Author name code: hood ADS astronomy entries on 2022-09-14 author:"Hood, Alan W." ------------------------------------------------------------------------ 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: A Fast and Accurate Method to Capture the Solar Corona/Transition Region Enthalpy Exchange in Multi-dimensional Magnetohydrodynamic Simulations Authors: Johnston, Craig; Hood, Alan; De Moortel, Ineke; Daldorff, Lars Bibcode: 2021AGUFMSH12B..03J Altcode: The brightness of the emission from coronal loops in the solar atmosphere is strongly dependent on the temperature and density of the confined plasma. Following an impulsive release of energy, the coronal plasma undergoes phases of upflow and downflow as it cools, with significant variations in its properties. In particular, the sudden increase in coronal temperature leads to an excess downward heat flux that the transition region (TR) is unable to radiate. This generates an upflow of mass and enthalpy from the TR to the corona, increasing the coronal density. The mass and enthalpy exchange is highly sensitive to the TR resolution in numerical simulations. With a numerically under-resolved TR, major errors occur in simulating the coronal density evolution and, thus, the predicted loop emission. We present a new method that addresses the difficulty of obtaining the correct interaction between the corona and corona/chromosphere interface. In the TR, an Adaptive Conduction method is used that artificially broadens any unresolved parts of the atmosphere, allowing them to be resolved while maintaining the correct physics. I will show that this approach, referred to as TRAC, successfully removes the influence of numerical resolution on the coronal density response to heating while maintaining high levels of agreement with fully resolved models. A detailed analytical assessment of the TRAC method will also be presented to demonstrate why the approach works through all phases of an impulsive heating event. Title: MHD Avalanches: Self-Consistent Heating in Model Active Regions Authors: Reid, Jack; Threlfall, James; Hood, Alan; Johnston, Craig Bibcode: 2021AGUFMSH15E2065R Altcode: MHD avalanches involve small, intensely localized instabilities that spread across neighbouring regions in a magnetic field. Cumulatively, many small events release vast amounts of stored magnetic energy. Straight cylindrical flux tubes, in Parker (1972)'s model of coronal loops, are liable to such avalanches: one unstable flux tube can cause instability to proliferate through reconnection, resulting in an ongoing chain of like events. True coronal loops are curved, arching between different footpoints on one photospheric plane. Using three-dimensional MHD simulations, we here verify the viability of MHD avalanches within the curved magnetic geometry of a multi-threaded coronal arcade. In contrast to the behaviour of straight cylindrical models, a modified ideal MHD kink mode occurs more readily and preferentially upwards in this new geometry. Such instability spreads over a region far wider than the original flux tubes, and wider than their photospheric footpoints. Consequently, substantial and sustained heating is produced, in a series of nanoflare-type events, contributing significantly to coronal heating. Overwhelmingly dominant is viscous heating, attributable to the shocks and jets produced around these small events. Reconnection is not the greatest contributor to heating, but rather the facilitator of those processes that are. Localized and intermittent, the heating shows no strong spatial preference, except for a small bias away from footpoints. Effects of realistic physical plasma parameters and the implications for thermodynamic models, with energetic transport, are discussed. Title: A fast multi-dimensional magnetohydrodynamic formulation of the transition region adaptive conduction (TRAC) method Authors: Johnston, C. D.; Hood, A. W.; De Moortel, I.; Pagano, P.; Howson, T. A. Bibcode: 2021A&A...654A...2J Altcode: 2021arXiv210603989J We have demonstrated that the transition region adaptive conduction (TRAC) method permits fast and accurate numerical solutions of the field-aligned hydrodynamic equations, successfully removing the influence of numerical resolution on the coronal density response to impulsive heating. This is achieved by adjusting the parallel thermal conductivity, radiative loss, and heating rates to broaden the transition region (TR), below a global cutoff temperature, so that the steep gradients are spatially resolved even when using coarse numerical grids. Implementing the original 1D formulation of TRAC in multi-dimensional magnetohydrodynamic (MHD) models would require tracing a large number of magnetic field lines at every time step in order to prescribe a global cutoff temperature to each field line. In this paper, we present a highly efficient formulation of the TRAC method for use in multi-dimensional MHD simulations, which does not rely on field line tracing. In the TR, adaptive local cutoff temperatures are used instead of global cutoff temperatures to broaden any unresolved parts of the atmosphere. These local cutoff temperatures are calculated using only local grid cell quantities, enabling the MHD extension of TRAC to efficiently account for the magnetic field evolution, without tracing field lines. Consistent with analytical predictions, we show that this approach successfully preserves the properties of the original TRAC method. In particular, the total radiative losses and heating remain conserved under the MHD formulation. Results from 2D MHD simulations of impulsive heating in unsheared and sheared arcades of coronal loops are also presented. These simulations benchmark the MHD TRAC method against a series of 1D models and demonstrate the versatility and robustness of the method in multi-dimensional magnetic fields. We show, for the first time, that pressure differences, generated during the evaporation phase of impulsive heating events, can produce current layers that are significantly narrower than the transverse energy deposition.

