium to occur when a type of solution ceases to exist. For example, hot or warm loops can cease to exist so that only cool solutions are possible when the arcade size or pressure is decreased, while warm or cool loops may give way to hot-cool loops when the heating is reduced or the pressure is increased. Title: Magnetic Field Evolution during Prominence Eruptions and Two-Ribbon Flares Authors: Priest, E. R.; Forbes, T. G. Bibcode: 1990SoPh..126..319P Altcode: Simple models for the MHD eruption of a solar prominence are presented, in which the prominence is treated as a twisted magnetic flux tube that is being repelled from the solar surface by magnetic pressure forces. The effects of different physical assumptions to deal with this magneto-hydrodynamically complex phenomenon are evaluated, such as holding constant the prominence current, radius, flux or twist or modelling the prominence as a current sheet. Including a background magnetic field allows the prominence to be in equilibrium initially with an Inverse Polarity and then to erupt due to magnetic non-equilibrium when the background magnetic field is too small or the prominence twist is too great. The electric field at the neutral point below the prominence rapidly increases to a maximum value and then declines. Including the effect of gravity also allows an equilibrium with Normal Polarity to exist. Finally, an ideal MHD solution is found which incorporates self-consistently a current sheet below the prominence and which implies that a prominence will still erupt and form a current sheet even if no reconnection occurs. When reconnection is allowed it is, therefore, driven by the eruption. Title: Energetics of compressible models of fast steady-state magnetic reconnection Authors: Jardine, M.; Priest, E. R. Bibcode: 1990JPlPh..43..141J Altcode: An understanding of the energy transfer that takes place during magnetic reconnection is crucial to the study of this fundamental process. It depends on two factors: the type of reconnection regime (which is determined by the boundary conditions) and the degree of compressibility. Here we examine the role of compressibility in the energetics of a family of reconnection models. When the inflow Mach number (or reconnection rate) Me is small the effects of compressibility may be more important than the differences between regimes. We find that for a slow-compression regime with Me = 0·005 compressibility decreases by 39% the efficiency of the shocks in converting magnetic energy and increases by 14% the ratio of thermal to kinetic energy in the outflow jet. This compares with a 13% decrease in the shock efficiency and a 7% decrease in the jet ratio obtained by choosing instead a flux-pile-up regime. As Me is increased, however, the differences between regimes become larger and may be comparable to or greater than the effects of compressibility. Thus when the above Mach number is doubled we find that a change of regime now has 1-6 times the effect on the jet energy ratio as the introduction of compressibility. For those regimes, therefore, which only exist at low inflow Mach numbers, compressibility will always be important. At higher values of Me the type of regime may be the dominant factor governing the energetics. Title: Physics of magnetic flux ropes Authors: Russell, C. T.; Priest, E. R.; Lee, L. C. Bibcode: 1990GMS....58.....R Altcode: 1990QB528.P48...... The present work encompasses papers on the structure, waves, and instabilities of magnetic flux ropes (MFRs), photospheric flux tubes (PFTs), the structure and heating of coronal loops, solar prominences, coronal mass ejections and magnetic clouds, flux ropes in planetary ionospheres, the magnetopause, magnetospheric field-aligned currents and flux tubes, and the magnetotail. Attention is given to the equilibrium of MFRs, resistive instability, magnetic reconnection and turbulence in current sheets, dynamical effects and energy transport in intense flux tubes, waves in solar PFTs, twisted flux ropes in the solar corona, an electrodynamical model of solar flares, filament cooling and condensation in a sheared magnetic field, the magnetopause, the generation of twisted MFRs during magnetic reconnection, ionospheric flux ropes above the South Pole, substorms and MFR structures, evidence for flux ropes in the earth magnetotail, and MFRs in 3D MHD simulations. Title: How to Form a Dip in a Magnetic Field Before the Formation of a Solar Prominence Authors: Démoulin, P.; Priest, E. R. Bibcode: 1990LNP...363..269D Altcode: 1990doqp.coll..269D; 1990IAUCo.117..269D Magnetic fields with downward curvature are not favourable for prominence formation since the presence of a small quantity of dense material at the summit of a low-beta arcade cannot deform sufficiently the magnetic field lines to remain there in a stable manner. Thus a dip at the field line summit is needed before a prominence can form. We investigate different ways of forming such an upward curvature. Results with a twisted flux tube or a sheared arcade are reviewed, and a third possibility, namely a quadrupolar region is proposed. Title: Magnetic Reconnection on the Sun Authors: Priest, E. R. Bibcode: 1990IAUS..142..271P Altcode: Several solar phenomena where reconnection is believed to be operating are described. The type of reconnection regime and the rate of reconnection are found to depend sensitively on the inflow boundary conditions, with the b = 0 and b = 1 solutions being particular members of a much wider class. Explanations are provided for four puzzling features that are not present in the classical models of reconnection: different types of inflow, separatrix jets, reversed current spikes, and highly curved field lines in the inflow region. The mechanisms at work in heating different parts of the corona are discussed. It is argued that as oppositely directed magnetic fragments come together, their magnetic field lines reconnect in the atmosphere above, creating one loop which moves out while another submerges. The question of how the global magnetic flux balance in the corona is maintained is addressed. Title: Hvar Reference Atmosphere of Quiescent Prominences Authors: Engvold, Oddbjørn; Hirayama, Tadashi; Leroy, Jean Louis; Priest, Eric R.; Tandberg-Hanssen, Einar Bibcode: 1990LNP...363..294E Altcode: 1990IAUCo.117..294E; 1990doqp.coll..294E No abstract at ADS Title: Two-Dimensional Magnetic Neutral Points Authors: Strachan, N. R.; Priest, E. R. Bibcode: 1990PDHO....7..168S Altcode: 1990ESPM....6..168S; 1990dysu.conf..168S No abstract at ADS Title: Magnetic reconnection theory Authors: Priest, E. R. Bibcode: 1990MmSAI..61..383P Altcode: There are many phenomena on the sun where magnetic reconnection is thought to be playing a central role, such as cancelling magnetic features, prominences, coronal heating and solar flares. A few recent advances in the basic theory of steady-state magnetic reconnection are reviewed. The classical theory due to Sweet, Parker, Petschek and Sonnerup has been unified in a theory which possesses many new regimes that depend on the boundary conditions at large distances. For example, the flux pile-up regime possesses diverging flows, a long central diffusion region and a reconnection rate that is much larger than the Petschek value. Recent numerical experiments however, often possess three features that are not present in the earlier theoretical models, namely highly curved inflow field lines, separatrix jets and reversed current spikes, and so an attempt is described to include these features in a new theoretical model. Also some new ideas on three-dinmensional aspects of reconnection are discussed. Title: Support of a Prominence by a Constant-Current Force-Free Field Authors: Ridgway, C.; Amari, T.; Priest, E. R. Bibcode: 1990PDHO....7..166R Altcode: 1990dysu.conf..166R; 1990ESPM....6..166R No abstract at ADS Title: Basic plasma processes on the sun Authors: Priest, E. R.; Krishan, V. Bibcode: 1990IAUS..142.....P Altcode: The present symposium on basic plasma processes on the sun discusses the solar interior, stellar plasmas, photospheric flows and magnetic fields, photospheric fluxtubes, chromospheric and coronal heating, magnetic reconnection and coronal evolution, solar flares, and solar radio emission. Attention is given to the interior structure of the sun, the electrodynamics of neutrinos in dispersive media, problems of solar convection, mechanisms for dynamo mode excitation, and plasma damping of gravitational waves. Topics addressed include magnetic braking, energy release in stellar flares, large-scale flow patterns in the solar atmosphere, the magnetohydrodynamics of sunspots, waves in magnetic flux tubes, and wave propagation in sunspots. Also discussed are relaxed states of MHD turbulence, the interaction of flux tubes with sound waves, the magnetic helicity of oscillating coronal loops, the existence of hydromagnetic interface waves in a structured atmosphere, and magnetic reconnection on the sun. Title: Fibril Structure of Solar Prominences Authors: Ballester, J. L.; Priest, E. R. Bibcode: 1990LNP...363..241B Altcode: 1990doqp.coll..241B; 1990IAUCo.117..241B No abstract at ADS Title: Effect of an External Magnetic Field on Prominence Properties Authors: Oliver, R.; Ballester, J. L.; Priest, E. R. Bibcode: 1990PDHO....7..170O Altcode: 1990dysu.conf..170O; 1990ESPM....6..170O No abstract at ADS Title: Thermal Equilibrium of Coronal Loops and Prominence Formation Authors: Steele, C. D. C.; Priest, E. R. Bibcode: 1990LNP...363..275S Altcode: 1990IAUCo.117..275S; 1990doqp.coll..275S No abstract at ADS Title: Magnetic Helicity of Oscillating Coronal Loops Authors: Krishan, V.; Priest, E. R. Bibcode: 1990IAUS..142..256K Altcode: No abstract at ADS Title: Fibril structure of solar prominences Authors: Ballester, J. L.; Priest, E. R. Bibcode: 1990GMS....58..321B Altcode: While previous modelings of solar active-region prominences have taken the form of single, cool loops, observations suggest a more accurate interpretation in terms of many loops of plasma that are inclined to the filament. An effort is presently made to follow those suggestions in the construction of a model for the fibrillar structure of solar prominences in terms of slender flux tubes reproducing the observed parameters of both quiescent and active region prominences. The model structure encompasses a hot component and a depressed cool component; the most realistic results include the effect of an external magnetic field in the corona. Title: Comparison of Energetics of Magnetic Reconnection for Compressible and Incompressible Models. Authors: Jardine, M.; Priest, E. R. Bibcode: 1990ppsa.conf..219J Altcode: No abstract at ADS Title: Heating of Coronal Arcades Authors: Steele, C. D. C.; Priest, E. R. Bibcode: 1990PDHO....7..164S Altcode: 1990dysu.conf..164S; 1990ESPM....6..164S The thermal structure of a coronal arcade can be found by considering it as an assembly of individual magnetic loops. This procedure is valid as the thermal conductivity parallel to the magnetic field is orders of magnitude greater than that perpendicular to the field. For the present work, the arcade considered is a cylindrical one with its axis on or below the photosphere. Title: Magnetic structure of prominences: (Invited Review) Authors: Priest, E. R. Bibcode: 1990LNP...363..150P Altcode: 1990IAUCo.117..150P; 1990doqp.coll..150P Models for magnetic structures of prominences are reviewed. Starting with the internal structure of the prominence sheet, the external prominence magnetic fields of normal polarity and of inverse polarity are considered, followed by brief comments on fibril structure and feet. A new flux tube model is summarized, and some comments about the longitudinal magnetic component and the long-term evolution of prominences are presented. Title: A three-dimensional model for solar prominences Authors: Démoulin, P.; Priest, E. R.; Anzer, U. Bibcode: 1990LNP...363..268D Altcode: 1990doqp.coll..268P; 1990LNP...363..268P; 1990IAUCo.117..268P We suggest here a model for the 3D structure of quiescent prominences by a superposition of two fields. A 3D force-free field with constant is assumed to exist in the corona prior to the prominence formation. The prominence itself is represented by a line current which interacts with the coronal field. The three-dimensional field is represented by analytical functions and concentration of the magnetic field at the photospheric level by convection cells is taken into account. When the field created by the photospheric pattern supports the prominence, the prominence feet are found to be located at supergranule centres otherwise; they are located at cell boundaries. Title: The Nonuniform Magnetohydrodynamic Nature of the Solar Corona. III. Cylindrical Geometry Authors: de Ville, A.; Priest, E. R. Bibcode: 1989ApJ...347.1167D Altcode: The method developed by Priest in 1988 for modeling steady MHD disturbances in the solar corona is extended to a cylindrical geometry, which is more realistic for three-dimensional structures, such as plumes and coronal holes, which are observed in the corona. Both axial symmetric and nonaxial magnetic fields are treated. The basic characteristics of the axisymmetric solutions are found to be similar to the previous Cartesian case. Quantitatively, the interactions are stronger in the central region and weaker at the outer boundary. Pressure gradients are also found to be smaller. Solutions dependent on all three spatial variables exhibit an asymmetry because of the angular dependence. They depend upon the azimuthal magnetic field imposed at the coronal base. The solutions found in this paper may be useful in interpreting the physics of MHD interactions observed in numerical experiments and also in the solar atmosphere. Title: A generalization of the Woltjer minimum-energy principle Authors: Dixon, A. M.; Berger, M. A.; Priest, E. R.; Browning, P. K. Bibcode: 1989A&A...225..156D Altcode: The theorem of Woltjer (1958) for the minimization of the magnetic energy of a magnetic structure is extended to include the case of a free boundary subjected to external magnetic or plasma pressure forces. The case where the boundary is not a magnetic surface is also treated. Applications to a finite cylindrical flux tube and a spheromak are given to illustrate the theory. It is also shown how the theory may be applied to the construction of stationary Euler flows. Title: Model for the fibril structure of solar prominences Authors: Ballester, J. L.; Priest, E. R. Bibcode: 1989A&A...225..213B Altcode: Limb observations of quiescent solar prominences have revealed them to be composed of many fine structures. Also observations in H-alpha and UV lines suggest that quiescent filaments are made up of many clusters of small-scale loops at different temperatures inclined to the filament axis, with the C IV structures more extended than the H-alpha ones. In H-alpha, the dimensions of these structures are about 7000 km long and 1000 km thick, and they evolve over a typical time scale of about 8 min. The aim has been to take into account such observations and to construct a model for the fibril structure of solar prominences in terms of slender magnetic flux tubes, in which the main observed parameters of both quiescent and active-region prominences are reproduced. Title: A three-dimensional model for solar prominences Authors: Demoulin, P.; Priest, E. R.; Anzer, U. Bibcode: 1989A&A...221..326D Altcode: In an attempt to model the external force field of a prominence, a three-dimensional linear force-free field configuration was studied. The model consists of a fundamental together with a harmonic that is periodic along the prominence. The variation of the prominence height along the prominence is calculated and it is suggested that feet occur where the prominence sags down to low heights. Title: A Twisted Flux-Tube Model for Solar Prominences. I. General Properties Authors: Priest, E. R.; Hood, A. W.; Anzer, U. Bibcode: 1989ApJ...344.1010P Altcode: It is proposed that a solar prominence consists of cool plasma supported in a large-scale curved and twisted magnetic flux tube. As long as the flux tube is untwisted, its curvature is concave toward the solar surface, and so it cannot support dense plasma against gravity. However, when it is twisted sufficiently, individual field lines may acquire a convex curvature near their summits and so provide support. Cool plasma then naturally tends to accumulate in such field line dips either by injection from below or by thermal condensation. As the tube is twisted up further or reconnection takes place below the prominence, one finds a transition from normal to inverse polarity. When the flux tube becomes too long or is twisted too much, it loses stability and its true magnetic geometry as an erupting prominence is revealed more clearly. Title: The Formation of Flare Loops by Magnetic Reconnection and Chromospheric Ablation Authors: Forbes, T. G.; Malherbe, J. M.; Priest, E. R. Bibcode: 1989SoPh..120..285F Altcode: Slow-mode shocks produced by reconnection in the corona can provide the thermal energy necessary to sustain flare loops for many hours. These slow shocks have a complex structure because strong thermal conduction along field lines dissociates the shocks into conduction fronts and isothermal subshocks. Heat conducted along field lines mapping from the subshocks to the chromosphere ablates chromospheric plasma and thereby creates the hot flare loops and associated flare ribbons. Here we combine a non-coplanar compressible reconnection theory with simple scaling arguments for ablation and radiative cooling, and predict average properties of hot and cool flare loops as a function of the coronal vector magnetic field. For a coronal field strength of 100 G the temperature of the hot flare loops decreases from 1.2 × 107 K to 4.0 × 106 K as the component of the coronal magnetic field perpendicular to the plane of the loops increases from 0% to 86% of the total field. When the perpendicular component exceeds 86% of the total field or when the altitude of the reconnection site exceeds 106km, flare loops no longer occur. Shock enhanced radiative cooling triggers the formation of cool Hα flare loops with predicted densities of ≈ 1013 cm−3, and a small gap of ≈ 103 km is predicted to exist between the footpoints of the cool flare loops and the inner edges of the flare ribbons. Title: Compressible models of fast steady-state magnetic reconnection Authors: Jardine, M.; Priest, E. R. Bibcode: 1989JPlPh..42..111J Altcode: We investigate the effects of compressibility on magnetic reconnection, using as a basis the incompressible models of Priest & Forbes and Jardine & Priest. Our results show that compressibility modifies the reconnection process, without changing its essential character. In the region of inflowing plasma, compressibility tends to increase the convergence or divergence of the flow. Also, for regimes with a compression in the inflow the maximum rate of reconnection is increased, while for regimes with an expansion in the inflow the magnetic Mach number at the entrance to the diffusion region is increased. In the region of outflowing plasma the main effects of compressibility are to produce faster and narrower outflow jets, with a lower magnetic field strength. Title: Solar Physics. (Book Reviews: The Physics of Solar Flares) Authors: Priest, Eric Bibcode: 1989Sci...245..770T Altcode: No abstract at ADS Title: Book Review: The physics of solar flares. / CUP, 1988 Authors: Priest, E. Bibcode: 1989Sci...245..770P Altcode: No abstract at ADS Title: A model for a non-Keplerian magnetic accretion disk with a magnetically heated corona Authors: Heyvaerts, J. F.; Priest, E. R. Bibcode: 1989A&A...216..230H Altcode: MHD stresses are used to model a thin disk dynamically interacting with a self-created magnetic corona. A simple model of the coronal magnetic structure produced by the turbulent MHD relaxation of the stresses exerted by the disk's differential rotation can explain the effect of coronal heating and the back reaction of the corona on the energy balance and angular momentum flow in the disk. The results show the disk to acquire a non-Keplerian rotation profile, with the trailing foot point of the magnetic loops being accelerated, and the leading one being decelerated, in comparison to a Keplerian distribution. It is found that the coronal heating and non-Keplerian effects are weak when the coronal scale becomes much larger than the disk size. Title: Book-Review - Dynamics and Structure of Quiescent Solar Prominences Authors: Priest, E. R. Bibcode: 1989JBAA...99..152P Altcode: No abstract at ADS Title: Book-Review - Dynamics and Structure of Quiescent Solar Prominences Authors: Priest, E. R. Bibcode: 1989S&T....77..619P Altcode: No abstract at ADS Title: The Nonuniform Magnetohydrodynamic Nature of the Solar Corona. II. Generalization of Basic Solutions Authors: de Ville, A.; Priest, E. R. Bibcode: 1989ApJ...340..579D Altcode: The method developed recently by Priest (1988) for modeling standing MHD disturbances in the solar corona is extended in several ways. Including inertial effects of the uniform plasma flow distorts the isobars and makes the flow and magnetic field vary with altitude in a manner that depends on the value of the flow speed relative to the cusp speed, the sound speed, and the Alfven speed. More general classes of solutions to the governing equation may be determined by seeking nonseparable solutions with a Green's function technique. Allowing magnetic flux to escape across the side boundaries leads to models which are relevant for coronal holes. The relation of this governing equation to the nonlinear MHD equations is indicated. Title: A twisted flux model for solar prominences. II - Formation of a dip in a magnetic structure before the formation of a solar prominence Authors: Demoulin, P.; Priest, E. R. Bibcode: 1989A&A...214..360D Altcode: The possibility of dip formation in a linear force-free field before the formation of a filament is investigated. The creation of a dip prior to prominence formation requires a greatly sheared magnetic field and a particular magnetic base flux. In the present work, attention is given to a bipolar region devoid of parasite polarity. Title: Steady Magnetic Reconnection in Three Dimensions Authors: Priest, E. R.; Forbes, T. G. Bibcode: 1989SoPh..119..211P Altcode: The concepts of magnetic reconnection that have been developed in two dimensions need to be generalised to three-dimensional configurations. Reconnection may be defined to occur when there is an electric field (E∥) parallel to field lines (known as potential singular lines) which are potential reconnection locations and near which the field has an X-type topology in a plane normal to that field line. In general there is a continuum of neighbouring potential singular lines, and which one supports reconnection depends on the imposed flow or electric field. For steady reconnection the nearby flow and electric field are severely constrained in the ideal region by the condition that E∥ = 0 there. Potential singular lines may occur in twisted prominence fields or in the complex magnetic configuration above sources of mixed polarity of an active region or a supergranulation cell. When reconnection occurs there is dynamic MHD behaviour with current concentration and strong plasma jetting along the singular line and the singular surfaces which map onto them. Title: Slow Shock Heating in POST Flare Arches Authors: Hick, P.; Priest, E. R. Bibcode: 1989SoPh..122..111H Altcode: The heating of a coronal arch, following the occurrence of a dynamic (two-ribbon) flare, is discussed. We investigate whether slow-shock heating, occurring during the reconnection process in the dynamic flare and responsible for the heating of the post-flare loops, is also a workable proposition for the heating of a coronal arch. Contrary to the flare loops, the shock structure in the arch is generally not modified greatly by thermal conduction effects. As a result slow-shock heating may be investigated in terms of the familiar MHD shock jump relations. The observed enhanced arch density with respect to the surrounding corona is explained as a direct consequence of the reconnection process. For a combination of high arch temperatures and low values of coronal magnetic field and density thermal conduction may become important and will lead to an extra density enhancement in the arch. Our interpretation of the arch of 21-22 May, 1980 suggests that the formation of the arch took approximately one hour, and that observed temperature, density and maximum energy content can be consistently explained by the slow-shock heating mechanism. Title: Non-equilibrium of a cylindrical magnetic arcade Authors: Steele, C. D. C.; Hood, A. W.; Priest, E. R.; Amari, T. Bibcode: 1989SoPh..123..127S Altcode: A cylindrically-symmetric magnetic arcade with its axis on the photosphere is perturbed by means of an alteration in the pressure along the base. The perturbation is examined with a view to finding equilibrium configurations close to the original equilibrium. It is found that equilibria can only be found when the integral of the excess pressure along the base is zero. In other cases no equilibria can be found and the arcade is likely either to collapse or, in the case of a coronal mass ejection, to erupt. For an initial arcade whose field increases linearly with radial distance from the axis, the neighbouring equilibria have been found. Title: The Eruption of a Prominence and Coronal Mass Ejection which Drive Reconnection Authors: Steele, C. D. C.; Priest, E. R. Bibcode: 1989SoPh..119..157S Altcode: Two possible limiting scenarios are proposed for the production of a coronal mass ejection. In the first the magnetic field around a prominence evolves until it loses equilibrium and erupts, which drives reconnection below the prominence and an eruption of the overlying magnetic arcade. In the second a large-scale magnetic arcade evolves until it loses equilibrium and erupts, thereby causing a prominence to erupt. In general it is likely to be the non-equilibrium of the coupled system which creates the eruption. Furthermore, large quiescent prominences are expected to be centred within the magnetic bubble of a coronal mass ejection whereas when active-region prominences erupt they are likely to be located initially to one side of the bubble. Title: The magnetic field around quiescent solar prominences computed from observational boundary conditions Authors: Demoulin, P.; Malherbe, J. M.; Priest, E. R. Bibcode: 1989A&A...211..428D Altcode: A generalization of Anzer's model (1972) for quiescent prominence support is presented. The coronal field is assumed to be current-free except inside the prominence where currents support dense material against gravity. The prominence is taken to be an infinitely thin current sheet of finite extent along the vertical axis. The hypothesis of two-dimensional fields allows the use of complex functions to solve the mixed boundary problem which is defined by the observed vertical field in the photosphere and the horizontal magnetic field in the prominence. These boundary conditions are not sufficient to determine a unique solution for the magnetic field. The indeterminacy is decreased by physical considerations, and some models for Normal (N) and Inverse (I) configurations are presented. In both cases it is possible to find field configurations which can support the fintie prominence against gravity. Title: Book-Review - Dynamics and Structure of Quiescent Solar Prominences Authors: Priest, E. R.; Tandberg-Hanssen, E. A. Bibcode: 1989SoPh..124..193P Altcode: No abstract at ADS Title: Thermal Equilibrium of Coronal Loops and Prominence Formation Authors: Steele, C. D. C.; Priest, E. R. Bibcode: 1989HvaOB..13..283S Altcode: No abstract at ADS Title: How to Form a Dip in a Magnetic Field Before the Formation of a Solar Prominence Authors: Demoulin, P.; Priest, E. R. Bibcode: 1989HvaOB..13..261D Altcode: No abstract at ADS Title: Dynamics and structure of quiescent solar prominences Authors: Priest, Eric Ronald Bibcode: 1989ASSL..150.....P Altcode: 1989dsqs.work.....P Recent observational and theoretical investigations of quiescent solar prominences (QSPs) are reviewed, in greatly expanded versions of lectures presented at the workshop. Chapters are devoted to an introduction to QSPs, the overall properties of QSPs and the role of steady flows, the QSP environment, observations of QSP magnetic fields, the formation of QSPs, the structure and equilibrium of QSPs, and stability and eruption phenomena. Extensive graphs, diagrams, and sample images are provided. Title: A Three-Dimensional Model for Solar Prominences Authors: Demoulin, P.; Priest, E. R.; Anzer, U. Bibcode: 1989HvaOB..13..253D Altcode: No abstract at ADS Title: Magnetic Energy Conversion on the Sun Authors: Priest, E. R. Bibcode: 1989ESASP.285...73P Altcode: 1989rsp..conf...73P For a 3D magnetic field such as exists above sunspots or magnetic fragments of complex polarity or in prominence fields, it is suggested that reconnection may be defined to occur when there is a singular line (a field line with neighboring X-type topology and an electric field along it). In general there is a continuum of potential singular lines and which one supports reconnection depends on the flow or electric field. An example is given of how to drive reconnection all along any curved field line in a configuration with shear and it is found that strong plasma jetting occurs along the singular line. Thus in a sheared coronal configuration of potential singular lines, coronal heating may occur at small current sheets created at singular lines by the appropriate flows. Title: Introduction to quiescent solar prominences Authors: Priest, E. R. Bibcode: 1989ASSL..150....1P Altcode: 1988dsqs.work....1P; 1989dsqs.work....1P The basic properties of quiescent solar prominences (QSPs) and the theoretical models used to characterize them are reviewed and illustrated with sample images. QSPs are located in the solar corona but have temperatures 100 times lower and densities 100 times greater than the corona. Particular attention is given to QSP development, structures, eruptions, and instabilities and to the governing magnetohydrodynamic, magnetohydrostatic, and wave equations for QSPs. Title: Structuring of plasmas by a magnetic field. Authors: Priest, E. R. Bibcode: 1989plap.work..189P Altcode: The highly structured nature of the solar corona is created by the magnetic field. It is suggested that such structure can be understood in terms of standing MHD disturbances of several types, spread over extended regions. They can be compressions, in which the plasma pressure increases, or expansions in which it decreases. Such interactions are also present in the inflow region of 2D steady-state magnetic reconnection models. Reconnection of 3D magnetic fields occurs when an electric field exists along a singular line. In general a sheared field possesses a continuum of potential singular lines and which one supports reconnection depends on the flow or electric field. Constraints on the electric field and flow are presented for reconnection at a given singular line. It is proposed that prominences located in large curved flux tubes are twisted up by Coriolis forces. When the twist is large enough the magnetic field near the summit has the required curvature to support plasma against gravity. As the twist increases the prominence grows in length and eventually loses equilibrium and erupts outwards into interplanetary space with a coronal mass ejection. Title: Thermal instability in a stratified plasma. Authors: Hermanns, D. F. M.; Priest, E. R. Bibcode: 1989plap.work...99H Altcode: The thermal instability mechanism has been studied in connection to observed coronal features, like, e.g. prominences or cool cores in loops. Although these features show a lot of structure, most studies concern the thermal instability in a uniform medium. The authors investigate the thermal instability and the interaction between thermal modes and the slow magneto-acoustic subspectrum for a stratified plasma slab. They formulate the relevant system of equations and give some straightforward properties of the linear spectrum of a non-uniform plasma slab, i.e. the existence of continuous parts in the spectrum. They present a numerical scheme with which one can investigate the linear spectrum for equilibrium states with stratification. The slow and thermal subspectra of a crude coronal model are given as a preliminary result. Title: Preflare activity. Authors: Priest, E. R.; Gaizauskas, V.; Hagyard, M. J.; Schmahl, E. J.; Webb, D. F.; Cargill, P.; Forbes, T. G.; Hood, A. W.; Steinolfson, R. S.; Chapman, G. A.; Deloach, A. C.; Gary, G. A.; Jones, H. P.; Karpen, J. T.; Martres, M. -J.; Porter, J. G.; Schmieder, B.; Smith, J. B., Jr.; Toomre, J.; Woodgate, B.; Waggett, P.; Bentley, R.; Hurford, G.; Schadee, A.; Schrijver, J.; Harrison, R.; Martens, P. Bibcode: 1989epos.conf....1P Altcode: Contents: 1. Introduction. 2. Magnetohydrodynamic instability. 3. Preflare magnetic and velocity fields. 4. Coronal manifestations of preflare activity. Title: Comparison of compressible and incompressible models of reconnection. Authors: Jardine, M.; Priest, E. R. Bibcode: 1989ESASP.285...45J Altcode: 1989rsp..conf...45J The authors consider two recent families of reconnection models, one for a compressible and one for an incompressible plasma and examine the differences between them. Title: Global energetics of fast magnetic reconnection Authors: Jardine, M.; Priest, E. R. Bibcode: 1988JPlPh..40..505J Altcode: We examine the global energetics of a recent weakly nonlinear theory of fast steady-state reconnection in an incompressible plasma (Jardine & Priest 1988). This is itself an extension to second order of the Priest & Forbes (1986) family of models, of which Petschek-like and Sonnerup-like solutions are special cases. While to first order we find that the energy conversion is insensitive to the type of solution (such as slow compression or flux pile-up), to second order not only does the total energy converted vary but so also does the ratio of the thermal to kinetic energies produced. For a slow compression with a strongly converging flow, the amount of energy converted is greatest and is dominated by the thermal contribution, while for a flux pile-up with a strongly diverging flow, the amount of energy converted is smallest and is dominated by the kinetic contribution. We also find that the total energy flowing out of the downstream region can be increased either by increasing the external magnetic Mach number Me or the external plasma beta βe Increasing Me also enhances the variations between different types of solutions. Title: Book Review: Cool stars, stellar systems and the sun. / Springer-Verlag, 1987 Authors: Priest, E. R. Bibcode: 1988Obs...108..234P Altcode: No abstract at ADS Title: Instability of a prominence supported in a linear force-free field Authors: Demoulin, P.; Priest, E. R. Bibcode: 1988A&A...206..336D Altcode: The authors analyse the equilibrium of a prominence by modelling it as a line of current under the action of gravity and of a two-dimensional constant force-free field. They show that a region of non-equilibrium may occur, if the field strength is great enough, for some distribution of the base flux. This occurs for both Kippenhahn-Schlüter and Kuperus-Raadu topologies and the region of non-equilibrium increases with the shear. Title: Weakly nonlinear theory of fast steady-state magnetic reconnection Authors: Jardine, M.; Priest, E. R. Bibcode: 1988JPlPh..40..143J Altcode: A family of models for fast steady-state reconnection has recently been presented by Priest and Forbes, of which the Petschek-like and Sonnerup-like solutions are special cases. This essentially linear treatment involves expanding about a uniform flow and field in powers of the external Alfvén Mach number Me, and hence is valid for small values of that parameter. To lowest order, the discrete slow-mode compressions attached to the diffusion region are straight, while downstream of them the plasma flows at simply the external Alfvén speed vAe and the field lines are straight. Here we present an extension of these solutions to the next order, which not only reveals that the wave itself is curved (as are the downstream magnetic field lines), but also that the downstream solution is sensitive to changes in the upstream boundary conditions. In the downstream solution there is a free parameter, which may be specified as a downstream boundary condition. Thus the boundary conditions at both the inflow and the outflow boundaries are crucial in determining the nature of the reconnection. Title: Nonuniform Magnetohydrodynamic Nature of the Solar Corona. I. Basic Solutions Authors: Priest, E. R. Bibcode: 1988ApJ...329.1009P Altcode: The highly structured nature of the solar corona is created largely by the magnetic field, and the author shows how such structure can be understood in terms of standing MHD disturbances of several types, spread over extended regions rather than being concentrated in narrow regions like shock waves. They can be compressions, in which the plasma pressure increases, or expansions in which it decreases. The compressions can be of fast-mode type if the magnetic field increases or of slow-mode type when it decreases, and vice-versa for the expansions. A general method is developed for describing these structures, and it is applied in simple examples to coronal plumes (fast-mode compressions), coronal holes or depletions (slow-mode compressions), the deflection of coronal rays (fast-mode compressions), and the legs of coronal mass ejections (fast-mode compressions). Title: The Initiation of Solar Coronal Mass Ejections by Magnetic Nonequilibrium Authors: Priest, E. R. Bibcode: 1988ApJ...328..848P Altcode: It is suggested that coronal mass ejections (CMEs) may be initiated when the plasma pressure of magnetic shear in a magnetic arcade (or helmet streamer) builds up so much that magnetic equilibrium is no longer possible. The resulting withdrawal of stabilizing magnetic field lines from the underlying prominence, as the CME moves out, then causes the prominence to rise slowly as a secondary effect, stretching out the neighboring field lines until reconnection allows a rapid eruption of the prominence - in the case of an active region prominence, this in turn may initiate a solar flare. Two simple examples of model coronal arcades are studied which suggest that eruption of arcades and therefore initiation of