Movies associated to Figs. 4 and 8 are available at https://www.aanda.org Title: Can Multi-threaded Flux Tubes in Coronal Arcades Support a Magnetohydrodynamic Avalanche? Authors: Threlfall, J.; Reid, J.; Hood, A. W. Bibcode: 2021SoPh..296..120T Altcode: 2021arXiv210708758T Magnetohydrodynamic (MHD) instabilities allow energy to be released from stressed magnetic fields, commonly modelled in cylindrical flux tubes linking parallel planes, but, more recently, also in curved arcades containing flux tubes with both footpoints in the same photospheric plane. Uncurved cylindrical flux tubes containing multiple individual threads have been shown to be capable of sustaining an MHD avalanche, whereby a single unstable thread can destabilise many. We examine the properties of multi-threaded coronal loops, wherein each thread is created by photospheric driving in a realistic, curved coronal arcade structure (with both footpoints of each thread in the same plane). We use three-dimensional MHD simulations to study the evolution of single- and multi-threaded coronal loops, which become unstable and reconnect, while varying the driving velocity of individual threads. Experiments containing a single thread destabilise in a manner indicative of an ideal MHD instability and consistent with previous examples in the literature. The introduction of additional threads modifies this picture, with aspects of the model geometry and relative driving speeds of individual threads affecting the ability of any thread to destabilise others. In both single- and multi-threaded cases, continuous driving of the remnants of disrupted threads produces secondary, aperiodic bursts of energetic release. Title: Linking computational models to follow the evolution of heated coronal plasma Authors: Reid, J.; Cargill, P. J.; Johnston, C. D.; Hood, A. W. Bibcode: 2021MNRAS.505.4141R Altcode: 2021MNRAS.tmp.1219R A 'proof of principle' is presented, whereby the Ohmic and viscous heating determined by a three-dimensional (3D) MHD model of a coronal avalanche are used as the coronal heating input for a series of field-aligned, one-dimensional (1D) hydrodynamic models. Three-dimensional coronal MHD models require large computational resources. For current numerical parameters, it is difficult to model both the magnetic field evolution and the energy transport along field lines for coronal temperatures much hotter than $1\, \mathrm{MK}$, because of severe constraints on the time step from parallel thermal conduction. Using the 3D MHD heating derived from a simulation and evaluated on a single field line, the 1D models give coronal temperatures of $1\, \mathrm{MK}$ and densities $10^{14}\textrm {--}10^{15}\, \mathrm{m}^{-3}$ for a coronal loop length of $80\, \mathrm{Mm}$. While the temperatures and densities vary smoothly along the field lines, the heating function leads to strong asymmetries in the plasma flows. The magnitudes of the velocities in the 1D model are comparable with those seen in 3D reconnection jets in our earlier work. Advantages and drawbacks of this approach for coronal modelling are discussed. Title: Line-tied Boundary Conditions Can Cause Resonant Absorption Models to Generate Unphysically Large Boundary Layers Authors: Prokopyszyn, A. P. K.; Wright, A. N.; Hood, A. W. Bibcode: 2021ApJ...914...15P Altcode: 2021arXiv210410497P This paper uses linear magnetohydrodynamics to model resonant absorption in coronal plasma with a Cartesian coordinate system. We impose line-tied boundary conditions and tilt the background magnetic field to be oblique to the transition region. Halberstadt & Goedbloed, Goedbloed & Halberstadt, and Arregui et al. show that line-tied boundary conditions cause their resonant absorption models to produce steep boundary layers/evanescent fast waves. We aim to study the importance of boundary layers and assess their significance in a solar context. We calculate solutions in a model where we impose line-tied boundary conditions and compare this with a model where we include the chromosphere instead. Results are calculated analytically and then verified numerically. We show that line-tied boundary conditions can cause the model to overestimate the boundary layers' amplitude significantly. If the fast waves can propagate in the chromosphere, then the line-tied model accurately predicts the boundary layers' amplitude. However, if the fast waves are evanescent, then the boundary layers' size is reduced significantly, and the line-tied model overestimates their amplitude. This leads to the counterintuitive result that length scales tangential to the transition region can play an essential role in determining line-tied boundary conditions' validity. The results suggest that line-tied boundary conditions can cause the model to generate unphysically large boundary layers. However, researchers may wish to continue to use them in their models for their simplicity and ability to significantly reduce computation time if they understand and are aware of their flaws. Title: How Is Helicity (and Twist) Partitioned in Magnetohydrodynamic Simulations of Reconnecting Magnetic Flux Tubes? Authors: Threlfall, James; Wright, Andrew N.; Hood, Alan W. Bibcode: 2020ApJ...898....1T Altcode: Magnetic helicity conservation provides a convenient way to analyze specific properties (namely, the linkage and twist) of reconnecting flux tubes and yield additional insight into the pre- and post-reconnection states of magnetic structures in the solar atmosphere. A previous study considered two flux tubes with footpoints anchored in two parallel planes. They showed that reconnection would add self-helicity equivalent to a half turn of twist to each flux tube. We address a related and fundamental question here: if two flux tubes anchored in a single plane reconnect, what are the resulting twists imparted to each of the reconnected tubes? Are they equal and do they have a simple exact value independent of footpoint location? To do this, we employ a new (computationally efficient) method which subdivides each flux tube into distinct elements and calculates the mutual helicity of many elemental pairs, the sum of which determines the self-helicity of the overall flux tube. Having tested the method using a simple analytical model, we apply the technique to a magnetohydrodynamic simulation where initially untwisted magnetic flux tubes are sheared and allowed to reconnect (based on a previous reconnection model). We recover values of self-helicity and twist in the final end state of the simulations which show excellent agreement with theoretical predictions. Title: Modelling the solar transition region using an adaptive conduction method Authors: Johnston, C. D.; Cargill, P. J.; Hood, A. W.; De Moortel, I.; Bradshaw, S. J.; Vaseekar, A. C. Bibcode: 2020A&A...635A.168J Altcode: 2020arXiv200201887J Modelling the solar Transition Region with the use of an Adaptive Conduction (TRAC) method permits fast and accurate numerical solutions of the field-aligned hydrodynamic equations, capturing the enthalpy exchange between the corona and transition region, when the corona undergoes impulsive heating. The TRAC method eliminates the need for highly resolved numerical grids in the transition region and the commensurate very short time steps that are required for numerical stability. When employed with coarse spatial resolutions, typically achieved in multi-dimensional magnetohydrodynamic codes, the errors at peak density are less than 5% and the computation time is three orders of magnitude faster than fully resolved field-aligned models. This paper presents further examples that demonstrate the versatility and robustness of the method over a range of heating events, including impulsive and quasi-steady footpoint heating. A detailed analytical assessment of the TRAC method is also presented, showing that the approach works through all phases of an impulsive heating event because (i) the total radiative losses and (ii) the total heating when integrated over the transition region are both preserved at all temperatures under the broadening modifications of the method. The results from the numerical simulations complement this conclusion. Title: Determining whether the squashing factor, Q, would be a good indicator of reconnection in a resistive MHD experiment devoid of null points Authors: Reid, J.; Parnell, C. E.; Hood, A. W.; Browning, P. K. Bibcode: 2020A&A...633A..92R Altcode: The squashing factor of a magnetic field, Q, is commonly used as an indicator of magnetic reconnection, but few studies seek to evaluate how reliable it is in comparison with other possible reconnection indicators. By using a full, self-consistent, three-dimensional, resistive magnetohydrodynamic experiment of interacting magnetic strands constituting a coronal loop, Q and several different quantities are determined. Each is then compared with the necessary and sufficient condition for reconnection, namely the integral along a field line of the component of the electric field parallel to the magnetic field. Among the reconnection indicators explored, we find the squashing factor less successful when compared with alternatives, such as Ohmic heating. In a reconnecting magnetic field devoid of null points, our work suggests that Q, being a geometric measure of the magnetic field, is not a reliable indicator of the onset or a diagnostic of the location of magnetic reconnection in some configurations. Title: Coronal energy release by MHD avalanches: Heating mechanisms Authors: Reid, J.; Cargill, P. J.; Hood, A. W.; Parnell, C. E.; Arber, T. D. Bibcode: 2020A&A...633A.158R Altcode: The plasma heating associated with an avalanche involving three twisted magnetic threads within a coronal loop is investigated using three-dimensional magnetohydrodynamic simulations. The avalanche is triggered by the kink instability of one thread, with the others being engulfed as a consequence. The heating as a function of both time and location along the strands is evaluated. It is shown to be bursty at all times but to have no preferred spatial location. While there appears to be a level of "background" heating, this is shown to be comprised of individual, small heating events. A comparison between viscous and resistive (Ohmic) heating demonstrates that the strongest heating events are largely associated with the Ohmic heating that arises when the current exceeds a critical value. Viscous heating is largely (but not entirely) associated with smaller events. Ohmic heating dominates viscous heating only at the time of the initial kink instability. It is also demonstrated that a variety of viscous models lead to similar heating rates, suggesting that the system adjusts to dissipate the same amount of energy. Title: Investigating the damping rate of phase-mixed Alfvén waves Authors: Prokopyszyn, A. P. K.; Hood, A. W. Bibcode: 2019A&A...632A..93P Altcode: 2019arXiv191012510P Context. This paper investigates the effectiveness of phase mixing as a coronal heating mechanism. A key quantity is the wave damping rate, γ, defined as the ratio of the heating rate to the wave energy.