CMEs may be produced if the magnetic flux or axial plasma (or magnetic) pressure become too great or if the external plasma (or magnetic) pressure or temperature become too small. Title: Reverse currents in fast magnetic reconnection Authors: Jardine, Mira; Priest, Eric R. Bibcode: 1988GApFD..42..163J Altcode: It is suggested that reverse currents seen in recent numerical reconnection experiments (Biskamp, 1986; Forbes and Priest, 1983) are caused by the choice of outflow boundary conditions. The specification of the normal velocity at the outflow boundary may result in a mismatch in velocity at the diffusion region which is manifested as a spike of reverse current. Title: Coronal heating by relaxation in a sunspot magnetic field Authors: Dixon, A. M.; Browning, P. K.; Priest, E. R. Bibcode: 1988GApFD..40..293D Altcode: The heating by resistive turbulence of solar coronal magnetic fields is evaluated by means of the Taylor-Heyvaerts hypothesis, which enables one to calculate the evolution of the magnetic helicity and magnetic field in the corona in response to prescribed motions of the photospheric footpoints. The relationship between the photospheric velocity field and the helicity generation rate is considered for a coronal arcade and the energy release is proved to be positive definite in general. Also, the evolution and dissipation is determined for the axisymmetric magnetic field above a single sunspot which is being twisted up from below. Title: A 2D prominence model. Authors: Ballester, J. L.; Priest, E. R. Bibcode: 1988dssp.conf..137B Altcode: A two-dimensional magnetohydrostatic model of a vertical prominence sheet is set up by allowing slow variations of the magnetic field and plasma properties with height. The width of the prominence is found to decrase with height and in many cases the field lines become less curved, while the strength of the horizontal magnetic field increases with height, in agreement with some observations. Title: Dynamics and structure of solar prominences. Proceedings of the workshop held November 18 - 20, 1987, at the Universitat de les Illes Balears, Palma de Mallorca, Spain Authors: Ballester, J. L.; Priest, E. R. Bibcode: 1988dssp.conf.....B Altcode: No abstract at ADS Title: The eruption of a prominence and coronal transient. Authors: Steele, C. D. C.; Priest, E. R. Bibcode: 1988dssp.conf..157S Altcode: A model is set up for the eruption of a magnetically coupled prominence and coronal mass ejection. The prominence is modelled as a twisted flux tube and the transient as an overlying bubble. Stable equilibrium is found when the magnetic flux below the prominence is small. However, when a threshold flux is reached, the equilibrium ceases to exist so that the prominence and the transient accelerate upwards before reaching constant velocities. Title: Solar plasma physics. Authors: Priest, E. R. Bibcode: 1988PhB....39...66P Altcode: No abstract at ADS Title: Dynamics of magnetic and velocity fields in coronal loops. Authors: Krishan, V.; Berger, M.; Priest, E. R. Bibcode: 1988sscd.conf..236K Altcode: The coronal loop plasma is represented by a superposition of the three lowest order Chandrasekhar-Kendall modes. The temporal evolution of the velocity and magnetic field in each of these mode is determined using ideal MHD equations under two simplified cases viz (1) allowing small departures from the equilibrium and (2) the pump approximation. Title: Non equilibrium of a prominence current in a linear force free field. Authors: Demoulin, P.; Priest, E. Bibcode: 1988dssp.conf...45D Altcode: The authors analyse the equilibrium of a prominence by modelling it as a line of current under the action of gravity and of a two dimensional constant force free field. They show that a region of non equilibrium may occur, if the field strength is great enough, for some distribution of the base flux. This occurs for both Kippenhahn-Schluter and Kuperus-Raadu topologies and the region of non equilibrium increases with the shear. Title: Book Review: Instabilities in space and laboratory plasmas. / CUP, 1986. Authors: Priest, E. R. Bibcode: 1987Obs...107..228P Altcode: 1987Obs...107..228M No abstract at ADS Title: Book-Review - Solar System Magnetic Fields Authors: Priest, E. R.; Schrijver, J. Bibcode: 1987SoPh..108..417P Altcode: No abstract at ADS Title: Line-Tied Magnetic Reconnection Authors: Robertson, J. A.; Priest, E. R. Bibcode: 1987SoPh..114..311R Altcode: We present two-dimensional numerical simulations of magnetic reconnection in a configuration relevant to two-ribbon solar flares. The calculations extend those of Forbes and Priest (1982a, b, 1983) and some puzzling aspects of their results are clarified. In particular, the roles of magnetic diffusion, of the tearing mode and of turbulence are individually examined. We stress the important part played by boundary conditions in determining the evolution of the initial current sheet and suggest that in future the evolution of the entire overlying magnetic arcade be modelled as well as the current sheet that is created below the rising arcade. Tearing at very high magnetic Reynolds numbers is likely to develop into an impulsive bursty regime of reconnection after a time which depends on the initial level of turbulence. Title: A Two-Dimensional Model for a Solar Prominence Authors: Ballester, J. L.; Priest, E. R. Bibcode: 1987SoPh..109..335B Altcode: A two-dimensional magnetohydrostatic model of a vertical prominence sheet is set up by allowing slow variations of the magnetic field and plasma properties with height. The width of the prominence is found to decrease with height and in many cases the field lines become less curved, while the strength of the horizontal magnetic field increases with height, in agreement with observations. Since we are only considering a local analysis, the model applies to a general prominence sheet, whether of Kippenhahn-Schlüter or Kuperus-Raadu type. The challenge in the future is to understand the detailed fine-scale microstructure which takes place in the mould formed by the present global macro-models. Title: Dynamical Model of Prominence Formation and Oscillation - Part One Authors: Sakai, J.; Colin, A.; Priest, E. Bibcode: 1987SoPh..114..253S Altcode: We investigate a dynamical model of prominence formation in a current sheet at the boundary between two regions of opposite magnetic polarity. Coupled nonlinear equations describing the temporal compression and condensation of plasma in the current sheet are set up as a natural extension of the usual equations for current sheet collapse (Imshennik and Syrovatskii, 1967). It is shown that under certain conditions the current sheet undergoes a nonlinear oscillation during the compression. The thermal instability with cooling is driven by a density enhancement produced during the current sheet formation stage. Title: Book Review: The sun and the heliosphere in three dimensions. / Reidel, 1986. Authors: Priest, E. R. Bibcode: 1987Obs...107...35P Altcode: 1987Obs...107...35M No abstract at ADS Title: The effect of gravity on the stability of a line-tied coronal magnetohydrostatic equilibrium Authors: Melville, J. P.; Hood, A. W.; Priest, E. R. Bibcode: 1987GApFD..39...83M Altcode: The magnetohydrodynamic stability of a class of magnetohydrostatic equilibria is investigated. The effect of gravity is included as well as the stabilising influence of the dense photospheric line-tying. Although the two-dimensional equilibria exhibit a catastrophe point, when the ratio of plasma pressure to magnetic pressure exceeds a critical value, arcade structures, with both footpoints connected to the photosphere, become unstable to three-dimensional disturbances before the catastrophe point is reached. Numerical results for field lines that are open into the solar corona suggest that they are completely stable. Although there is no definite proof of stability, this would allow the point of non-equilibrium to be reached. Title: Appearance and Disappearance of Magnetic Flux at the Solar surface Authors: Priest, E. R. Bibcode: 1987rfsm.conf..297P Altcode: Theory and observation of the emergence and submergence of magnetic flux and the role of magnetic reconnection are briefly reviewed, together with a new unified theory for fast steady-state reconnection that has recently been proposed. New flux appears on a wide variety of scales due to magnetic buoyancy or convective motions. However, only a small fraction of the flux which emerges is likely to escape. Active regions seem to disappear by the fragmentation and cancellation of flux. Cancelling magnetic features (discovered by Sara Martin and coworkers) probably represent sites where magnetic flux is disappearing on small scales by reconnection submergence rather than by simple submergence. On large scales flux is also escaping in coronal transients and is probably submerging below quiescent prominences. Title: Magnetic Reconnection in Flares Authors: Priest, E. R. Bibcode: 1987sman.work..157P Altcode: A review of the basic theory of reconnection in current sheets is given, including current sheet formation, tearing modes, fast nonlinear reconnection regimes (such as the Petschek-Sonnerup, flux pile-up and impulsive bursty regimes) and recent numerical experiments. Title: The Eruption of a Prominence and Coronal Transient Authors: Steele, C.; Priest, E. R. Bibcode: 1987dssp.work..157S Altcode: 1987ASSL..150..157S No abstract at ADS Title: Solar magneto-hydrodynamics. Authors: Priest, E. R. Bibcode: 1987smh..book.....P Altcode: No abstract at ADS Title: A Two-Dimensional Prominence Model Authors: Ballester, J. L.; Priest, E. R. Bibcode: 1987dssp.work..137B Altcode: 1987ASSL..150..137B No abstract at ADS Title: Theoretical Description of Magnetic Fields Authors: Priest, E. Bibcode: 1987mfeo.conf...17P Altcode: 1991mfeo.conf...17P No abstract at ADS Title: Nonequilibrium of a Prominence Current in a Linear Force-Free Field Authors: Demoulin, P.; Priest, E. R. Bibcode: 1987dssp.work...45D Altcode: 1987ASSL..150...45D No abstract at ADS Title: Magnetohydrodynamic instability Authors: Priest, E. R.; Cargill, P.; Forbes, T. G.; Hood, A. W.; Steinolfson, R. S. Bibcode: 1986epos.conf..1.3P Altcode: 1986epos.confA...3P There have been major advances in the theory of magnetic reconnection and of magnetic instability, with important implications for the observations, as follows: (1) Fast and slow magnetic shock waves are produced by the magnetohydrodynamics of reconnection and are potential particle accelerators. (2) The impulsive bursty regime of reconnection gives a rapid release of magnetic energy in a series of bursts. (3) The radiative tearing mode creates cool filamentary structures in the reconnection process. (4) The stability analyses imply that an arcade can become unstable when either its height or twist of plasma pressure become too great. Title: The Preflare State Authors: Priest, E. R.; Gaizauskas, V.; Hagyard, M. H.; Schmahl, E. J.; Webb, D. F. Bibcode: 1986epos.conf..1.1P Altcode: 1986epos.confA...1P No abstract at ADS Title: Book-Review - Solar System Magnetic Fields Authors: Priest, E. R.; Russell, C. T. Bibcode: 1986SSRv...44..394P Altcode: No abstract at ADS Title: The Shape of Buoyant Coronal Loops in a Magnetic Field and the Eruption of Coronal Transients and Prominences Authors: Browning, P. K.; Priest, E. R. Bibcode: 1986SoPh..106..335B Altcode: The equilibrium and non-equilibrium properties of a coronal loop embedded in a stratified isothermal atmosphere are investigated. The shape of the loop is determined by a balance between magnetic tension, buoyancy, and external pressure gradients. The footpoints of the loop are anchored in the photosphere; if they are moved too far apart, no equilibrium is possible and the loop erupts upwards. This critical separation is independent of the pressure differential between the loop and the external medium if the loop has enhanced magnetic field, but varies if instead the loop pressure is increased. The maximum width is proportional to the larger of the gravitational scale-height and the length-scale of the ambient field. In some circumstances, it is shown that multiple solutions exist for the tube path. These results may be relevant to the eruption of prominences during the preflare phase of two-ribbon flares and to the onset of coronal loop transients. Such eruptions may occur if the footpoint separation, internal pressure or internal magnetic field are too great. Title: Book-Review - Solar System Magnetic Fields Authors: Priest, E. R. Bibcode: 1986S&T....72...41P Altcode: No abstract at ADS Title: The Ideal Magnetohydrodynamic Stability of a Line-Tied Coronal Magnetohydrostatic Equilibrium Authors: Melville, J. P.; Hood, A. W.; Priest, E. R. Bibcode: 1986SoPh..105..291M Altcode: An energy method is used to determine a condition for local instability of field lines in magnetohydrostatic equilibrium which are rooted in the photosphere. The particular equilibrium studied is isothermal and two-dimensional and may model a coronal arcade of loops where variations along the axis of the arcade are weak enough to be ignorable. If line tying conditions are modelled by perturbations that vanish on the photosphere, then, when the field is unsheared, the condition for stability is necessary and sufficient. However, when the axial field component is non-zero, so that the field is sheared, the stability condition is only sufficient. Title: Book-Review - Solar System Magnetic Fields Authors: Priest, E. R. Bibcode: 1986Sci...232.1656P Altcode: No abstract at ADS Title: New models for fast steady state magnetic reconnection Authors: Priest, E. R.; Forbes, T. G. Bibcode: 1986JGR....91.5579P Altcode: A new unified family of models for incompressible, steady state magnetic reconnection in a finite region is presented. They are obtained by expanding in powers of the Alfvén Mach number and may be used to elucidate some of the puzzling properties of numerical experiments on reconnection which are not present in the classical models. The conditions imposed on the inflow boundary of the finite region determine which member of the family occurs. Petscheklike and Sonneruplike solutions are particular members. The Sonneruplike regime is a special case of a weak slow mode expansion in the inflow region, and it separates two classes of members with reversed currents. These are the hybrid regime with a mixture of strong fast mode and slow mode expansions and the flux pileup regime with a stong slow mode expansion, in which the magnetic field strength increases as it approaches the diffusion region and the flow diverges. The Petscheklike regime is a singular case of a weak fast mode expansion, and it separates the hybrid regime from a regime of slow mode compressions. The hybrid expansions are fast mode in character in the center of the inflow and slow mode near the edges of the region, while the flux pileup expansions possess long thin diffusion regions and no maximum reconnection rate. The maximum rate is calculated for the other solutions as a function of the magnetic Reynolds number and compared with the classical Sweet-Parker and Petschek rates. For the flux pileup and hybrid regimes, reconnection can be ;much faster than the maximum Petschek rate. Care should be taken in deciding which type of reconnection is operating in a numerical experiment. Indeed, no experiment to date has used boundary conditions appropriate for demonstrating steady state Petschek reconnection. Title: Viscous Normal Modes on Coronal Inhomogeneities and Their Role as a Heating Mechanism Authors: Steinolfson, R. S.; Priest, E. R.; Poedts, S.; Nocera, L.; Goossens, M. Bibcode: 1986ApJ...304..526S Altcode: Viscous damping of Alfven surface waves is examined both analytically and numerically using incompressible MHD. Normal modes are shown to exist on discontinuous as well as continuously varying interfaces in Alfven speed. The waves experience negligible decay below the transition zone. High-frequency waves damp just above the transition region, while those of lower frequency lose energy further out. A comparison of dissipative decay rates shows that wave damping by viscosity proceeds approximately two orders of magnitude faster than by resistivity. Title: Coronal heating in closely-packed flux tubes: a Taylor-Heyvaerts relaxation theory. Authors: Browning, P. K.; Sakurai, T.; Priest, E. R. Bibcode: 1986A&A...158..217B Altcode: The aim of this paper is to take a more quantitative and detailed look at dissipation in an array of closely-packed flux tubes. An initially potential coronal loop is investigated, whose footpoints are twisted up by cellular photospheric motions, forming a network of twisted flux tubes. The motions are assumed to be slow compared with the reconnection time-scale, so that the stressed field reconnects and dissipates some of its energy as heat. The generalised Taylor's hypothesis is used to investigate the effects of reconnection on the flux tubes and to determine the efficiency of the dissipation. A basic mathematical model is set up and the procedure for calculating the evolution is outlined. The authors investigate the response of the field to the footpoint motions and evaluate the heating produced. The results are discussed, applications to the coronal heating problem are considered, and the predictions are compared with the known heating requirements of the corona. Title: Magnetic field-line reconnection with jets Authors: Soward, A. M.; Priest, E. R. Bibcode: 1986JPlPh..35..333S Altcode: Some recent numerical simulations of driven magnetic field-line reconnection by Biskamp show no evidence of the Petschek mechanism when the reconnection rate or magnetic Reynolds number are large. Instead, an electric current sheet forms on the symmetry axis, across which a magnetic field is annihilated. The sheet terminates at a Y-point. Fluid driven into the current sheet escapes as jets along the separatrices emanating from the Y-point. This paper shows how many of the features such as the jets can be explained by a simple analytical model. Since the numerical simulations are necessarily on a bounded domain, the importance of the external boundary conditions in setting up a steady-state solution is stressed by illustrative examples. Title: Heating of coronal arcades by magnetic tearing turbulence, using the Taylor-Heyvaerts hypothesis Authors: Browning, P. K.; Priest, E. R. Bibcode: 1986A&A...159..129B Altcode: The heating of the solar corona by direct currents, which are dissipated by magnetic reconnection, is studied. The coronal field responds to slow photospheric motions by evolving through a series of equilibria, which may be unstable to resistive modes. According to a generalization of Taylor's hypothesis (Heyvaerts and Priest, 1984), the field reconnects and relaxes to a linear force-free state (satisfying Delta X B = alpha B), where the parameter alpha is uniform. During the relaxation process, the field reconnects and dissipates some magnetic energy as heat. The value of alpha at each time and the energy released during relaxation may be determined from the evolution of magnetic helicity. Two theorems concerning this method are proved: First, the invariance of the method with respect to gauge transformations of the vector potential is discussed, and it is shown that the helicity evolution equation in any gauge predicts the same evolution of the field. Second, it is shown that the energy release always vanishes in the limit of infinitely fast reconnection. It is found that similar footpoint motions heat an arcade more efficiently if it is already strongly sheared, such as in a rapidly evolving active region. The general conclusion is that tearing turbulence is a viable heating mechanism for the solar corona. Title: Magnetohydrodynamic Theories of Solar Flares Authors: Priest, E. R. Bibcode: 1986SoPh..104....1P Altcode: Our current understanding of the MHD of the flare process is summarised, with some emphasis on processes which produce strong impulsive electric fields and current filamentation. As an introduction, a description of the two main types of flare (i.e., simple-loop and two-ribbon) is given, together with an account of the two branches of reconnection theory (tearing modes and the Petschek-Sonnerup mechanism). Modern numerical experiments of reconnection suggest impulsive bursty acceleration of particles in many small regions of width a hundred kilometres or less. This is followed by a discussion of the eruptive instability thought to initiate a large flare and of the reconnection process of energy release. Finally, the role of emerging flux and horizontally moving satellite sunspots is discussed briefly. Title: Criteria for the stability of a line-tied magnetohydrostatic equilibrium in the solar corona Authors: Melville, J.; Hood, A.; Priest, E. R. Bibcode: 1986AdSpR...6f..49M Altcode: 1986AdSpR...6...49M Arcades of loop structures in the solar corona have been associated with the onset of solar flares. Changes in the plasma and/or magnetic pressure could initiate a flare if the equilibrium structure becomes unstable. It is shown that for a model magnetohydrostatic equilibrium, if the plasma β > β* where β* is the β-value for which a magnetic island just appears on the photosphere, then the closed field lines and some field lines tied to the photosphere are unstable to localised linear perturbations. If the field remains unsheared by photospheric motions, then the condition β < β* for stability is necessary and sufficient. Title: Preflare activity. Authors: Priest, E. R.; Gaizauskas, V.; Hagyard, M. J.; Schmahl, E. J.; Webb, D. F.; Cargill, P.; Forbes, T. G.; Hood, A. W.; Steinolfson, R. S.; Chapman, G. A.; Deloach, A. C.; Gary, G. A.; Jones, H. P.; Karpen, J. T.; Martres, M. -J.; Porter, J. G.; Schmieder, B.; Smith, J. B., Jr.; Toomre, J.; Woodgate, B.; Waggett, P.; Bentley, R.; Hurford, G.; Schadee, A.; Schrijver, J.; Harrison, R.; Martens, P. Bibcode: 1986NASCP2439....1P Altcode: Contents: 1. Introduction: the preflare state - a review of previous results. 