Aims: We investigate whether or not laminar phase-mixed Alfvén waves can have a large enough value of γ to heat the corona. We also investigate the degree to which the γ of standing Alfvén waves which have reached steady-state can be approximated with a relatively simple equation. Further foci of this study are the cause of the reduction of γ in response to leakage of waves out of a loop, the quantity of this reduction, and how increasing the number of excited harmonics affects γ.
Methods: We calculated an upper bound for γ and compared this with the γ required to heat the corona. Analytic results were verified numerically.
Results: We find that at observed frequencies γ is too small to heat the corona by approximately three orders of magnitude. Therefore, we believe that laminar phase mixing is not a viable stand-alone heating mechanism for coronal loops. To arrive at this conclusion, several assumptions were made. The assumptions are discussed in Sect. 2. A key assumption is that we model the waves as strictly laminar. We show that γ is largest at resonance. Equation (37) provides a good estimate for the damping rate (within approximately 10% accuracy) for resonant field lines. However, away from resonance, the equation provides a poor estimate, predicting γ to be orders of magnitude too large. We find that leakage acts to reduce γ but plays a negligible role if γ is of the order required to heat the corona. If the wave energy follows a power spectrum with slope -5/3 then γ grows logarithmically with the number of excited harmonics. If the number of excited harmonics is increased by much more than 100, then the heating is mainly caused by gradients that are parallel to the field rather than perpendicular to it. Therefore, in this case, the system is not heated mainly by phase mixing. Title: Eruptions and flaring activity in emerging quadrupolar regions Authors: Syntelis, P.; Lee, E. J.; Fairbairn, C. W.; Archontis, V.; Hood, A. W. Bibcode: 2019A&A...630A.134S Altcode: 2019arXiv190901446S Context. Solar observations suggest that some of the most dynamic active regions are associated with complex photospheric magnetic configurations such as quadrupolar regions, and especially those that have a δ-spot configuration and a strong polarity inversion line (PIL).
Aims: We study the formation and eruption of magnetic flux ropes in quadrupolar regions.
Methods: We performed 3D magnetohydrodynamics simulations of the partial emergence of a highly twisted flux tube from the solar interior into a non-magnetised stratified atmosphere. We introduced a density deficit at two places along the length of the subphotospheric flux tube to emerge as two Ω-shaped loops, forming a quadrupolar region.
Results: At the photosphere, the emerging flux forms two initially separated bipoles, which later come in contact, forming a δ-spot central region. Above the two bipoles, two magnetic lobes expand and interact through a series of current sheets at the interface between them. Two recurrent confined eruptions are produced. In both cases, the reconnection between sheared low-lying field lines forms a flux rope. The reconnection between the two lobes higher in the atmosphere forms field lines that retract down and push against the flux rope, creating a current sheet between them. It also forms field lines that create a third magnetic lobe between the two emerged lobes, that later acts as a strapping field. The flux rope eruptions are triggered when the reconnection between the flux ropes and the field above the ropes becomes efficient enough to remove the tension of the overlying field. These reconnection events occur internally in the quadrupolar system, as the atmosphere is non-magnetised. The flux rope of the first, weaker, eruption almost fully reconnects with the overlying field. The flux rope of the second, more energetic, eruption is confined by the overlying strapping field. During the second eruption, the flux rope is enhanced in size, flux, and twist, similar to confined-flare-to-flux-rope observations. Proxies of the emission reveal the two erupting filaments channels. A flare arcade is only formed in the second eruption owing to the longer lasting and more efficient reconnection at the current sheet below the flux rope. Title: Magnetohydrodynamic waves in braided magnetic fields Authors: Howson, T. A.; De Moortel, I.; Reid, J.; Hood, A. W. Bibcode: 2019A&A...629A..60H Altcode: 2019arXiv190803089H
Aims: We investigate the propagation of transverse magnetohydrodynamic (MHD) wave fronts through a coronal plasma containing a braided magnetic field.
Methods: We performed a series of three dimensional MHD simulations in which a small amplitude, transverse velocity perturbation is introduced into a complex magnetic field. We analysed the deformation of the wave fronts as the perturbation propagates through the braided magnetic structures and explore the nature of Alfvénic wave phase mixing in this regime. We considered the effects of viscous dissipation in a weakly non-ideal plasma and evaluate the effects of field complexity on wave energy dissipation.
Results: Spatial gradients in the local Alfvén speed and variations in the length of magnetic field lines ensure that small scales form throughout the propagating wave front due to phase mixing. Additionally, the presence of complex, intricate current sheets associated with the background field locally modifies the polarisation of the wave front. The combination of these two effects enhances the rate of viscous dissipation, particularly in more complex field configurations. Unlike in classical phase mixing configurations, the greater spatial extent of Alfvén speed gradients ensures that wave energy is deposited over a larger cross-section of the magnetic structure. Further, the complexity of the background magnetic field ensures that small gradients in a wave driver can map to large gradients within the coronal plasma.