2. Magnetohydrodynamic instability: magnetic reconnection, nonlinear tearing, nonlinear reconnection experiments, emerging flux and moving satellite sunspots, main phase reconnection in two-ribbon flares, magnetic instability responsible for filament eruption in two-ribbon flares. 3. Preflare magnetic and velocity fields: general morphology of the preflare magnetic field, magnetic field shear, electric currents in the preflare active region, characterization of the preflare velocity field, emerging flux. 4. Coronal manifestations of preflare activity: defining the preflare regime, specific illustrative events, comparison of preflare X-rays and ultraviolet, preflare microwave intensity and polarization changes, non-thermal precursors, precursors of coronal mass ejections, short-lived and long-lived HXIS sources as possible precursors. Title: Book-Review - Solar Flare Magnetohydrodynamics - the Fluid Mechanics of Astrophysics and Geophysics - Volume I Authors: Priest, E. R.; Staude, H. Bibcode: 1986AN....307..288P Altcode: No abstract at ADS Title: Magnetic Reconnection on the Sun Authors: Priest, E. R. Bibcode: 1986MitAG..65...41P Altcode: A brief review is given of the process of magnetic reconnection on the Sun, where it can convert magnetic energy into heat and other forms and where it is probably responsible for solar flares and coronal heating. Recent numerical experiments are linking the classical theory of resistive instability and fast steady-state reconnection and are revealing a regime of impulsive bursty reconnection. The current discoveries about plasma behaviour on the Sun are potentially of great value for the rest of astrophysics. Title: Nonlinear development of phase-mixed alfvén waves Authors: Nocera, L.; Priest, E. R.; Hollweg, J. V. Bibcode: 1986GApFD..35..111N Altcode: We derive an equation governing the nonlinear propagation of a linearly polarized Alfvén wave in a two-dimensional, anisotropic, slightly compressible, highly magnetized, viscous plasma, where nonlinearities arise from the interaction of the Alfvén wave with fast and slow magnetoacoustic waves. The phase mixing of such a wave has been suggested as a mechanism for heating the outer solar atmosphere (Heyvaerts and Priest, 1983). We find that cubic wave damping dominates shear linear dissipation whenever the Alfvén wave velocity amplitude vy exceeds a few times ten metres per second. In the nonlinear regime, phase-mixed waves are marginally stable, while non-phase-mixed waves of wavenumber ka are damped over a timescale kuRe0|δ vy/vA|-2, Re0 being the Reynolds number corresponding to the Braginskij viscosity coefficient η0 and vA the Alfvén speed. Dissipation is most effective where β = (vs/vA)2 ≈ 1, vs being the speed of sound. Title: Onset of an energy cascade and nonperiodic behaviour in the nonlinear propagation of MHD waves in the solar atmosphere Authors: Nocera, Luigi; Priest, Eric R. Bibcode: 1986GApFD..37..193N Altcode: We study the nonlinear stability of MHD waves propagating in a two-dimensional, compressible, highly magnetized, viscous plasma. These waves are driven by a weak, shear body force which could be imposed by large scale internal fluctuations present in the solar atmosphere. The effects of anisotropic viscosity (leading to a cubic damping) and of the nonlinear coupling of the Alfven and the magnetoacoustic waves are analysed using Galerkin and multiple-scale analysis: the MHD equations are reduced to a set of nonlinear ordinary differential equations which is then suitably truncated to give a model dynamical system, representing the interaction of two complex Galerkin modes. For propagation oblique to the background magnetic field, analytical integration shows that the low-wavenumber mode is physically unstable. For propagation parallel to the background magnetic field the high-wavenumber wave can undergo saddlenode bifurcations, in way that is similar to the van der Pol oscillator; these bifurcations lead to the appearance of a hysteresis cycle. A numerical integration of the dynamical system shows that a sequence of Hopf bifurcations takes place as the Reynolds number is increased, up to the onset of nonperiodic behaviour. It also shows that energy can be transferred from the low- wavenumber to the high-wavenumber mode. Title: The MHD of solar flares. Authors: Priest, E. R. Bibcode: 1986RALR...85..140P Altcode: The object of this review is to summarize the kind of problems that are met when studying the magnetohydrodynamics of solar flares. Comments are given on flare observations of relevance and recent developments in basic magnetic reconnection theory are reviewed. Title: Magnetic Reconnection Authors: Priest, E. Bibcode: 1986ppm..conf....1P Altcode: A brief review is given of reconnection on the sun, where it is probably responsible for a wide variety of phenomena including coronal heating, solar flares and the newly discovered cancelling magnetic features. Title: Role of magnetic reconnection in solar flares Authors: Priest, E. R. Bibcode: 1986AdSpR...6f..73P Altcode: 1986AdSpR...6...73P The behaviour of the magnetic field in the solar atmosphere is governed by the equations of MHD rather than the electromagnetism of wires. In particular, the roles of magnetic reconnection are: to create small flares; to trigger large flares; and to release magnetic energy in large flares. Observational evidence for reconnection is reviewed together with recent theory and observation of (post-) flare loops, which enable one to deduce the reconnection electric field from the motion of either the flare loops or Hα ribbons. Also, an account is given of a new unified theory for fast steady-state reconnection which includes the Sweet-Parker, Petschek and Sonnerup-like models as special cases. Title: Corrigendum Authors: Forbes, T. G.; Priest, E. R.; Hood, A. W. Bibcode: 1985JPlPh..34..481F Altcode: Numerical solutions were obtained by Forbes, Priest & Hood (1982) for the resistive decay of a current sheet in an MHD fluid. To check the accuracy of the numerical solutions, a linear, analytical solution was also deived for the regime where diffusion is dominant. In a subsequent reinvestigation of this problem an error in the linear, analytical solution has been discovered. For the parameter values used in the numerical solution this error is too small ( 2%) to produce any significant change in the previous test comparison between the numerical and analytical solutions. However, for parameter values much different from those used in the numerical solution, the error in the linear solution can be significant. Title: REVIEW ARTICLE: The magnetohydrodynamics of current sheets Authors: Priest, E. R. Bibcode: 1985RPPh...48..955P Altcode: Examples of current sheets are summarized and their formation is described. A universal phenomenon in cosmic plasmas is the creation of sheets off intense current near X-type neutral points (where the magnetic field vanishes). These sheets are important as sites where the magnetic-field energy is converted efficiently into heat and bulk kinetic energy and where particles can be accelerated to high energies. Examples include disruptions in laboratory tokamaks, substorms in the earth's magnetosphere, and flares on the sun. The basic behavior of a one-dimensional sheet is presented, together with an account of the linear tearing-mode instability that can cause the field lines in such a sheet to reconnect. Such reconnection may develop in different ways: it may arise from a spontaneous instability or it may be driven, either from outside by motions or locally by a resistivity enhancement. Various processes are described that may occur during the nonlinear development of tearing, along with the many numerical and laboratory experiments that are aiding our understanding of this intriguing cosmical process. Title: Small-Scale Reconnection Authors: Priest, E. R. Bibcode: 1985ESASP.235..137P Altcode: 1985fmsh.work..137P; 1985shpp.rept..137P The basic theory of reconnection consists of two branches, namely linear tearing modes and the fast nonlinear state of Petschek-Sonnerup reconnection. Recent developments have linked them and have revealed two fast unsteady regimes, namely the flux pile-up regime and the impulsive bursty regime. Applications include: mini flux-transfer events discovered by the AMPTE satellite at the magnetopause; cancelling magnetic features in photospheric magnetograms from Big Bear Solar Observatory; and the heating of the solar corona by tearing turbulence at many small current sheets. Title: Remarks on the Magnetic Support of Quiescent Prominences Authors: Anzer, U.; Priest, E. Bibcode: 1985SoPh...95..263A Altcode: The development of magnetic field structures which can lead to prominence configurations of the Kuperus-Raadu type is discussed. Starting from streamer type configurations and preserving the total current in the system we find that simple two-dimensional static configurations lead to prominences which in general lie systematically much lower than the heights found from observations. We therefore conclude that either more complex field configurations are needed to explain the recent observations by Leroy et al. (1983) or the initial configurations must be very special. Title: Introduction to solar activity. Authors: Priest, E. R. Bibcode: 1985ssmf.conf....1P Altcode: The article summarises some of the basic properties of the sun, reminds the reader of the magnetohydrodynamic equations and outlines some of the major problems in solar activity. Title: The Magnetohydrodynamics of Solar Flares Authors: Priest, E. R. Bibcode: 1985spit.conf...73P Altcode: No abstract at ADS Title: Current sheets in solar flares Authors: Priest, E. R. Bibcode: 1985IAUS..107..233P Altcode: Until recently magnetic reconnection in solar flares was discussed simplistically in terms of either a spontaneous tearing mode instability or a driven Petschek mode. Now the subtle relationship between these two extremes is much better understood. Current sheets may form and reconnection may be initiated in many different ways. There are also a variety of nonlinear pathways from a reconnection instability and several types of driven reconnection. In solar flares current sheets may be important as new flux emerges from below the photosphere and also as a magnetic arcade closes down after being blown open by an eruptive instability. Numerical simulations of these sheets are described. Title: Phase Mixing of Propagating Alfven Waves Authors: Nocera, L.; Leroy, B.; Priest, E. R. Bibcode: 1985IAUS..107..365N Altcode: Among MHD waves, Alfvén waves have been proved to be the best candidates to reach the solar corona and, eventually, to be responsible for the heating of this outer part of the solar atmosphere. The problem concerning the mechanism able to transform the energy stored in the waves into heat is considered. Title: Coronal heating in closely packed flux tubes: a Taylor-Heyvaerts relaxation theory. Authors: Browning, P. K.; Sakurai, T.; Priest, E. R. Bibcode: 1985MPARp.181.....B Altcode: No abstract at ADS Title: Solar system magnetic fields. Based on lectures presented at the Summer School on Solar System Plasmas, held at Imperial College, London, September 1984. Authors: Priest, E. R. Bibcode: 1985ssmf.conf.....P Altcode: The physics of solar-system plasmas is explored in introductory chapters reviewing the results of recent theoretical investigations and observational studies. Topics examined include solar activity, magnetospheric MHD, MHD waves, MHD instabilities, magnetic reconnection, magnetoconvection, dynamo theory, the solar wind and the earth bow shock, planetary magnetospheres, and comets. Graphs, photographs, diagrams, and drawings are provided. Title: Coronal heating by turbulent phase mixed MHD waves. Authors: Nocera, L.; Priest, E. R. Bibcode: 1984ESASP.220..249N Altcode: 1984ESPM....4..249N The authors study the possibility of transferring mechanical and magnetic energy from MHD waves propagating in the solar corona to smaller and smaller scales via nonlinear effects, starting from a phase-mixed configuration. The efficiency of this turbulent cascade and the turbulent spectra (both in space and time) are worked out numerically. The time spectrum suggests the onset of chaotic behaviour. The resulting heating rate meets the energetic requirements to heat the corona. Title: A numerical simulation of the formation of solar prominences. Authors: Malherbe, J. M.; Forbes, T. G.; Priest, E. R. Bibcode: 1984ESASP.220..119M Altcode: 1984ESPM....4..119M The radiative-resistive MHD equations are numerically solved in two-dimensions for a magnetic field configuration that starts with a vertical current sheet which is line-tied at its base and is in mechanical, but not radiative, equilibrium. The aim of the present study is to determine whether this initial configuration can achieve a prominence-like equilibrium in the presence of magnetic reconnection and tearing in the current-sheet. Title: The development and cooling of a solar limb-flare Authors: Veck, N. J.; Strong, K. T.; Jordan, C.; Simnett, G. M.; Cargill, P. J.; Priest, E. R. Bibcode: 1984MNRAS.210..443V Altcode: Observations of a flare that began in soft X-rays at 20:37 UT on 1980 April 12, at the west limb of the Sun are discussed. The Solar Maximum Mission (SMM) satellite was used to obtain X-ray images before the flare and for a period during the decay phase. Hα photographs and the soft X-ray flux measured by the GOES-3 satellite are available throughout the flare. Some alternative models are discussed but insufficient data are available for a full treatment. Overall, the observations are best fitted qualitatively by a model where pre-existing magnetic loop structures are perturbed by the intrusion of new magnetic flux. Title: Numerical Simulation of Reconnection in an Emerging Magnetic Flux Region Authors: Forbes, T. G.; Priest, E. R. Bibcode: 1984SoPh...94..315F Altcode: The resistive MHD equations are numerically solved in two dimensions for an initial-boundary-value problem which simulates reconnection between an emerging magnetic flux region and an overlying coronal magnetic field. The emerging region is modelled by a cylindrical flux tube with a poloidal magnetic field lying in the same plane as the external, coronal field. The plasma betas of the emerging and coronal regions are 1.0 and 0.1, respectively, and the magnetic Reynolds number for the system is 2 × 103. At the beginning of the simulation the tube starts to emerge through the base of the rectangular computational domain, and, when the tube is halfway into the computational domain, its position is held fixed so that no more flux of plasma enters through the base. Because the time-scale of the emergence is slower than the Alfvén time-scale, but faster than the reconnection time-scale, a region of closed loops forms at the base. These loops are gradually opened and reconnected with the overlying, external magnetic field as time proceeds. Title: Coronal heating by reconnection in DC current systems - A theory based on Taylor's hypothesis Authors: Heyvaerts, J.; Priest, E. R. Bibcode: 1984A&A...137...63H Altcode: The rate of coronal heating expected from complex reconnection processes is analyzed by adapting Taylor's hypothesis to solar and stellar physical conditions. The fact that the magnetic helicity of a region which is not a closed flux tube is not a gauge-invariant quantity is addressed, and the time evolution of a magnetic arcade undergoing slow footpoint motions and infinitely rapid relaxation by reconnection is calculated. It is shown that, when the stresses are relaxed instantaneously the amount of heating vanishes exactly. A second order theory is developed which permits the heating effect due to a small but finite reconnection time to be calculated. It is concluded that DC current coronal heating is mainly due to motions comparable in size to or smaller than the characteristic size of the magnetic structure, and that these motions must tend to produce a nonconstant alpha force-free magnetic structure. The theory illuminates the connection between general coronal heating and solar flares. Title: Book-Review - Solar Magnetohydrodynamics Authors: Priest, E. R.; Livshits, M. A. Bibcode: 1984SvA....28..484P Altcode: No abstract at ADS Title: The Magnetic Non-Equilibrium of Buoyant Flux Tubes in the Solar Corona Authors: Browning, P. K.; Priest, E. R. Bibcode: 1984SoPh...92..173B Altcode: The equilibrium shape of a slender flux tube in the stratified solar atmosphere is studied. The path is determined by a balance between the downwards magnetic tension, which depends on