Conclusions: The phase mixing of transverse MHD waves in a complex magnetic field will progress throughout the braided volume. As a result, in a non-ideal regime wave energy will be dissipated over a greater cross-section than in classical phase mixing models. The formation rate of small spatial scales in a propagating wave front is a function of the complexity of the background magnetic field. As such, if the coronal field is sufficiently complex it remains plausible that phase mixing induced wave heating can contribute to maintaining the observed temperatures. Furthermore, the weak compressibility of the transverse wave and the observed phase mixing pattern may provide seismological information about the nature of the background plasma. Title: The effects of numerical resolution, heating timescales and background heating on thermal non-equilibrium in coronal loops Authors: Johnston, C. D.; Cargill, P. J.; Antolin, P.; Hood, A. W.; De Moortel, I.; Bradshaw, S. J. Bibcode: 2019A&A...625A.149J Altcode: 2019arXiv190407287J Thermal non-equilibrium (TNE) is believed to be a potentially important process in understanding some properties of the magnetically closed solar corona. Through one-dimensional hydrodynamic models, this paper addresses the importance of the numerical spatial resolution, footpoint heating timescales and background heating on TNE. Inadequate transition region (TR) resolution can lead to significant discrepancies in TNE cycle behaviour, with TNE being suppressed in under-resolved loops. A convergence on the periodicity and plasma properties associated with TNE required spatial resolutions of less than 2 km for a loop of length 180 Mm. These numerical problems can be resolved using an approximate method that models the TR as a discontinuity using a jump condition, as proposed by Johnston et al. (2017a, A&A, 597, A81; 2017b, A&A, 605, A8). The resolution requirements (and so computational cost) are greatly reduced while retaining good agreement with fully resolved results. Using this approximate method we (i) identify different regimes for the response of coronal loops to time-dependent footpoint heating including one where TNE does not arise and (ii) demonstrate that TNE in a loop with footpoint heating is suppressed unless the background heating is sufficiently small. The implications for the generality of TNE are discussed. Title: Coronal loop seismology using standing kink oscillations with a lookup table Authors: Pascoe, David J.; Hood, Alan W.; Van Doorsselaere, Tom Bibcode: 2019FrASS...6...22P Altcode: The transverse structure of coronal loops plays a key role in the physics but the small transverse scales can be difficult to observe directly. For wider loops the density profile may be estimated by forward modelling of the transverse intensity profile. The transverse density profile may also be estimated seismologically using kink oscillations in coronal loops. The strong damping of kink oscillations is attributed to resonant absorption and the damping profile contains information about the transverse structure of the loop. However, the analytical descriptions for damping by resonant absorption presently only describe the behaviour for thin inhomogeneous layers. Previous numerical studies have demonstrated that this thin boundary approximation produces poor estimates of the damping behaviour in loops with wider inhomogeneous layers. Both the seismological and forward modelling approaches suggest loops have a range of layer widths and so there is a need for a description of the damping behaviour that accurately describes such loops. We perform a parametric study of the damping of standing kink oscillations by resonant absorption for a wide range of inhomogeneous layer widths and density contrast ratios, with a focus on the values most relevant to observational cases. We describe the damping profile produced by our numerical simulations without prior assumption of its shape and compile our results into a lookup table which may be used to produce accurate seismological estimates for kink oscillation observations. Title: Phase mixing of nonlinear Alfvén waves Authors: Prokopyszyn, A. P. K.; Hood, A. W.; De Moortel, I. Bibcode: 2019A&A...624A..90P Altcode: 2019arXiv190308093P
Aims: This paper presents 2.5D numerical experiments of Alfvén wave phase mixing and aims to assess the effects of nonlinearities on wave behaviour and dissipation. In addition, this paper aims to quantify how effective the model presented in this work is at providing energy to the coronal volume.
Methods: The model is presented and explored through the use of several numerical experiments which were carried out using the Lare2D code. The experiments study footpoint driven Alfvén waves in the neighbourhood of a two-dimensional x-type null point with initially uniform density and plasma pressure. A continuous sinusoidal driver with a constant frequency is used. Each experiment uses different driver amplitudes to compare weakly nonlinear experiments with linear experiments.
Results: We find that the wave trains phase-mix owing to variations in the length of each field line and variations in the field strength. The nonlinearities reduce the amount of energy entering the domain, as they reduce the effectiveness of the driver, but they have relatively little effect on the damping rate (for the range of amplitudes studied). The nonlinearities produce density structures which change the natural frequencies of the field lines and hence cause the resonant locations to move. The shifting of the resonant location causes the Poynting flux associated with the driver to decrease. Reducing the magnetic diffusivity increases the energy build-up on the resonant field lines, however, it has little effect on the total amount of energy entering the system. From an order of magnitude estimate, we show that the Poynting flux in our experiments is comparable to the energy requirements of the quiet Sun corona. However a (possibly unphysically) large amount of magnetic diffusion was used however and it remains unclear if the model is able to provide enough energy under actual coronal conditions. Title: Successful and Failed Flux Tube Emergence in the Solar Interior Authors: Syntelis, P.; Archontis, V.; Hood, A. Bibcode: 2019ApJ...874...15S Altcode: 2019arXiv190207969S We report on our 3D magnetohydrodynamic simulations of cylindrical weakly twisted flux tubes emerging from 18 Mm below the photosphere. We perform a parametric study by varying the initial magnetic field strength (B 0), radius (R), twist (α), and length of the emerging part of the flux tube (λ) to investigate how these parameters affect the transfer of the magnetic field from the convection zone to the photosphere. We show that the efficiency of emergence at the photosphere (i.e., how strong the photospheric field will be in comparison to B 0) depends not only on B 0, but also on the morphology of the emerging field and on the twist. We show that parameters such as B 0 and magnetic flux alone cannot determine whether a flux tube will emerge to the solar surface. For instance, high-B 0 (weak-B 0) fields may fail (succeed) to emerge at the photosphere, depending on their geometrical properties. We also show that the photospheric magnetic field strength can vary greatly for flux tubes with the same B 0 but different geometric properties. Moreover, in some cases we have found scaling laws, whereby the magnetic field strength scales with the local density as B ∝ ρ κ , where κ ≈ 1 deeper in the convection zone and κ < 1 close to the photosphere. The transition between the two values occurs approximately when the local pressure scale (H p ) becomes comparable to the diameter of the flux tube (H p ≈ 2R). We derive forms to explain how and when these scaling laws appear and compare them with the numerical simulations. Title: Coronal energy release by MHD avalanches: continuous driving Authors: Reid, J.; Hood, A. W.; Parnell, C. E.; Browning, P. K.; Cargill, P. J. Bibcode: 2018A&A...615A..84R Altcode: Previous work has confirmed the concept of a magnetohydrodynamic (MHD) avalanche in pre-stressed threads within a coronal loop. We undertook a series of full, three-dimensional MHD simulations in order to create three threads by twisting the magnetic field through boundary motions until an instability ensues. We find that, following the original instability, one unstable thread can disrupt its neighbours with continued driving. A "bursty" heating profile results, with a series of ongoing energy releases, but no evident steady state. For the first time using full MHD, we show that avalanches are a viable mechanism for the storing and release of magnetic energy in the solar corona, as a result of photospheric motions. 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: Flare particle acceleration resulting from the interaction of twisted coronal flux ropes Authors: Threlfall, James; Hood, Alan; Browning, Philippa Bibcode: 2018EGUGA..20.5145T Altcode: Solar flares are highly explosive events which release significant quantities of energy (upto 10^32 ergs) from specific magnetic configurations in the solar atmosphere. As part of this process, flares produce unique signatures across the entire electromagnetic spectrum, from radio to ultra-violet (UV) and X-ray wavelengths, over extremely short length and timescales. Many of the observed signals are indicative of strong particle acceleration, where highly energised electron and proton populations rapidly achieve MeV/GeV energies and therefore form a significant fraction of the energy budget of each event. It is almost universally accepted that magnetic reconnection plays a fundamental role (on some level) in the acceleration of particles to such incredible energies. I will briefly summarise a recent investigation of non-thermal particle behaviour in a three-dimensional (3D) magnetohydrodynamical (MHD) model of unstable multi-threaded flaring coronal loops. Using the test-particle approach, I will describe how particle orbits respond to the reconnection and fragmentation in MHD simulations wherein the onset of the kink instability in a single loop thread can lead to the destabilisation and fragmentation of other loop threads. I will also compare the test particle energy distributions and final positions with other theoretical particle acceleration models in the context of observed energetic particle populations during solar flares. Title: Human Forward Contamination Assessment: Just How Leaky are Space Suits and What Do They Leak? Authors: Bell, M. S.; Regberg, A. B.; Rucker, M.; Hood, A.; Walker, M. Bibcode: 2018LPI....49.2285B Altcode: A team at NASA/JSC has developed a prototype tool designed to sample space suits to determine the present day microbial load and eventually the rate of leakage. Title: Flare particle acceleration in the interaction of twisted coronal flux ropes Authors: Threlfall, J.; Hood, A. W.; Browning, P. K. Bibcode: 2018A&A...611A..40T Altcode: 2018arXiv180102907T Aim. The aim of this work is to investigate and characterise non-thermal particle behaviour in a three-dimensional (3D) magnetohydrodynamical (MHD) model of unstable multi-threaded flaring coronal loops.