the curvature of the loop, and the upwards buoyancy force. Previous results for untwisted slender tubes are extended to include twisted tubes embedded in an external magnetic field. Title: Magnetohydrostatic Structures in the Solar Atmosphere Authors: Melville, J. P.; Hood, A. W.; Priest, E. R. Bibcode: 1984SoPh...92...15M Altcode: Separable two-dimensional solutions to the isothermal magnetohydrostatic equations are presented which include the effect of gravity. Examples of three types of linear solution are given in which photospheric magnetic fields are prescribed and the field topologies are discussed. In addition, a new nonlinear solution is discussed. The functional form of the pressure distribution is restricted by the separable assumption. An analysis suggests that these are the only separable analytical solutions. Title: Phase mixing of propagating Alfven waves Authors: Nocera, L.; Priest, E. R.; Leroy, B. Bibcode: 1984A&A...133..387N Altcode: The fundamental wave solution found by Heyvaerts and Priest (1983) for the propagation and damping of shear Alfven waves in an inhomogeneous medium is checked against their assumptions, and a range of self-consistency is provided. By analyzing wave behavior outside this range, novel wave propagation properties are discovered. In the limit of weak damping, a uniformly valid solution is obtained by the method of multiple scales. For long wavelengths, the diffusion of energy in the direction transverse to the wave propagation is found to be important, and leads to weaker damping laws than those found by Heyvaerts and Priest. Title: Book-Review - Solar and Stellar Magnetic Fields - Origins and Effects - I.A.U. Symposium NO.102 Authors: Stenflo, J. O.; Priest, E. R. Bibcode: 1984Obs...104..102S Altcode: No abstract at ADS Title: Global magnetohydrostatic fields in stellar atmosphere Authors: Browning, P. K.; Priest, E. R. Bibcode: 1984GApFD..28..141B Altcode: The equilibrium properties of the magnetic field of an axisymmetric star are studied. A family of analytical solutions to the magnetohydrostatic equations is found, which are used to model the slow evolution of the field through a series of equilibria. Firstly, a model is set up for a force-free dipole-like field, which has a toroidal field component; it is found that, as such a field is twisted up, a critical point is reached, at which the field topology changes. If the twist is increased beyond this point, there is no physically reasonable equilibrium. Next, an untwisted magnetostatic dipole-like field is studied, with an increasing pressure differential between pole and equator. A critical point again occurs when the pressure differential becomes too large. Finally a force-free quadrupole-like field is modelled, which is being twisted up, for example by differential rotation; this has similar properties to the dipole-like field. In each case, it is suggested that, when the critical point is reached, the field will no longer evolve smoothly, but will change catastrophically to a new stable, releasing energy. Such an event could represent the onset of a stellar flare or some other dynamic stellar process. Title: Book-Review - Solar Magnetohydrodynamics Authors: Priest, E. R.; Jordan, C. Bibcode: 1984Obs...104...32P Altcode: No abstract at ADS Title: Kelvin-Helmholtz instability of a phased-mixed Alfven wave Authors: Browning, P. K.; Priest, E. R. Bibcode: 1984A&A...131..283B Altcode: The development of the Kelvin-Helmholtz instability at the velocity antinodes of a standing Alfven wave is studied. The problem is investigated at large times, when the velocity profile has a sinusoidal form, and at the onset of instability. At large times it is found that the growth rates of the sinusoidal profile are much smaller, and that the most unstable wavelengths are about 12 times the phase-mixed velocity inhomogeneity length scale, whereas for the square wave, short waves are the most unstable. In a temporally local stability analysis, a critical time is found after which the instability grows significantly within one Alfven wave period. This critical time is related to the dimensionless wave frequency Omega1 = (k-parallel)(a)/M, where k-parallel is the Alfven wavenumber and M is the magnetic Mach number. The growth rate of the instability is determined as a function of time for several values of Omega1, and the critical time is found at which the growth rate is equal to the wave frequency. It is shown that the instability develops within very few wave periods, thus it is expected that a shear Alfven wave would rapidly be disrupted by Kelvin-Helmholtz instability. Title: Role of newly emerging flux in the flare process Authors: Priest, E. R. Bibcode: 1984AdSpR...4g..37P Altcode: 1984AdSpR...4...37P New flux emerging from below the photosphere is believed to give rise to small flares and also to be capable of triggering large events when extra energy is stored in the overlying field. A summary is given of the observations of emerging flux, together with the current theoretical ideas on its behaviour. Title: Magnetic reconnection at the sun Authors: Priest, E. R. Bibcode: 1984GMS....30...63P Altcode: Theoretical models of magnetic reconnection processes in the sun are reviewed and illustrated with diagrams, drawings, graphs, and visual and X-ray images. Topics examined include pathways to reconnection (nonlinear development of tearing instabilities; ideal versus resistive instability; and Petschek-Sonnerup, supercritical/flux-pile-up, and impulsive-bursty regimes of fast reconnection), quiescent solar prominences, coronal heating, (wave heating and tearing turbulence in slowly evolving fields), and solar flares (observations, small flares with emerging flux, and large two-ribbon flares). Some important similarities between solar and magnetospheric phenomena are indicated. Title: Report of ESA's topical team on solar and heliospheric physics. Authors: Christensen-Dalsgaard, J.; Delache, P.; Hoyng, P.; Priest, E. R.; Schwenn, R.; Stenflo, J. O. Bibcode: 1984ESASP1070...26C Altcode: No abstract at ADS Title: Magnetic Reconnection at the Sun Authors: Priest, E. R. Bibcode: 1984mrsl.conf...63P Altcode: No abstract at ADS Title: Book-Review: Solar Magnetohydrodynamics Authors: Priest, E. R.; Martens, P. C. H. Bibcode: 1984Ruimt..33..119P Altcode: No abstract at ADS Title: Solar magneto-hydrodynamics Authors: Priest, Eric Ronald Bibcode: 1984smh..book.....P Altcode: No abstract at ADS Title: Reconnection of magnetic fields. Authors: Sonnerup, B. U. Ö.; Baum, P. J.; Birn, J.; Cowley, S. W. H.; Forbes, T. G.; Hassam, A. B.; Kahler, S. W.; Matthaeus, W. H.; Park, W.; Paschmann, G.; Priest, E. R.; Russell, C. T.; Spicer, D. S.; Stenzel, R. Bibcode: 1984NASRP1120....1S Altcode: No abstract at ADS Title: Remarks on the magnetic support of quiescent prominences. Authors: Anzer, U.; Priest, E. Bibcode: 1984MPARp.157.....A Altcode: No abstract at ADS Title: Book-Review - Cosmic Electrodynamics Authors: Piddington, J. H.; Priest, E. R. Bibcode: 1983SSRv...36..422P Altcode: No abstract at ADS Title: Book-Review - Solar Magnetohydrodynamics Authors: Priest, E. R.; Kuperus, M. Bibcode: 1983SSRv...36..424P Altcode: No abstract at ADS Title: BOOK REVIEW: Solar Magnetohydrodynamics Authors: Gokhale, M. H.; Priest, E. R. Bibcode: 1983BASI...11..347G Altcode: No abstract at ADS Title: Book-Review - Solar Magnetohydrodynamics Authors: Priest, E. R.; Karlicky, M. Bibcode: 1983BAICz..34..378P Altcode: No abstract at ADS Title: Book reviews Authors: Kleczek, J.; Nussbaumer, H.; van der Hucht, K. A.; De Greve, J. P.; Ooms, G.; Rutten, R. J.; van der Laan, H.; Jäger, F. W.; Reijnen, G. C. M.; Bijleveld, W.; Kistemaker, J.; de Jager, C.; Mustel, E. R.; Ne'Eman, Y.; Priest, E. R.; Stiller, H.; Seifert, W.; Namba, O.; Kuperus, M.; Hoekstra, Roel; Stumpers, F. L. H. M.; Frank, S.; Zimmerman, J. T. F.; De Loore, C.; Gendrin, R.; Schrijver, J.; Mulder, P. S.; Pounds, K. A.; Young, R. S.; Houziaux, L.; Engvold, O.; Bok, B. J.; de Graaff, W. Bibcode: 1983SSRv...36..415K Altcode: No abstract at ADS Title: Current sheet models for solar prominences. II - Energetics and condensation process Authors: Malherbe, J. M.; Priest, E. R.; Forbes, T. G.; Heyvaerts, J. Bibcode: 1983A&A...127..153M Altcode: A steady state dynamic model for solar prominences of the Kuperus and Raadu type was previously proposed by Malherbe and Priest (1983), but only the motion through series of quasi-static states was investigated there. The mechanisms for formation, condensation and cooling of plasma in this model are studied. As hot coronal material approaches the filament sheet, it is expected to cool and condense. Cold material is then carried up through the prominence by rising magnetic field lines due to converging photospheric motions below the filament. Two possible ways are suggested of triggering a thermal instability and so producing such a stationary condensation process: a larger pressure in the sheet, or a smaller wave heating in the reconnected field than in the surrounding corona. This paper presents a simple model to simulate the plasma condensation: the thermodynamics of the cooling process, as well as the dynamics of new material entering the prominence sheet, are described in detail. Title: Mass upflows in `post'-flare loops Authors: Forbes, T. G.; Priest, E. R. Bibcode: 1983SoPh...88..211F Altcode: A self-consistent numerical model of a reconnecting magnetic field configuration similar to that occurring during the main-phase of two-ribbon flares is used to estimate the upflow caused by the fast-mode expansion of the magnetic field moving into the reconnection region. Such an expansion creates a field-aligned pressure gradient which accelerates plasma upward from the chromospheric base of magnetic field lines in the region external to the loops. The numerical results imply that the amount of mass sucked up in this way is even smaller than was previously estimated by Kopp and Pneuman who used a kinematic model. Therefore, some indirect mechanism (such as evaporation), which would probably derive its motive power from the thermal energy generated by the reconnection, is required to explain the large mass upflows inferred from observations. Title: Solar and stellar magnetic fields Authors: Priest, E. R.; Weiss, N. O. Bibcode: 1983Obs...103..239P Altcode: No abstract at ADS Title: Magnetic equilibrium in coronal arcades. Authors: Melville, J. P.; Hood, A. W.; Priest, E. R. Bibcode: 1983SoPh...87..301M Altcode: An analytical solution to the magnetohydrostatic equations is presented that generalises a solution due to Birn et al. (1978) to include the effect of gravity. There exist two solutions to the same boundary conditions for small base pressures. If the base pressure exceeds a critical value, then `non-equilibrium' may occur and initiate a two-ribbon flare. Title: Magnetic Theories of Solar Flares Authors: Priest, E. R. Bibcode: 1983SoPh...86...33P Altcode: The basic processes of evaporation and magnetic reconnection have recently been developed in much greater detail. They may be important in the two main types of flaring event, namely simple-loop flares and two-ribbon flares. The first type could be produced by kink instability, thermal nonequilibrium, or emerging flux. The second type is thought to be the result of an eruptive MHD instability that is either spontaneous or triggered from outside. After the eruption the magnetic field lines that have been blown open reconnect back down in a way that has now been simulated numerically. Title: Current sheet models for solar prominences. I Magnetohydrostatics of support and evolution through quasi-static models Authors: Malherbe, J. M.; Priest, E. R. Bibcode: 1983A&A...123...80M Altcode: Several 2D current sheet models for solar prominences, supported against gravity by potential magnetic configurations, are presented. Simple magnetostatic solutions, both of Kuperus-Raadu type (KR) and of Kippenhahn-Schlüter type (KS) are built with the help of complex functions and discussed. The authors suggest that, in the case of KS models, slow (<100 ms-1) diverging photospheric flows below prominences could explain the upward motions reported by Malherbe et al. (1983) in disk filaments; while, in the case of KR models, slow converging flows could explain them. To account for such motions and magnetic field observations by Leroy et al. (1983) it is proposed in Raadu's spirit (1979), a quasi-static reconnection model, in which new material entering the prominence condenses and is brought up through it by the moving magnetic field. The resulting dynamics is studied in a simple magnetic geometry of KR type. Title: A Numerical Experiment Relevant to Line-Tied Reconnection in Two-Ribbon Flares Authors: Forbes, T. G.; Priest, E. R. Bibcode: 1983SoPh...84..169F Altcode: The nonlinear evolution of a reconnecting magnetic field configuration similar to that occurring just before the onset of `post'-flare loops in two-ribbon flares is determined. The evolution, which is obtained by numerically solving the resistive MHD equations, shows two new features that have not yet been incorporated into contemporary models of `post'-flare loops. The first of these new features is the formation of a nearly stationary fast-mode shock above the region corresponding to the top of the loops. This fast-mode shock occurs just below the magnetic neutral line and between the slow-mode shocks associated with fast magnetic reconnection at the neutral line. The second new feature is the creation and annihilation of large-scale magnetic islands in the current sheet above the loops. The annihilation of the islands occurs very rapidly and appears to be a manifestation of the coalescence instability. The creation and annihilation of magnetic islands could be important in understanding the energetics of `post'-flare loops since the coalescence instability can produce an intermittent energy release more than an order of magnitude faster than that predicted by steady-state reconnection theories. Title: Book-Review - Solar Magnetohydrodynamics Authors: Priest, E. R. Bibcode: 1983Sci...220..338P Altcode: No abstract at ADS Title: The Decay of a Large Limb Flare Authors: Cargill, P. J.; Veck, N. J.; Jordan, C.; Strong, K. T.; Simnett, G. M.; Priest, E. R. Bibcode: 1983BAAS...15..712C Altcode: No abstract at ADS Title: The heating of postflare loops Authors: Cargill, P. J.; Priest, E. R. Bibcode: 1983ApJ...266..383C Altcode: The heating of postflare loops by slow MHD shocks is considered. Although such loops were once thought to represent the dying remnant of a two-ribbon flare, it is now realized that they are the main part of such an event and begin very early on. It is shown that, if the local temperature of a loop, its local angle of inclination to the vertical, and ambient coronal conditions are known from observations, then simple analytical formulae give the rise speed of the shocks and the magnitude of the evaporative flow incident upon them. The formulae are applied as an example to the 1973 July 29 and 1980 May 21 two-ribbon flares, and reasonable agreement with rise-speed observations is found. It is therefore claimed that shock heating is a viable method for heating postflare loops for the long times observed. Title: The structure of twisted magnetic flux tubes Authors: Browning, P. K.; Priest, E. R. Bibcode: 1983ApJ...266..848B Altcode: The basic physics of untwisted flux tubes confined by an external plasma pressure has been developed by Parker (1979). However, observations indicate that in many situations on the sun flux tubes are twisted. There is, for instance, evidence for helical structures in erupting prominences. It is, therefore, important to extend the results already found for untwisted tubes to include the effects of twist. The present investigation is concerned with the structure of a thick twisted flux tube in an inhomogeneous atmosphere. Previous work on untwisted flux tubes and straight cylindrical twisted tubes is generalized, in order to describe the properties of twisted flux tubes confined by a varying external pressure. The governing equations are nonlinear, and, if the confining pressure is specified, they define a free surface problem. This problem is solved analytically in certain limiting cases, for which the complete structure of the field is found. Two exact solutions for force-free fields are studied in detail. Title: Book-Review - Solar Magneto-Hydrodynamcs Authors: Priest, E. R. Bibcode: 1983JBAA...93..100P Altcode: No abstract at ADS Title: On reconnection and plasmoids in the geomagnetic tail Authors: Forbes, T. G.; Priest, E. R. Bibcode: 1983JGR....88..863F Altcode: The nonlinear evolution of the collisional tearing mode is numerically determined for a two-dimensional current sheet configuration whose magnetic field lines are tied at one end to a stationary surface. The configuration is analogous to that occurring in the geomagnetic tail at the start of a substorm. The numerical results suggest that the formation of a near-earth neutral line at substorm onset is due to the asymmetric tearing that occurs because the field lines in the geomagnetic tail are partly line-tied, or anchored, by the earth's ionosphere. The results also suggest that during substorm recovery the neutral line in the tail moves away from the earth at a speed on the order of the speed of the plasma flowing into the neutral line region. Overall, the solution is consistent with proposed reconnection models of the substorm but suggests that the recovery phase may be more complex than previously expected, due to the growth and coalescence of multiple magnetic islands (i.e., plasmoids). Title: The magnetohydrodynamics of solar activity Authors: Priest, E. R. Bibcode: 1983PlPh...25..161P Altcode: No abstract at ADS Title: Coronal heating by phase-mixed shear Alfven waves. Authors: Heyvaerts, J.; Priest, E. R. Bibcode: 1983A&A...117..220H Altcode: The authors consider the physical processes which occur when a shear Alfvén wave propagates in a structure with a large gradient of the Alfvén velocity. Although these waves do not possess local resonances (unlike magneto acoustic modes) they nevertheless suffer intense phase mixing during which the oscillations of neighbouring field lines become rapidly out of phase. The authors study this effect and show that the resulting large growth of gradients dramatically enhances the viscous and ohmic dissipation. The cases of propagating and standing waves are considered, and a detailed calculation is given of the rate of dissipation achieved in a finite length structure like a loop, in the presence of a random excitation at its ends. The authors prove that, after a long enough time, phase mixing can actually ensure the dissipation of all the wave mechanical energy that a loop can pick up from the excitation, in agreement with a previous claim by Ionson. The general conclusion of the study is that phase mixing is the process most able to ensure the dissipation of shear Alfvén waves in loops and in open regions of strong reflectivity, and that loops, in particular, must be in a permanent state of Kelvin-Helmholtz and tearing turbulence. Title: Solar Magneto-hydrodynamics Authors: Priest, E. R. Bibcode: 1983C&T....99..159P Altcode: No abstract at ADS Title: Book-Review - Solar Magnetohydrodynamics Authors: Priest, E. R. Bibcode: 1983S&T....66R..36P Altcode: No abstract at ADS Title: Magnetic instabilities in stellar atmospheres Authors: Priest, E. R. Bibcode: 1983ASSL..102..545P Altcode: 1983IAUCo..71..545P; 1983ards.proc..545P The extensive theory for magnetohydrodynamic instability of a flux tube is briefly reviewed, together with its application to tokamaks and solar flares. In a star a single coronal loop whose footprints are anchored in the dense photosphere may become unstable to the kink instability when it is twisted too much. Magnetic arcades may also be subject to an eruptive instability when they are sheared too much. After the eruption the magnetic field closes back down by reconnection and continues to heat the plasma long after the impulsive phase. Global instability of a large part of the coronal magnetic field is also possible when the stored energy is too great. Title: Numerical Study of Line-Tied Magnetic Reconnection Authors: Forbes, T. G.; Priest, E. R. Bibcode: 1982SoPh...81..303F Altcode: A two-dimensional configuration, analogous to that at the start of the main phase in two-ribbon flares, is modelled numerically by self-consistently solving the time-dependent MHD equations. The initial state consists of a vertical current sheet with an external plasma beta value of 0.1 and a magnetic Reynolds number of 10−3. Although the model does not yet include gravity or a full energy equation, many of the principal dynamical features of the main phase in a flare are present. In particular, the numerical results confirm the earlier prediction of the kinematic Kopp-Pneuman (1976) model that a neutral line forms at the base of the corona and rises upwards as open, extended field lines close back down to form loops (i.e., `post'-flare loops). By the end of the computation a state of nonlinear reconnection containing slow shocks has developed, and the velocity of the plasma flowing into the neutral line region is approximately 0.06 times the corresponding inflow Alfvén velocity - a value consistent with the steady-state nonlinear reconnection theory of Soward and Priest (1977). The speed at which the neutral line rises in the numerical simulation varies from an initial value of ≲ 0.02 to a final value of ∼- 0.12 times the inflow Alfvén speed. Title: Neutral line motion due to reconnection in two-ribbon solar flares and magnetospheric substorms Authors: Forbes, T. G.; Priest, E. R. Bibcode: 1982P&SS...30.1183F Altcode: Two kinematic models of line-tied reconnection are considered which describe the motion of a magnetic neutral line (NL) during the main phase of a two-ribbon solar flare and during the recovery phase of a magnetospheric substorm in the geomagnetic tail. The models are kinematic in that they use only the magnetic induction equation, which suffices to determine the position and velocity of the NL as functions of time if the rate of reconnection is prescribed. The solar flare model shows that the observed large decrease in the rate at which "post"-flare loops rise upward from the photosphere during the main phase does not require a corresponding decrease in the rate of reconnection. Instead it is found that a constant rate of reconnection can account for the motion of the loops for almost the entire period during which they are observed. By contrast, application of the same procedures to the recovery phase of the magnetospheric substorm in the tail predicts a slightly increasing speed of NL motion if the rate of reconnection is constant. Furthermore, it is found that the motion of the NL relative to the ambient medium may account for much of the observed asymmetry in the magnetic field in the plasma sheet during recovery. Due to this motion, the plasma sheet thickness may be up to 4 times smaller and the normal magnetic field component up to 2 times weaker in the region tailward of the NL than in the corresponding region earthward of the NL. Title: Thermally Isolated Coronal Loops in Hydrostatic Equilibrium Authors: Wragg, M. A.; Priest, E. R. Bibcode: 1982SoPh...80..309W Altcode: Numerical solutions are presented for the summit temperature and heating in a thermally isolated coronal loop that is in hydrostatic equilibrium. The extent to which gravity modifies the usual uniform-pressure scaling law is shown, and plots of the differential emission measure are also given. Title: Fast magnetic field-line reconnexion in a compressible fluid. Part 1. Coplanar field lines Authors: Soward, A. M.; Priest, E. R. Bibcode: 1982JPlPh..28..335S Altcode: The Petschek model for incompressible reconnexion has been put on a firm mathematical foundation in an earlier paper by Soward & Priest, who discovered a ‘local’ similarity solution for the process. The present paper extends that analysis to compressible reconnexion, in which the previous Alfvén waves are replaced by slow magneto-acoustic shocks of switch-off type. By contrast with a previous suggestion, it is found unnecessary to include intermediate waves standing ahead of the slow shocks. The maximum reconnexion rate is typically half of Petschek's stated value, though faster rates are achieved when the external gas pressure is sufficiently low. Title: The structure of untwisted magnetic flux tubes Authors: Browning, P. K.; Priest, E. R. Bibcode: 1982GApFD..21..237B Altcode: The equilibrium structure of an axisymmetric magnetic flux tube confined by an external pressure pe(Z) that varies along the length of the tube is studie. In the past, most work has concentrated on slender flux tubes, where the effects of transverse structure and radial fields are neglected. Here the aim is to explore the properties of thick tubes, in order to see to what extent the slender tube theory is valid. The main results are: Title: The thermal stability of solar coronal loops in hydrostatic equilibrium Authors: Wragg, M. A.; Priest, E. R. Bibcode: 1982A&A...113..269W Altcode: Many static models of solar coronal loops have been set up, and more recently there have been attempts to look at their stability. A loop is globally stable or unstable to thermal effects depending on whether the net conduction (stabilizing) or the net radiation (destabilizing) dominates. It has previously been found that uniform-pressure loops are unstable if the base heat flux is too small. In particular, thermally isolated loops are always unstable. In the present paper the effects of gravity are included by considering a basic state in hydrostatic equilibrium. It is found that the inclusion of gravity is a stabilizing influence because it lowers the density (and hence the radiation) in the upper parts of a loop. Thermally isolated loops are shown to be thermally unstable when they are short but stable when they are long enough. Thus, small coronal loops would be expected to exhibit dynamic fluctuations and longer ones to possess a steadier emission. Title: Book-Review - Solar Flare Magnetohydrodynamics Authors: Priest, E. R.; Rosner, R. Bibcode: 1982Natur.298..691P Altcode: No abstract at ADS Title: Present Theories for Simple-Loop and Two-Ribbon Flares Authors: Priest, E. Bibcode: 1982Obs...102..118P Altcode: No abstract at ADS Title: Slow-shock heating and the Kopp-Pneuman model for `post'-flare loops Authors: Cargill, P. J.; Priest, E. R. Bibcode: 1982SoPh...76..357C Altcode: The heating of `post'-flare loops in the Kopp-Pneuman (1976) model is here reconsidered. In that kinematic model the loops are heated by gas-dynamic shocks to at most 3-4 × 106 K. However, in a full dynamic model they would be replaced by slow magnetohydrodynamic shocks, which may provide more heating due to the additional release of magnetic energy. It is shown from a local compressible analysis that such shock waves can account for the observed temperatures of 5 × 106-107 K and also for the observed upward loop speeds of 1-50 km s-1. The above values are obtained when the ambient plasma beta is 0.01 and the shocks propagate at highly sub-Alfvénic velocities. However, if the velocity of shock propagation approaches the Alfvén speed, then temperatures of 108 K are produced. This may explain the extremely high temperatures that have been observed with the Solar Maximum Mission, when it is realised that the `post'-flare loop phenomenon may well be occurring very early on in the flare. Title: Evolution of current sheets following the onset of enhanced resistivity Authors: Forbes, T. G.; Priest, E. R.; Hood, A. W. Bibcode: 1982JPlPh..27..157F Altcode: An important aspect of pre-flare current sheets in the solar atmosphere is the sudden enhancement of the effective electrical resistivity in the sheet due to the onset of a plasma micro-instability. Numerical and analytical solutions to the isothermal MHD equations are here presented that describe the evolution of a current sheet subsequent to such an enhancement in the resistivity. The solutions show that, if the initial width of the current sheet is less than the acoustic-diffusion length obtained by dividing the resistivity by the sound speed, then isomagnetic shocks are formed. These shocks propagate outward from the the centre of the current sheet and are transformed into fast-mode magneto-acoustic waves when they reach the edges of the current sheet. The fast-mode waves thus formed continue to propagate outward beyond the confines of the current sheet. In contrast to a previous study by Cheng, the present solutions demonstrate that flow speeds several times greater than the local fast-mode wave speed can be produced if the plasma beta parameter and the initial sheet width are sufficiently small. The results may be relevant to the triggering of a solar flare, as in the emerging flux model of flares. Title: Solar magneto-hydrodynamics Authors: Priest, Eric Ronald Bibcode: 1982soma.book.....P Altcode: 1982QB539.M23P74... No abstract at ADS Title: Solar magneto-hydrodynamics. Authors: Priest, E. R. Bibcode: 1982GAM....21.....P Altcode: No abstract at ADS Title: Theories for simple-loop and two-ribbon solar flares Authors: Priest, E. R. Bibcode: 1982FCPh....7..363P Altcode: 1982FCoPh...7..363P A review of several basic flare processes is presented that includes hydrodynamic motions in a loop, magnetic reconnection, and particle acceleration. This is followed by a description of several possible mechanisms for the two types of flares. It is noted that there are two possibilities for explaining the types of flare. One is that simple-loop and two-ribbon events are effected by completely different instabilities, one being a local loop instability and the other a global arcade instability. The other possibility is that the basic instability is in essence the same in both cases (a kink instability, for instance) but that in the one case the overlying field is so strong that the instability is contained, whereas in the other the instability spreads to other loops and the ambient field is too weak to contain the explosion. This would make possible the eruption and subsequent close down to give 'post' -flare loops as a consequence of the rupture. Title: Book-Review - Solar Flare Magnetohydrodynamics Authors: Priest, E. R.; Machado, M. E. Bibcode: 1982SSRv...32..468P Altcode: No abstract at ADS Title: The energetics of steady - state flows in the solar corona Authors: Cargill, P. J.; Priest, E. R. Bibcode: 1982GApFD..20..227C Altcode: In this paper the energetics of steady-state flows in coronal loops are examined as an example of flows in flux tubes. The equations of continuity, momentum, energy and state are solved numerically (with some analytical special cases) subject to prescribed temperatures and pressures at the footpoints. A large range of subsonic and supersonic solutions is found, and it is pointed out that the static solutions discussed previously in the literature are just one of a large family of more general dynamic solutions. A steady flow is found to remove the symmetry present in static loops and to lower the maximum loop temperature. Also, the possibility of a catastrophe, which can exist in static loops as non-equilibrium, is found to be enhanced by the presence of a flow; it implies that for certain pressure and temperature differences between the footpoints, a hot (>106K) steady flow is impossible, and so either a cool (<105 K) steady flow or an unsteady flow ensues. If the footpoint density is lowered, the threshold for catastrophe is raised. Title: Effect of pressure gradients and line-tying on the magnetic stability of coronal loops Authors: Hood, A. W.; Priest, E. R.; Einaudi, G. Bibcode: 1982GApFD..20..247H Altcode: In this paper we study the stability of an idealised magnetostatic coronal loop, incorporating both the effect of line-tying, due to the dense photosphere, and of pressure gradients. The stability equations may be solved analytically for our particular equilibrium. From the marginally stable case, the critical conditions separating instability from stability are derived. It is found that stretching or twisting a loop eventually makes it kink unstable. Title: Thermal Nonequilibrium - a Trigger for Solar Flares Authors: Hood, A. W.; Priest, E. R. Bibcode: 1981SoPh...73..289H Altcode: In this paper, we suggest that a solar flare may be triggered by a lack of thermal equilibrium rather than by a magnetic instability. The possibility of such a thermal nonequilibrium (or catastrophe) is demonstrated by solving approximately the energy equation for a loop under a balance between thermal conduction, optically thin radiation and a heating source. It is found that, if one starts with a cool equilibrium at a few times 104 K and gradually increases the heating or decreases the loop pressure (or decreases the loop length), then, ultimately, critical metastable conditions are reached beyond which no cool equilibrium exists. The plasma heats up explosively to a new quasi-equilibrium at typically 107 K. During such a thermal flaring, any magnetic disruption or particle acceleration are secondary in nature. For a simple-loop (or compact) flare, the cool core of an active-region loop heats up and the magnetic tube of plasma maintains its position. For a two-ribbon flare, the material of an active-region (or plage) filament heats up and expands along the filament; it slowly rises until, at a critical height, the magnetic configuration becomes magnetohydrodynamically unstable and erupts violently outwards. In this case thermal nonequilibrium acts as a trigger for the magnetic eruption and subsequent magnetic energy release as the field closes back down. Title: Book-Review - Solar Flare Magnetohydrodynamics Authors: Priest, E. R. Bibcode: 1981Sci...214..356P Altcode: No abstract at ADS Title: Internal Structure of Reconnecting Current Sheets and the Emerging Flux Model for Solar Flares Authors: Milne, A. M.; Priest, E. R. Bibcode: 1981SoPh...73..157M Altcode: We present a steady-state model for reconnecting current sheets, which relates the central values of temperature, density and pressure within the sheet to the prescribed external values of these parameters as well as the magnetic field strength and inflow velocity (or reconnection rate). The simplifying feature of our model is the assumption of quasi-one-dimensionality so that only variations across the sheet at the centre of symmetry are considered in detail. The dimensions of the sheet, the spatial profiles and their variation with the prescribed dimensionless parameters are obtained from the model. We also obtain the conditions on the dimensionless parameters for the existence of a steady state. A beta-limitation is discovered, such that steady reconnection is impossible when the plasma beta is too small. Also, the sheet dimensions may be an order of magnitude larger than previously thought. Finally, these general results are applied to the emerging flux model for solar flares. A state of thermal nonequilibrium ensues when the current sheet between the emerging and ambient flux reaches a critical height. The effect of the beta-limitation is to make this critical height decrease with increasing magnetic field strength. Title: The Temperature-Density Structure of Coronal Loops in Hydrostatic Equilibrium Authors: Wragg, M. A.; Priest, E. R. Bibcode: 1981SoPh...70..293W Altcode: The temperature and density structure are computed for a comprehensive set of coronal loops that are in hydrostatic and thermal equilibrium. The effect of gravity is to produce significant deviations from the usual uniform-pressure scaling law (T∼(pL)1/3) when the loops are taller than a scale height. For thermally isolated loops it lowers the pressure throughout the loop, which in turn lowers the density significantly and also the temperature slightly; this modifies the above scaling law considerably. For more general loops, where the base conductive flux does not vanish, gravity lowers the summit pressure and so makes the radiation decrease by more than the heating. This in turn raises the temperature above its uniform pressure value for loops of moderate length but lowers it for longer loops. A divergence in loop cross-section increases the summit temperature by typically a factor of 2, and decreases the density, while an increase in loop height (for constant loop length) changes the temperature very little but can halve the density. Title: Models of the Open Solar Atmosphere Authors: Wragg, M. A.; Priest, E. R. Bibcode: 1981SoPh...69..257W Altcode: McWhirter et al. (1975) have presented a standard model for the transition region and inner corona that matches with the Harvard Smithsonian Reference Atmosphere. They assume an open field line configuration and solve numerically the equations of energy and hydrostatic equilibrum. The purpose of the present paper is to generalise their model for the temperature and density as functions of height in several ways and, in particular, to determine the temperature maxium and its location. The effect of varying the following characteristics of the model is determined: Title: Solar flares: magnetohydrodynamic instabilities. Authors: Hood, A. W.; Priest, E. R. Bibcode: 1981ASIC...68..509H Altcode: 1981spss.conf..509H It is pointed out that most solar flares are either simple-loop (or compact) flares or two-ribbon flares. A single loop brightens and decays without moving, whereas the appearance of the two-ribbon type involves the eruption of a magnetic arcade. The present investigation is concerned with the basic MHD instabilities which may be responsible for the solar flares. A summary of some basic theoretical concepts is provided, taking into account the tearing-mode instability, magnetic reconnection, and the energy method. Three mechanisms for producing a simple-loop flares are discussed, giving attention to the kink instability, a thermal nonequilibrium, and the theory of the emerging flux model. It is found that a two-ribbon flare is probably caused by the instability of the sheared magnetic configuration in which a filament is situated. Title: Critical conditions for magnetic instabilities in force-free coronal loops Authors: Hood, A. W.; Priest, E. R. Bibcode: 1981GApFD..17..297H Altcode: The remarkable magnetohydrodynamic stability of solar coronal loops has been attributed to the anchoring of the ends of loops in the dense photosphere. However, all the previous analyses of such line-tying have been approximate, in the sense that they give only upper or lower bounds on the