Methods: We have used a numerical scheme which solves the relativistic guiding centre approximation to study the motion of electrons and protons. The scheme uses snapshots from high resolution numerical MHD simulations of coronal loops containing two threads, where a single thread becomes unstable and (in one case) destabilises and merges with an additional thread.
Results: The particle responses to the reconnection and fragmentation in MHD simulations of two loop threads are examined in detail. We illustrate the role played by uniform background resistivity and distinguish this from the role of anomalous resistivity using orbits in an MHD simulation where only one thread becomes unstable without destabilising further loop threads. We examine the (scalable) orbit energy gains and final positions recovered at different stages of a second MHD simulation wherein a secondary loop thread is destabilised by (and merges with) the first thread. We compare these results with other theoretical particle acceleration models in the context of observed energetic particle populations during solar flares. Title: Conducting Science-Driven Extravehicular Activities During Planetary Surface Exploration — The NEEMO (NASA Extreme Environment Mission Operations) 22 Mission Authors: Young, K. E.; Graff, T. G.; Coan, D.; Reagan, M.; Todd, W.; Naids, A.; Walker, M.; Hood, A.; Dougan, K. E.; Bellantuono, A.; Merselis, D.; Thinesh, T.; Rodriguez-Lanetty, M.; Rampe, E.; Evans, C.; Pace, L.; Garrison, D.; Zacny, K.; Rehnmark, F.; Wei, B.; Chu, P. Bibcode: 2018LPI....49.2422Y Altcode: The NEEMO 22 mission investigated objectives relevant to future crewed planetary surface exploration using an integrated EVA and science team. Title: Comparison of methods for modelling coronal magnetic fields Authors: Goldstraw, E. E.; Hood, A. W.; Browning, P. K.; Cargill, P. J. Bibcode: 2018A&A...610A..48G Altcode: 2017arXiv171107458G
Aims: Four different approximate approaches used to model the stressing of coronal magnetic fields due to an imposed photospheric motion are compared with each other and the results from a full time-dependent magnetohydrodynamic (MHD) code. The assumptions used for each of the approximate methods are tested by considering large photospheric footpoint displacements.
Methods: We consider a simple model problem, comparing the full non-linear MHD, determined with the Lare2D numerical code, with four approximate approaches. Two of these, magneto-frictional relaxation and a quasi-1D Grad-Shafranov approach, assume sequences of equilibria, whilst the other two methods, a second-order linearisation of the MHD equations and Reduced MHD, are time dependent.
Results: The relaxation method is very accurate compared to full MHD for force-free equilibria for all footpoint displacements, but has significant errors when the plasma β0 is of order unity. The 1D approach gives an extremely accurate description of the equilibria away from the photospheric boundary layers, and agrees well with Lare2D for all parameter values tested. The linearised MHD equations correctly predict the existence of photospheric boundary layers that are present in the full MHD results. As soon as the footpoint displacement becomes a significant fraction of the loop length, the RMHD method fails to model the sequences of equilibria correctly. The full numerical solution is interesting in its own right, and care must be taken for low β0 plasmas if the viscosity is too high. Title: Supporting Future Lunar Surface Exploration Through Ongoing Field Activities Authors: Young, K. E.; Graff, T. G.; Bleacher, J. E.; Coan, D.; Whelley, P. L.; Garry, W. B.; Kruse, S.; Reagan, M.; Garrison, D.; Miller, M.; Delgado, F.; Rogers, A. D.; Glotch, T. D.; Evans, C. A.; Naids, A.; Walker, M.; Hood, A. Bibcode: 2017LPICo2041.5011Y Altcode: We present results from several ongoing field deployments that are working to explore 1) lunar surface trafficability, 2) radiation shielding, and 3) lunar habitat, life support, and mobility. Title: A new approach for modelling chromospheric evaporation in response to enhanced coronal heating. II. Non-uniform heating Authors: Johnston, C. D.; Hood, A. W.; Cargill, P. J.; De Moortel, I. Bibcode: 2017A&A...605A...8J Altcode: 2017arXiv170504054J We proposed that the use of an approximate "jump condition" at the solar transition region permits fast and accurate numerical solutions of the one dimensional hydrodynamic equations when the corona undergoes impulsive heating. In particular, it eliminates the need for the very short timesteps imposed by a highly resolved numerical grid. This paper presents further examples of the applicability of the method for cases of non-uniform heating, in particular, nanoflare trains (uniform in space but non-uniform in time) and spatially localised impulsive heating, including at the loop apex and base of the transition region. In all cases the overall behaviour of the coronal density and temperature shows good agreement with a fully resolved one dimensional model and is significantly better than the equivalent results from a 1D code run without using the jump condition but with the same coarse grid. A detailed assessment of the errors introduced by the jump condition is presented showing that the causes of discrepancy with the fully resolved code are (I) the neglect of the terms corresponding to the rate of change of total energy in the unresolved atmosphere; (II) mass motions at the base of the transition region and (III) for some cases with footpoint heating, an over-estimation of the radiative losses in the transition region. Title: A relaxation model of coronal heating in multiple interacting flux ropes Authors: Hussain, A. S.; Browning, P. K.; Hood, A. W. Bibcode: 2017A&A...600A...5H Altcode: Context. Heating the solar corona requires dissipation of stored magnetic energy, which may occur in twisted magnetic fields. Recently published numerical simulations show that the ideal kink instability in a twisted magnetic thread may trigger energy release in stable twisted neighbours, and demonstrate an avalanche of heating events.
Aims: We aim to construct a Taylor relaxation model for the energy release from two flux ropes and compare this with the outcomes of the simulations. We then aim to extend the model to large numbers of flux ropes, allowing the possibility of modelling a heating avalanche, and calculation of the energy release for ensembles of twisted threads with varying twist profiles.
Methods: The final state is calculated by assuming a helicity-conserving relaxation to a minimum energy state. Multiple scenarios are examined, which include kink-unstable flux ropes relaxing on their own, as well as stable and unstable flux ropes merging into a single rope as a result of magnetic reconnection. We consider alternative constraints that determine the spatial extent of the final relaxed state.
Results: Good agreement is found between the relaxation model and the magnetohydrodynamic simulations, both for interactions of two twisted threads and for a multi-thread avalanche. The model can predict the energy release for flux ropes of varying degrees of twist, which relax individually or which merge through reconnection into a single flux rope. It is found that the energy output of merging flux ropes is dominated by the energy of the most strongly twisted rope.
Conclusions: The relaxation approach provides a very good estimate of the energy release in an ensemble of twisted threads of which one is kink-unstable. Title: NEEMO 21: Tools, Techniques, Technologies, and Training for Science Exploration Authors: Graff, T.; Young, K.; Coan, D.; Merselis, D.; Bellantuono, A.; Dougan, K.; Rodriguez-Lanetty, M.; Nedimyer, K.; Chappell, S.; Beaton, K.; Hood, A.; Reagan, M.; Rampe, E.; Todd, W.; Poffenberger, J.; Garrison, D. Bibcode: 2017LPI....48.2391G Altcode: NEEMO 21 was a highly integrated operational field test and evaluation of tools, techniques, technologies, and training for science driven exploration during EVA. Title: A new approach for modelling chromospheric evaporation in response to enhanced coronal heating. I. The method Authors: Johnston, C. D.; Hood, A. W.; Cargill, P. J.; De Moortel, I. Bibcode: 2017A&A...597A..81J Altcode: 2016arXiv160905075J We present a new computational approach that addresses the difficulty of obtaining the correct interaction between the solar corona and the transition region, in response to rapid heating events. In the coupled corona, transition region, and chromosphere system, an enhanced downward conductive flux results in an upflow (chromospheric evaporation). However, obtaining the correct upflow generally requires high spatial resolution in order to resolve the transition region. With an unresolved transition region, artificially low coronal densities are obtained because the downward heat flux "jumps" across the unresolved region to the chromosphere, underestimating the upflows. Here, we treat the lower transition region as a discontinuity that responds to changing coronal conditions through the imposition of a jump condition that is derived from an integrated form of energy conservation. To illustrate and benchmark this approach against a fully resolved one-dimensional model, we present field-aligned simulations of coronal loops in response to a range of impulsive (spatially uniform) heating events. We show that our approach leads to a significant improvement in the coronal density evolution than just when using coarse spatial resolutions insufficient to resolve the lower transition region. Our approach compensates for the jumping of the heat flux by imposing a velocity correction that ensures that the energy from the heat flux goes into driving the transition region dynamics, rather than being lost through radiation. Hence, it is possible to obtain improved coronal densities. The advantages of using this approach in both one-dimensional hydrodynamic and three-dimensional magnetohydrodynamic simulations are discussed. 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: Sunspot rotation. II. Effects of varying the field strength and twist of an emerging flux tube Authors: Sturrock, Z.; Hood, A. W. Bibcode: 2016A&A...593A..63S Altcode: 2016arXiv160507378S Context. Observations of flux emergence indicate that rotational velocities may develop within sunspots. However, the dependence of this rotation on sub-photospheric field strength and twist remains largely unknown.
Aims: We investigate the effects of varying the initial field strength and twist of an emerging sub-photospheric magnetic flux tube on the rotation of the sunspots at the photosphere.
Methods: We consider a simple model of a stratified domain with a sub-photospheric interior layer and three overlying atmospheric layers. A twisted arched flux tube is inserted in the interior and is allowed to rise into the atmosphere. To achieve this, the magnetohydrodynamic equations are solved using the Lagrangian-remap code, Lare3d. We perform a parameter study by independently varying the sub-photospheric magnetic field strength and twist.