critical amount of twist (or the critical loop-length) required for the breakdown of stability. The object of the present paper is to remove these approximations and determine the exact value for the critical twist. When it is exceeded the magnetic field becomes kink unstable and a flare may be initiated. A simple analytic stability calculation is described for an idealised loop. This is followed by the development of a general numerical technique for any loop profile, which involves solving the partial differential equations of motion. It is found, for example, that a force-free field of uniform twist possesses a critical twist of 2.49 , by comparison with the previous bounds of 2, for stability, and 3.3, for instability. Title: Solar flare magnetohydrodynamics Authors: Priest, E. R. Bibcode: 1981sfmh.book.....P Altcode: This book is aimed at first-year postgraduate students, with each chapter presenting a simple description of previous work and also some more recent unpublished calculations. Flare observations are considered along with current sheets. Simple-loop flares are discussed, taking into account magnetic instabilities and aspects of thermal evolution. Attention is also given to magnetostatic equilibria in the case of two-ribbon flares, postflare loops, and particle acceleration in solar flares. Information presented in connection with an introduction is related to the basic description of a flare, recent advances concerning the understanding of the flare phenomenon, earlier theories for the solar flare, and the magnetohydrodynamic equations. Title: Current sheets Authors: Priest, E. R. Bibcode: 1981sfmh.book..139P Altcode: Current sheets are of central importance for solar flare models since they represent regions of greatly enhanced magnetic dissipation and are a possible site for particle acceleration, either by direct electric fields or by time-varying fields as current sheets explode or in regions between the shocks that emanate from current sheets. Means of formation are considered, taking into account the X-type collapse, nonequilibrium, forced magnetic evolution, and the development of current sheets during the course of an instability. The behavior of current sheets is discussed, giving attention to magnetic annihilation in one-dimensional sheets, the interchange instability, the growth of reconnection, the nonlinear phase of steady reconnection, laboratory experiments, and numerical experiments. The role of current sheets in flare models is investigated, and a description of the emerging (or evolving) flux model is presented. Title: Theory of loop flows and instability. Authors: Priest, E. R. Bibcode: 1981sars.work..213P Altcode: A preliminary theory for the steady and transient coronal loop flows in solar active regions and their magnetohydrodynamic instability is presented. Siphon flow is shown to be possible in the loops if a pressure difference is maintained between the footpoints, and to account for the presence of cool cores and appearances of only half a loop. The evolution of active region magnetic loops is found to lead to the continual evaporation and draining of the plasma contained within them, particularly as a result of an increase in heating rate. Consideration of static models for thermally isolated loops reveals them to be thermally unstable, implying that in the absence of some atmospheric stabilizing mechanism, the loops must be in a dynamic state of thermal activity. It is shown that kilogauss photospheric fields may be formed by an intense magnetic field instability, with an associated transient downflow which may induce coronal flows at enhanced velocities. Magnetohydrodynamic stability analysis suggests that the major cause of magnetic stability may be line-tying of loop footpoints in the dense photosphere. Title: Globular cluster systems - Implications for galaxy formation Authors: Priest, E. R. Bibcode: 1981seng.proc..251P Altcode: 1981seng.proc..251F Some properties of globular cluster systems in galaxies relevant to an understanding of galaxy formation are reviewed. Consideration is given to globular cluster populations in elliptical and spiral galaxies, the galactic distribution of globular clusters, abundance gradients among globular clusters in the same galaxy, cluster ages in relation to abundances, the abundance distribution of Galactic globular clusters, globular cluster initial mass functions, and the orbital properties of galactic globular clusters. It is noted that these properties reveal significant differences between the cluster systems and diffuse outer halo populations of galaxies, suggestive of different chemical and dynamical histories, and the probable earlier formation of the cluster systems. Title: Introduction Authors: Priest, E. R. Bibcode: 1981sfmh.book....1P Altcode: An outline is provided of the two main types of solar flare, taking into account the simple-loop (or compact) flare, the two-ribbon flare, and the flare theories which have been proposed. Attention is given to ground-based observations, space observations from Skylab, the preflare build-up, an analysis of the instabilities, the energy release, bulk motions, aspects of particle acceleration, the produced radiation, the storage of magnetic energy and its release, the flux-loop models, the current-sheet theories, and the magnetohydrodynamic equations. It is pointed out that the solar flare owes its existence to the magnetic field. The behavior of the magnetic field during the flare is considered, taking into account the control of the flare plasma by the magnetic field. Title: Are solar coronal loops in thermal equilibrium Authors: Hood, A. W.; Priest, E. R. Bibcode: 1980A&A....87..126H Altcode: Many authors have recently set up static models for coronal loops. In this paper the thermal stability of such loops is tested by the development of two simple methods which apply to a wide class of equilibria. Stability is found to depend on the boundary conditions adopted but not critically on the form of the heating. A loop is shown to be stable if its base conductive flux is large enough that it lies on the upper of two equilibrium branches. One particular model that has attracted much attention is the thermally isolated loop, which has a vanishing conductive flux at its base; it is found to be unstable to perturbations that maintain the value of either the base temperature or the base flux. Individual coronal loops may therefore be in a dynamic state of ceaseless thermal activity unless some stabilizing mechanism exists. Title: Magnetic instability of coronal arcades as the origin of two-ribbon flares Authors: Hood, A. W.; Priest, E. R. Bibcode: 1980SoPh...66..113H Altcode: The generally accepted scenario for the events leading up to a two-ribbon flare is that a magnetic arcade (supporting a plage filament) responds to the slow photospheric motions of its footpoints by evolving passively through a series of (largely) force-free equilibria. At some critical amount of shear the configuration becomes unstable and erupts outwards. Subsequently, the field closes back down in the manner modelled by Kopp and Pneuman (1976); but the main problem has been to explain the eruptive instability. Title: Force-Free Magnetic Arcades Relevant to Two-Ribbon Solar Flares Authors: Priest, E. R.; Milne, A. M. Bibcode: 1980SoPh...65..315P Altcode: Simple analytic models for the passive evolution of arcade-like magnetic fields through a series of force-free equilibria are presented. At the photospheric boundary, the normal magnetic field component is prescribed together with either the longitudinal field component or the photospheric shear. Analytic progress is made by considering either cylindrically symmetric solutions or using the separation of variables technique. Title: Siphon Flows in Coronal Loops - Part One - Adiabatic Flow Authors: Cargill, P. J.; Priest, E. R. Bibcode: 1980SoPh...65..251C Altcode: It is now known that the corona is filled with a multitude of loop-like structures. The likelihood of these loops being in static equilibrium is small and so this paper explores the possibility of steady isothermal or adiabatic flows, driven by a pressure difference between the loop feet. For a symmetric loop the flow becomes supersonic at the summit and is then retarded by a shock-wave at some point on the downflowing leg. The effect of adiabatic flow is to lower both pressure and temperature by at least a factor of two and so provide a possible explanation for the cool cores that are sometimes observed in coronal loops. Title: The Structure of Coronal Arcades and the Formation of Solar Prominences Authors: Priest, E. R.; Smith, E. A. Bibcode: 1979SoPh...64..267P Altcode: The temperature and density are obtained for coronal plasma in thermal and hydrostatic equilibrium and located in a force-free magnetic arcade. The isotherms are found to be inclined to the magnetic field lines and so care should be taken in inferring the magnetic structure from observed emission. Title: Kink Instability of Solar Coronal Loops as the Cause of Solar Flares Authors: Hood, A. W.; Priest, E. R. Bibcode: 1979SoPh...64..303H Altcode: Solar coronal loops are observed to be remarkably stable structures. A magnetohydrodynamic stability analysis of a model loop by the energy method suggests that the main reason for stability is the fact that the ends of the loop are anchored in the dense photosphere. In addition to such line-tying, the effect of a radial pressure gradient is incorporated in the analysis. Title: A model for quiescent solar prominences. Authors: Milne, A. M.; Priest, E. R.; Roberts, B. Bibcode: 1979ApJ...232..304M Altcode: A one-dimensional model is computed for a quiescent prominence in both magnetohydrostatic equilibrium and thermal equilibrium (under a balance between the thermal condition, radiation, and wave heating). The effects of changing the coronal plasma pressure, the horizontal magnetic field strength, and the inclination of the horizontal magnetic field to the prominence normal are investigated. It is found that an equilibrium state is impossible when either the plasma beta or the magnetic field shear is too high. One feature of this model is that the magnetohydrostatics is coupled to the energetics, giving a fourth-order two-point boundary value problem, with two symmetric conditions applied at the center of the structure and the coronal temperature and density specified at a fixed outer edge. Title: The equilibrium of solar coronal magnetic loops. Authors: Hood, A. W.; Priest, E. R. Bibcode: 1979A&A....77..233H Altcode: A method is described for obtaining the temperature and density along a magnetic field line for plasma that is in thermal equilibrium at uniform pressure. One of the main features of the results is that, when the pressure becomes too great or the length of the field line too large, a lack of thermal equilibrium ensues and the plasma cools down to a new equilibrium below 100,000 K. The stretching of a coronal loop may be caused either by the straightforward motion of the photospheric footprints or by the twisting up of a field that remains force-free. It is suggested, therefore, that such an increase in pressure or length is what causes some coronal loops to develop very cool cores. This is proposed as a mechanism for the creation of active region filaments or prominences. Title: A Modified KIPPENHAHN-SCHLÜTER Model for Quiescent Prominences. Authors: Priest, E. R.; Milne, A. M.; Roberts, B. Bibcode: 1979phsp.coll..184P Altcode: 1979IAUCo..44..184P The effect of varying magnetic field strengths and shears on a model quiescent solar prominence is assessed. Following Kippenhahn and Schlueter (1957) the prominence is modeled by a one-dimensional slab configuration. Their work is extended to include thermal effects, using an energy equation which expresses a balance between thermal conduction, radiative loss and wave heating. At some specified distance from the center of the prominence, the coronal temperature and pressure are prescribed while at the center of the prominence there are two symmetry conditions, which results in a two-point boundary value problem. Title: A trigger mechanism for the emerging flux model of solar flares. Authors: Tur, T. J.; Priest, E. R. Bibcode: 1978SoPh...58..181T Altcode: The energetics of a current sheet that forms between newly emerging flux and an ambient field are considered. As more and more flux emerges, so the sheet rises in the solar atmosphere. The various contributions to the thermal energy balance in the sheet are approximated and the resulting equation solved for the internal temperature of the sheet. It is found that, for certain choices of the ambient magnetic field strength and velocity, the internal temperature increases until, when the sheet reaches some critical height, no neighbouring equilibrium state exists. The temperature then increases rapidly, seeking a hotter branch of the solution curve. During this dynamic heating, the threshold temperature for the onset of plasma microinstabilities may be attained. It is suggested that this may be a suitable trigger mechanism for the recently proposed `emerging flux' model of a solar flare. Title: The structure of coronal loops. Authors: Priest, E. R. Bibcode: 1978SoPh...58...57P Altcode: With the advent of space telescopes, coronal magnetic loops, both within and outside active regions, are being observed with renewed interest. This paper is an attempt to outline some general physical considerations pertinent to such loops, as a prelude to more sophisticated modelling. For example, a loop that is stretched (or possibly twisted) too much may be subject to a thermal instability that cools its core to a new equilibrium below 105 K. Also a simple consequence of hydrostatic balance along an equilibrium loop is that, under some circumstances, the density inside a cool loop can be comparable with that outside, despite the much smaller scale height. Finally, when the equilibrium loop density is less than the ambient density, several small scale magnetohydrodynamic instabilities are sometimes efficient enough to generate a circulation that tends to equalize the densities. Title: An emerging flux model for the solar phenomenon. Authors: Heyvaerts, J.; Priest, E. R.; Rust, D. M. Bibcode: 1977ApJ...216..123H Altcode: An outline is presented of the physical processes involved in the emerging flux model, which appears to explain naturally many solar flare observations. The separate physical phases of the basic model include a preflare heating phase as the new flux emerges, an impulsive phase as high-energy particles are accelerated, a flash (or explosive) phase when the H-alpha intensity increases, and a main phase while it decreases. The extent and morphology of the main phase emission depend on the structure of the magnetic field region in which the new flux finds itself imbedded. It is suggested that a (small) simple loop flare occurs if the new flux appears in a region where no great amount of magnetic energy in excess of potential is stored. A two-ribbon flare occurs if the flux emerges near the polarity inversion line of an active region that has begun to develop filaments. Title: An emerging flux model for solar flares. Authors: Heyvaerts, J.; Priest, E.; Rust, D. M. Bibcode: 1977SoPh...53..255H Altcode: No abstract at ADS Title: The formation of solar prominences by thermal instability in a current sheet. Authors: Smith, E. A.; Priest, E. R. Bibcode: 1977SoPh...53...25S Altcode: The energy balance equation for the upper chromosphere or lower corona contains a radiative loss term which is destabilizing, because a slight decrease in temperature from the equilibrium value causes more radiation and hence a cooling of the plasma; also a slight increase in temperature has the effect of heating the plasma. In spite of this tendency towards thermal instability, most of the solar atmosphere is remarkably stable, since thermal conduction is very efficient at equalizing any temperature irregularity which may arise. However, the effectiveness of thermal conduction in transporting heat is decreased considerably in a current sheet or a magnetic flux tube, since heat can be conducted quickly only along the magnetic field lines. This paper presents a simple model for the thermal equilibrium and stability of a current sheet. It is found that, when its length exceeds a certain maximum value, no equilibrium is possible and the plasma in the sheet cools. The results may be relevant for the formation of a quiescent prominence. Title: Fast magnetic field line reconnection Authors: Soward, A. M.; Priest, E. R. Bibcode: 1977RSPTA.284..369S Altcode: 1977RSLPT.284..369S Petschek's (1964) model of fast magnetic-field-line reconnection is placed on a sound mathematical basis by obtaining asymptotic solutions that contain only one discontinuity in each quadrant. A detailed self-consistent analytical model is developed in which the magnetic-field strength varies to the lowest order as the square root of the logarithm of the distance from the origin, increases with distance in the inflow region, and decreases in the outflow region; also, the Alfven lines curve away from the incoming flows. The solutions are found to be valid everywhere outside the central diffusion region when the inflow Alfven Mach number is much less than unity and to be valid at large distances from the diffusion region when that Mach number is of the order of unity. The results are compared with those obtained by Sonnerup (1970), Yeb and Axford (1970), and Roberts and Priest (1975). Title: The formation of current sheets during the emergence of new magnetic flux from below the photosphere. Authors: Tur, T. J.; Priest, E. R. Bibcode: 1976SoPh...48...89T Altcode: Solar flares are frequently observed to occur where new magnetic flux is emerging and pressing up against strong active region magnetic fields. Since the solar plasma is highly conducting, current sheets develop at the boundary between the emergent and ambient flux, provided the two magnetic fields are inclined at a non-zero angle to one another. Title: Current Sheets Authors: Priest, E. R. Bibcode: 1976RSPTA.281..497P Altcode: 1976RSLPT.281..497P Current sheets are believed to be of prime importance in the solar atmosphere. Low down they may form at supergranulation boundaries, whereas up in the corona they have been suggested as a prominence formation site. In addition, they may occur when rapidly emerging flux presses up against pre-existing magnetic fields: if rapid magnetic field annihilation and reconnection is then triggered, a surge or a flare may be produced. Comments are given about three aspects of general current sheet theory. The position and shape of the current sheet which forms between two-dimensional dipole sources is calculated. The thermal instability which occurs when the length of the sheet exceeds a critical value is described. Finally, a simple model of magnetic field annihilation is presented. Title: Thermal evolution of current sheets and flash phase of solar flares. Authors: Heyvaerts, J.; Priest, E. R. Bibcode: 1976SoPh...47..223H Altcode: The physical conditions in a stationary flow of the Petchek type, allowing reconnection between flux emerging from below the solar photosphere and a preexisting magnetic field, are discussed. It is shown that, when rising