Results: Altering the initial magnetic field strength and twist of the flux tube significantly affects the tube's evolution and the rotational motions that develop at the photosphere. The rotation angle, vorticity, and current show a direct dependence on the initial field strength. We find that an increase in field strength increases the angle through which the fieldlines rotate, the length of the fieldlines extending into the atmosphere, and the magnetic energy transported to the atmosphere. This also affects the amount of residual twist in the interior. The length of the fieldlines is crucial as we predict the twist per unit length equilibrates to a lower value on longer fieldlines. No such direct dependence is found when we modify the twist of the magnetic field owing to the complex effect this has on the tension force acting on the tube. However, there is still a clear ordering in quantities such as the rotation angle, helicity, and free energy with higher initial twist cases being related to sunspots that rotate more rapidly, transporting more helicity and magnetic energy to the atmosphere. Title: NEEMO 20: Science Training, Operations, and Tool Development Authors: Graff, T.; Miller, M.; Rodriguez-Lanetty, M.; Chappell, S.; Naids, A.; Hood, A.; Coan, D.; Abell, P.; John, K.; Todd, W.; Reagan, M.; Janoiko, B.; Beaton, K.; Poffenberger, J. Bibcode: 2016LPI....47.2212G Altcode: A summary of the scientific training, scientific operations, and tool development conducted during the NEEMO 20 mission. Title: Energy Release in Driven Twisted Coronal Loops Authors: Bareford, M. R.; Gordovskyy, M.; Browning, P. K.; Hood, A. W. Bibcode: 2016SoPh..291..187B Altcode: 2015arXiv150601312B; 2015SoPh..tmp..177B We investigate magnetic reconnection in twisted magnetic fluxtubes, representing coronal loops. The main goal is to establish the influence of the field geometry and various thermodynamic effects on the stability of twisted fluxtubes and on the size and distribution of heated regions. In particular, we aim to investigate to what extent the earlier idealised models, based on the initially cylindrically symmetric fluxtubes, are different from more realistic models, including the large-scale curvature, atmospheric stratification, thermal conduction and other effects. In addition, we compare the roles of Ohmic heating and shock heating in energy conversion during magnetic reconnection in twisted loops. The models with straight fluxtubes show similar distribution of heated plasma during the reconnection: it initially forms a helical shape, which subsequently becomes very fragmented. The heating in these models is rather uniformly distributed along fluxtubes. At the same time, the hot plasma regions in curved loops are asymmetric and concentrated close to the loop tops. Large-scale curvature has a destabilising influence: less twist is needed for instability. Footpoint convergence normally delays the instability slightly, although in some cases, converging fluxtubes can be less stable. Finally, introducing a stratified atmosphere gives rise to decaying wave propagation, which has a destabilising effect. Title: An MHD Avalanche in a Multi-threaded Coronal Loop. Authors: Hood, A. W.; Cargill, P. J.; Browning, P. K.; Tam, K. V. Bibcode: 2016ApJ...817....5H Altcode: 2015arXiv151200628H For the first time, we demonstrate how an MHD avalanche might occur in a multithreaded coronal loop. Considering 23 non-potential magnetic threads within a loop, we use 3D MHD simulations to show that only one thread needs to be unstable in order to start an avalanche even when the others are below marginal stability. This has significant implications for coronal heating in that it provides for energy dissipation with a trigger mechanism. The instability of the unstable thread follows the evolution determined in many earlier investigations. However, once one stable thread is disrupted, it coalesces with a neighboring thread and this process disrupts other nearby threads. Coalescence with these disrupted threads then occurs leading to the disruption of yet more threads as the avalanche develops. Magnetic energy is released in discrete bursts as the surrounding stable threads are disrupted. The volume integrated heating, as a function of time, shows short spikes suggesting that the temporal form of the heating is more like that of nanoflares than of constant heating. Title: Transverse, propagating velocity perturbations in solar coronal loops Authors: De Moortel, I.; Pascoe, D. J.; Wright, A. N.; Hood, A. W. Bibcode: 2016PPCF...58a4001D Altcode: 2015arXiv151000976D As waves and oscillations carry both energy and information, they have enormous potential as a plasma heating mechanism and, through seismology, to provide estimates of local plasma properties which are hard to obtain from direct measurements. Being sufficiently near to allow high-resolution observations, the atmosphere of the Sun forms a natural plasma laboratory. Recent observations have revealed that an abundance of waves and oscillations is present in the solar atmosphere, leading to a renewed interest in wave heating mechanisms.

This short review paper gives an overview of recently observed transverse, propagating velocity perturbations in coronal loops. These ubiquitous perturbations are observed to undergo strong damping as they propagate. Using 3D numerical simulations of footpoint-driven transverse waves propagating in a coronal plasma with a cylindrical density structure, in combination with analytical modelling, it is demonstrated that the observed velocity perturbations can be understood in terms of coupling of different wave modes in the inhomogeneous boundaries of the loops. Mode coupling in the inhomogeneous boundary layers of the loops leads to the coupling of the transversal (kink) mode to the azimuthal (Alfvén) mode, observed as the decay of the transverse kink oscillations. Both the numerical and analytical results show the spatial profile of the damped wave has a Gaussian shape to begin with, before switching to exponential decay at large heights. In addition, recent analysis of CoMP (Coronal Multi-channel Polarimeter) Doppler shift observations of large, off-limb, trans-equatorial loops shows that Fourier power at the apex appears to be higher in the high-frequency part of the spectrum than expected from theoretical models. This excess high-frequency FFT power could be tentative evidence for the onset of a cascade of the low-to-mid frequency waves into (Alfvénic) turbulence. Title: Sunspot rotation. I. A consequence of flux emergence Authors: Sturrock, Z.; Hood, A. W.; Archontis, V.; McNeill, C. M. Bibcode: 2015A&A...582A..76S Altcode: 2015arXiv150802437S Context. Solar eruptions and high flare activity often accompany the rapid rotation of sunspots. The study of sunspot rotation and the mechanisms driving this motion are therefore key to our understanding of how the solar atmosphere attains the conditions necessary for large energy release.
Aims: We aim to demonstrate and investigate the rotation of sunspots in a 3D numerical experiment of the emergence of a magnetic flux tube as it rises through the solar interior and emerges into the atmosphere. Furthermore, we seek to show that the sub-photospheric twist stored in the interior is injected into the solar atmosphere by means of a definitive rotation of the sunspots.
Methods: A numerical experiment is performed to solve the 3D resistive magnetohydrodynamic equations using a Lagrangian-Remap code. We track the emergence of a toroidal flux tube as it rises through the solar interior and emerges into the atmosphere investigating various quantities related to both the magnetic field and plasma.
Results: Through detailed analysis of the numerical experiment, we find clear evidence that the photospheric footprints or sunspots of the flux tube undergo a rotation. Significant vertical vortical motions are found to develop within the two polarity sources after the field emerges. These rotational motions are found to leave the interior portion of the field untwisted and twist up the atmospheric portion of the field. This is shown by our analysis of the relative magnetic helicity as a significant portion of the interior helicity is transported to the atmosphere. In addition, there is a substantial transport of magnetic energy to the atmosphere. Rotation angles are also calculated by tracing selected fieldlines; the fieldlines threading through the sunspot are found to rotate through angles of up to 353° over the course of the experiment. We explain the rotation by an unbalanced torque produced by the magnetic tension force, rather than an apparent effect.

The movies associated to Figs. 3, 5, and 11 are available in electronic form at http://www.aanda.org Title: Coronal heating in multiple magnetic threads Authors: Tam, K. V.; Hood, A. W.; Browning, P. K.; Cargill, P. J. Bibcode: 2015A&A...580A.122T Altcode: 2015arXiv150700259T Context. Heating the solar corona to several million degrees requires the conversion of magnetic energy into thermal energy. In this paper, we investigate whether an unstable magnetic thread within a coronal loop can destabilise a neighbouring magnetic thread.
Aims: By running a series of simulations, we aim to understand under what conditions the destabilisation of a single magnetic thread can also trigger a release of energy in a nearby thread.
Methods: The 3D magnetohydrodynamics code, Lare3d, is used to simulate the temporal evolution of coronal magnetic fields during a kink instability and the subsequent relaxation process. We assume that a coronal magnetic loop consists of non-potential magnetic threads that are initially in an equilibrium state.