in the solar atmosphere, the reconnection region has at first a rather low temperature as compared with its environment. Above a certain critical height, however, this low temperature thermal equilibrium often ceases to be possible, and the sheet rapidly heats, seeking a new thermal equilibrium. During this dynamical process, current-driven microinstabilities may be triggered in the current sheet, giving rise to an enhanced resistivity. High energy particles might be produced by the induced electric field developed during the rapid readjustment of MHD flows that results from this change in the transport properties of the plasma. Title: Current sheet models of solar flares. Authors: Priest, E. R. Bibcode: 1976SoPh...47...41P Altcode: Current sheets have been suggested as the site for flare energy release because they can convert magnetic energy very rapidly into both heat and directed plasma energy. Also they contain electric fields with the potential of accelerating particles to high energies. Title: Report on the solar physics - plasma physics workshop. held at Stanford University, 17 - 20 September 1974. Authors: Sturrock, P. A.; Baum, P. J.; Beckers, J. M.; Newman, C. E.; Priest, E. R.; Rosenberg, H.; Smith, D. F.; Wentzel, D. G. Bibcode: 1976SoPh...46..411S Altcode: This report summarizes the proceedings of a meeting held on 17-20 September 1974, at Stanford University. The purpose was to explore plasma physics problems which arise in the study of solar physics. Sessions were concerned with specific questions including the following: Is the solar plasma thermal or non-thermal? What spectroscopic data are required? What types of magnetic field structures exist? Do MHD instabilities occur? Do resistive or non-MHD instabilities occur? What mechanisms of particle acceleration have been proposed? What information do we have concerning shock waves? Very few questions were answered categorically but, for each question, there was discussion concerning the observational evidence, theoretical analyses, and existing or potential laboratory and numerical experiments. Title: The solar flare phenomenon. Authors: Priest, E. R. Bibcode: 1976pspe.proc..144P Altcode: 1976pspe.conf..144P The basic features of a solar flare are first described in terms of a preflare heating phase, an impulsive phase, a flash phase and a main phase. Then some recent observations are surveyed, including the results of recent high resolution H-alpha photography and photospheric magnetic and velocity field measurements; they indicate the importance of new flux which emerges from below the photosphere prior to the start of the flare. Also, the structure and time evolution of the high energy flare plasma which emits X-radiation is described. Finally, flare theories are classified into flux tube and current sheet types. In the former category, the Alfven-Carlqvist and 'Alfven-wave' theories are described, while, in the latter, Syrovatsky's mechanism and Sturrock's model are summarized, as well as a new 'emerging flux model'. Title: On Fast Magnetic Field Reconnection Authors: Priest, E. R.; Soward, A. M. Bibcode: 1976IAUS...71..353P Altcode: No abstract at ADS Title: On the maximum rate of magnetic-field reconnexion for Petschek's mechanism Authors: Roberts, B.; Priest, E. R. Bibcode: 1975JPlPh..14..417R Altcode: The standard model for fast magnetic-field reconnexion (Petschek 1964) is qualitatively valid, despite numerous criticisms of its quantitative details. It contains four slow magnetohydrodynamic shock waves, which radiate from a central diffusion region. On the basis of Petschek's rough analysis, it is generally stated that, for large values of the magnetic Reynolds number Rm, reconnexion can occur at a rate no faster than a fraction π/(4 log Rm) of the Alfvén speed. Alternative models of the region outside that of diffusion have been put forward by Yeh & Axford (1970), whose general solutions Vasyliusnas (1975) proved invalid, and by Sonnerup (1970), whose model is mathematically useful, but of limited practical applicability. But their results suggest that reconnexion can occur at any rate whatsoever, with the diffusion-region dimensions responding accordingly. The present paper analyses the external region for Petschek's mechanism in greater detail than hitherto, with the object of deciding whether or not there is a maximum rate. The inclinations of the shock waves are calculated as a function of the fluid speed ve at large distances, which is taken as a measure of the reconnexion rate. It is found that, in agreement with Petschek's rough analysis, there is indeed an upper limit on the allowable rate of magnetic-field reconnexion. Its variation with Rm is calculated, and it is shown, for log10 Rm 1, to be approximately 20% of Petschek's value. Typical values are 0·10vAe for Rm = 10·2 and 0·02vAe for Rm = 106. (vAe is the Alfvén speed at large distances from the diffusion region.) Title: Some comments on magnetic field reconnection Authors: Priest, E. R.; Cowley, S. W. H. Bibcode: 1975JPlPh..14..271P Altcode: Some comments are made about how to determine the speed with which magnetic flux is carried towards an X-type neutral point and reconnected. Conditions in the diffusion region near the neutral point are also investigated, with the conclusion that the streamlines and magnetic field lines cannot both be locally hyperbolic. Instead, two distinct modes may be possible. In the first, the magnetic field lines are straight, and the diffusion region does not differ greatly from that described by Parker (1963). In the second, the fluid velocity components increase cubically away from the neutral point with the result that, for a given reconnection rate, the diffusion region is typically five times greater than in the Parker model. Title: Resistive MHD stagnation-point flows at a current sheet Authors: Sonnerup, B. U. O.; Priest, E. R. Bibcode: 1975JPlPh..14..283S Altcode: A family of exact solutions to the MHD equations is presented for steady incompressible two- and three-dimensional flow in the vicinity of the stagnation point, which forms in a current sheet separating two colliding plasma streams. The magnetic field in each plasma is strictly parallel to the current sheet, but can have different magnitudes and directions. Resistive and viscous effects are accounted for. These flows are of considerable interest in connexion with the magnetic field merging process. They represent the limit of resistive field annihilation with zero reconnexion. Title: Preflare Current Sheets in the Solar Atmosphere Authors: Priest, E. R.; Raadu, M. A. Bibcode: 1975SoPh...43..177P Altcode: Neutral current sheets are expected to form in the solar atmosphere when photospheric motions or the emergence of new magnetic flux causes oppositely directed magnetic fields to be pressed together. Magnetic energy may thus be stored slowly in excess of the minimum energy associated with a purely potential field and released suddenly during a solar flare. For simplicity, we investigate the neutral sheet which forms between two parallel line dipoles when either the distance between them decreases or their dipole moments increase. It is found that, when the dipoles have approached by an amount equal to a tenth of their original separation distance, the stored energy is comparable with that released in a major flare. In addition, a similarity solution for one-dimensional magnetohydro-dynamic flow within such a neutral sheet is presented; it demonstrates that rapid conversion of magnetic energy into heat is possible provided conditions at the edge of the neutral sheet are changing sufficiently quickly. Title: A model for the solar flare Authors: Canfield, R. C.; Priest, E. R.; Rust, D. M. Bibcode: 1975STIN...7615007C Altcode: It is suggested that many solar flares occur due to an interaction between newly emerging magnetic flux and an active region filament. A current sheet forms between the new and old flux and, when its electric current density exceeds a critical value, rapid magnetic fields reconnection takes place. Electrons are then accelerated to high energies and follow the magnetic field lines down to the chromosphere where they produce several (typically three) bright H alpha knots. Magnetic energy is continuously released as reconnected prominence fields are allowed to untwist. Two ribbons of H alpha emission are produced by one or more of three mechanisms: energetic particles, thermal conduction or shocks due to infalling material. Title: Theories of magnetic field annihilation. Authors: Priest, E. R.; Sonnerup, B. U. Oe. Bibcode: 1975GeoJ...41..405P Altcode: 1975GeoJI..41..405P No abstract at ADS Title: A Clue to the Trigger for Both the Type III Solar Radioburst and the Solar Flare Authors: Priest, E. R.; Heyvaerts, J. Bibcode: 1974SoPh...36..433P Altcode: Recent observations of `neutral line absorbing features' in the solar atmosphere may give an important clue to the mechanism whereby both type III solar radiobursts and solar flares are triggered. It is suggested that as new satellite magnetic flux emerges at the edge of an active region in an area of opposite polarity a neutral sheet builds up between the new and old flux. When the sheet has a length of about a megametre its thermal insulation from the surrounding plasma is effective enough for a thermal instability to occur. The resulting compression and inflow of plasma is observed in Hα on the disc as a neutral line absorbing feature. Furthermore, the electric field of the accompanying collisionless tearing mode instability in a thin slab near the centre of the sheet exceeds the runaway field; it may therefore accelerate electrons to high enough energies to produce the type III burst which usually occurs at the same time as the absorbing feature. Perhaps the flare which sometimes ensues is triggered when the quasi-equilibrium state is destroyed by the development of turbulence in the neutral sheet. Title: The Influence of Non-Uniform Solar Wind Expansion on the Angular Momentum Loss from the Sun Authors: Priest, E. R.; Pneuman, G. W. Bibcode: 1974SoPh...34..231P Altcode: The influence on the rate of angular momentum loss from the Sun of magnetic geometries which are not spherically symmetric is estimated. Departures from spherical symmetry are expected to influence significantly the loss rate by two effects - the presence of closed magnetic field regions with no loss and also the variability in the radial distance to the Alfvénic point, as stressed by Mestel (1968). Title: On Neutral Line Absorbing Features Authors: Heyvaerts, J.; Priest, E. Bibcode: 1974cesra...4..147H Altcode: No abstract at ADS Title: Solar physics. Plasma physics workshop. Authors: Baum, P. J.; Beckers, J. M.; Newman, C. E.; Priest, E. R.; Rosenberg, H.; Smith, D. F.; Sturrock, P. A.; Wentzel, D. G. Bibcode: 1974sppp.book.....B Altcode: No abstract at ADS Title: The Nonlinear Acceleration of a Magnetic Disturbance in the Solar Corona Authors: Altschuler, Martin D.; Smith, Dean F.; Swarztrauber, Paul N.; Priest, Eric R. Bibcode: 1973SoPh...32..153A Altcode: The simple form of Ohm's law (SI units)J = σ(E+ v × B)is valid for high density magnetofluids (where the mean free path for collisions is less than the Larmor radius) but is not strictly valid for the tenuous solar corona. We examine the nonlinear evolution of a magnetic disturbance using a more general form of Ohm's law which includes the Hall term. The Hall term dominates MHD development in the corona when the product of the magnetic scale length and the square root of the density is small enough; in particular when (1) the electron density is less than about 1013 m-3 and (2) the scale length is less than a few hundred meters. For these parameters, a magnetic disturbance may carry electrons at a drift speed in excess of the Alfvén speed. We believe this nonlinear phenomenon may be important for the impulsive acceleration of charged particles in the solar corona. Title: The Trapped Magnetoatmospheric Waves Authors: Nakagawa, Y.; Priest, E. R.; Wellck, R. E. Bibcode: 1973ApJ...184..931N Altcode: The trapped (vertically nonpropagating) magnetoatmospheric waves are examined on the basis of local dispersion relations governing the propagation of magnetoacoustic and magnetogravitational waves in an inviscid atmosphere of infinite electrical conductivity permeated by a uniform magnetic field. It is shown from the necessary condition that trapped waves are possible, (1) when the magnetic field is purely horizontal, (2) when the magnetic field is purely vertical, and (3) when the magnetic field has both vertical and horizontal components for waves propagating perpendicular to the magnetic field. Through examinations of the sufficient conditions for each of these three specific circumstances, the domain of trapped waves is determined in the (angular frequency, horizontal wavenumber)-plane. It is shown that for a horizontal magnetic field, most of the magnetoatmospheric waves become trapped, except for the magnetoacoustic waves. It is shown also that for a vertical or a general magnetic field, most of the magnetoatmospheric waves with the frequency below the local Brunt- frequency could become trapped. The physical significance and possible practical application of the results to solar observations are discussed. Subject headings: atmospheres, solar - hydromagnetics - solar atmospheric motions Title: On Steady Magnetic-Field Reconnection Authors: Priest, E. R. Bibcode: 1973ApJ...181..227P Altcode: Magnetic-field reconnection may be essential in a variety of solar and astrophysical phenomena, and there has been much debate as to the maximum allowable rate of reconnection. Petschek's mechanism, for instance, permits a maximum rate of about one-tenth of the Alfven speed, UA, but is probably unworkable. Yeh and Axford, on the other hand, have recently claimed that any rate is possible up to UA. A more careful matching of the internal and external regions in Yeh and Axford's mechanism is here performed, with the condusion. that the highest rate of reconnection is about UA/l8. Subject headings: flares, solar - hydromagnetics - plasmas Title: Evolution of a Magnetic Disturbance in the Solar Corona With a General Ohm's Law Authors: Altschuler, M. D.; Smith, D. F.; Swarztrauber, P.; Priest, E. R. Bibcode: 1973BAAS....5S.268A Altcode: No abstract at ADS Title: Erratum: Current Limitation in Solar Flares Authors: Smith, Dean F.; Priest, E. R. Bibcode: 1973ApJ...180..667S Altcode: No abstract at ADS Title: The Energy Spectrum of Small-Scale Solar Magnetic Fields Authors: Nakagawa, Y.; Priest, E. R. Bibcode: 1973ApJ...179..949N Altcode: On the basis of observations that magnetic flux is transported by fluid motions at the photospheric level of the Sun, the possible interpretation of the energy spectra of small-scale solar magnetic fields in terms of a passive response of the (longitudinal) magnetic field to turbulent fluid motions is examined. In consideration of the prevailing physical conditions, a theory is developed which accounts for the two-dimensional passive response of longitudinal magnetic fields to a three- dimensionally isotropic turbulent convection at the level of vanishing vertical velocity. The theoretical results are compared with the energy spectra of small-scale magnetic fields obtained from longitudinal magnetograms for typical active, quiet, and mixed regions of the Sun. It is shown that the observed spectra can be interpreted in terms of the theory developed with the choice of eddy kinematic viscosity 1014 cm2 5 -` and eddy magnetic diffusivity 1012 cm2 -1, including differences in the spectral shape for different regions of solar activity. The details of the theory are described together with discussions on the limitations and other implications of the results. Subject headings: hydromagnetics - magnetic fields, solar - turbulence Title: A Possible New Interpretation of Power Spectra of Solar-Granulation Brightness Fluctuations Authors: Nakagawa, Y.; Priest, E. R. Bibcode: 1972ApJ...178..251N Altcode: The brightness fluctuations of solar granulation are attributed to local temperature fluctuations through the photosphere. It is plausible to consider that the temperature fluctuations result from a passive response of temperature to turbulent fluid convections. The theoretical spectrum governing such a passive response given by Batchelor is compared with the power spectra derived by Edmonds from Stratoscope photographs, and it is shown that a satisfactory agreement can be obtained. Discrepancies between this result and observations from the ground are discussed. Title: Current Sheets in Coronal Streamers Authors: Priest, E. R.; Smith, D. F. Bibcode: 1972ApL....12...25P Altcode: No abstract at ADS Title: Current Limitation in Solar Flares Authors: Smith, Dean F.; Priest, E. R. Bibcode: 1972ApJ...176..487S Altcode: It is shown that the ion-sound current instability will be the relevant mechanism of current dissipation in most instances in the fully ionized part of the solar atmosphere (upper chromosphere and corona). Since this instability has the same initial threshold as the Alfven-Cariqvist instability, but a considerably lower threshold once the instability has started toward saturation, the Affven-Carlqvist instability will not occur. The linear and nonlinear stages of the ion-sound current instability are examined and a turbulent resistivity is given for the saturated state which is in agreement with laboratory experiments. This turbulent resistivity is applied to the Alfven-Carlqvist model of a cylindrical current filament, and it is shown that enough energy could not be dissipated sufficiently fast for a solar flare. This turbulent resistivity is also applied to the "hard" phase of Syrovatsky's dynamic dissipation model, and it is shown that Syrovatsky's electromagnetic instability for instantaneous current-sheet interruption cannot occur. The possibility that the ion-sound can systematically accelerate a select group of particles is investigated. It is concluded that heating rather than acceleration will result. It is suggested that a small electric field acting over large distances is a potentially much more efficient accelerating mechanism. Title: Current Limitation in Solar Flares Authors: Smith, D. F.; Priest, E. R. Bibcode: 1972BAAS....4Q.392S Altcode: No abstract at ADS Title: An Inconsistency in Petschek's Mechanism Authors: Priest, E. R. Bibcode: 1972BAAS....4R.389P Altcode: No abstract at ADS Title: A modification and criticism of Petschek's mechanism Authors: Priest, E. R. Bibcode: 1972MNRAS.159..389P Altcode: Petschek's mechanism is shown to be internally inconsistent when variations in magnetic field strength along the current sheet are included. The inconsistency can be removed for both incompressible and compressible flow provided the magnetic field lines in the narrow region between a pair of shock waves are pulled out into long loops rather than being only slightly bowed. If the mechanism is modified in this way, the rate of energy conversion is not significantly altered. However, there are several difficulties which remain and, unless they can be overcome, Petschek's mechanism must be considered unworkable. Title: Magnetohydrodynamic neutral point theory Authors: Priest, Eric Ronald Bibcode: 1970PhDT........87P Altcode: No abstract at ADS