Results: The non-linear kink instability in one magnetic thread forms a helical current sheet and initiates magnetic reconnection. The current sheet fragments, and magnetic energy is released throughout that thread. We find that, under certain conditions, this event can destabilise a nearby thread, which is a necessary requirement for starting an avalanche of energy release in magnetic threads.
Conclusions: It is possible to initiate an energy release in a nearby, non-potential magnetic thread, because the energy released from one unstable magnetic thread can trigger energy release in nearby threads, provided that the nearby structures are close to marginal stability. Title: Excitation and damping of broadband kink waves in the solar corona Authors: Pascoe, D. J.; Wright, A. N.; De Moortel, I.; Hood, A. W. Bibcode: 2015A&A...578A..99P Altcode: Context. Observations such as those by the Coronal Multi-Channel Polarimeter (CoMP) have revealed that broadband kink oscillations are ubiquitous in the solar corona.
Aims: We consider footpoint-driven kink waves propagating in a low β coronal plasma with a cylindrical density structure. We investigate the excitation and damping of propagating kink waves by a broadband driver, including the effects of different spatial profiles for the driver.
Methods: We employ a general spatial damping profile in which the initial stage of the damping envelope is approximated by a Gaussian profile and the asymptotic state by an exponential one. We develop a method of accounting for the presence of these different damping regimes and test it using data from numerical simulations.
Results: Strongly damped oscillations in low density coronal loops are more accurately described by a Gaussian spatial damping profile than an exponential profile. The consequences for coronal seismology are investigated and applied to observational data for the ubiquitous broadband waves observed by CoMP. Current data cannot distinguish between the exponential and Gaussian profiles because of the levels of noise. We demonstrate the importance of the spatial profile of the driver on the resulting damping profile. Furthermore, we show that a small-scale turbulent driver is inefficient at exciting propagating kink waves. Title: Shock heating in numerical simulations of kink-unstable coronal loops Authors: Bareford, M. R.; Hood, A. W. Bibcode: 2015RSPTA.37340266B Altcode: An analysis of the importance of shock heating within coronal magnetic fields has hitherto been a neglected area of study. We present new results obtained from nonlinear magnetohydrodynamic simulations of straight coronal loops. This work shows how the energy released from the magnetic field, following an ideal instability, can be converted into thermal energy, thereby heating the solar corona. Fast dissipation of magnetic energy is necessary for coronal heating and this requirement is compatible with the time scales associated with ideal instabilities. Therefore, we choose an initial loop configuration that is susceptible to the fast-growing kink, an instability that is likely to be created by convectively driven vortices, occurring where the loop field intersects the photosphere (i.e. the loop footpoints). The large-scale deformation of the field caused by the kinking creates the conditions for the formation of strong current sheets and magnetic reconnection, which have previously been considered as sites of heating, under the assumption of an enhanced resistivity. However, our simulations indicate that slow mode shocks are the primary heating mechanism, since, as well as creating current sheets, magnetic reconnection also generates plasma flows that are faster than the slow magnetoacoustic wave speed. Title: Helical Blowout Jets in the Sun: Untwisting and Propagation of Waves Authors: Lee, E. J.; Archontis, V.; Hood, A. W. Bibcode: 2015ApJ...798L..10L Altcode: 2014arXiv1412.4853L We report on a numerical experiment of the recurrent onset of helical "blowout" jets in an emerging flux region. We find that these jets are running with velocities of ~100-250 km s-1 and they transfer a vast amount of heavy plasma into the outer solar atmosphere. During their emission, they undergo an untwisting motion as a result of reconnection between the twisted emerging and the non-twisted pre-existing magnetic field in the solar atmosphere. For the first time in the context of blowout jets, we provide direct evidence that their untwisting motion is associated with the propagation of torsional Alfvén waves in the corona. Title: Recurrent Explosive Eruptions and the "Sigmoid-to-arcade" Transformation in the Sun Driven by Dynamical Magnetic Flux Emergence Authors: Archontis, V.; Hood, A. W.; Tsinganos, K. Bibcode: 2014ApJ...786L..21A Altcode: 2014arXiv1405.6955A We report on three-dimensional MHD simulations of recurrent mini coronal mass ejection (CME)-like eruptions in a small active region (AR), which is formed by the dynamical emergence of a twisted (not kink unstable) flux tube from the solar interior. The eruptions develop as a result of the repeated formation and expulsion of new flux ropes due to continuous emergence and reconnection of sheared field lines along the polarity inversion line of the AR. The acceleration of the eruptions is triggered by tether-cutting reconnection at the current sheet underneath the erupting field. We find that each explosive eruption is followed by reformation of a sigmoidal structure and a subsequent "sigmoid-to-flare arcade" transformation in the AR. These results might have implications for recurrent CMEs and eruptive sigmoids/flares observations and theoretical studies. Title: Coronal heating and nanoflares: current sheet formation and heating Authors: Bowness, R.; Hood, A. W.; Parnell, C. E. Bibcode: 2013A&A...560A..89B Altcode:
Aims: Solar photospheric footpoint motions can produce strong, localised currents in the corona. A detailed understanding of the formation process and the resulting heating is important in modelling nanoflares, as a mechanism for heating the solar corona.
Methods: A 3D MHD simulation is described in which an initially straight magnetic field is sheared in two directions. Grid resolutions up to 5123 were used and two boundary drivers were considered; one where the boundaries are continuously driven and one where the driving is switched off once a current layer is formed.
Results: For both drivers a twisted current layer is formed. After a long time we see that, when the boundary driving has been switched off, the system relaxes towards a lower energy equilibrium. For the driver which continuously shears the magnetic field we see a repeating cycle of strong current structures forming, fragmenting and decreasing in magnitude and then building up again. Realistic coronal temperatures are obtained. Title: The Emergence of Weakly Twisted Magnetic Fields in the Sun Authors: Archontis, V.; Hood, A. W.; Tsinganos, K. Bibcode: 2013ApJ...778...42A Altcode: We have studied the emergence of a weakly twisted magnetic flux tube from the upper convection zone into the solar atmosphere. It is found that the rising magnetized plasma does not undergo the classical, single Ω-shaped loop emergence, but it becomes unstable in two places, forming two magnetic lobes that are anchored in small-scale bipolar structures at the photosphere, between the two main flux concentrations. The two magnetic lobes rise and expand into the corona, forming an overall undulating magnetic flux system. The dynamical interaction of the lobes results in the triggering of high-speed and hot jets and the formation of successive cool and hot loops that coexist in the emerging flux region. Although the initial emerging field is weakly twisted, a highly twisted magnetic flux rope is formed at the low atmosphere, due to shearing and reconnection. The new flux rope (hereafter post-emergence flux rope) does not erupt. It remains confined by the overlying field. Although there is no ejective eruption of the post-emergence rope, it is found that a considerable amount of axial and azimuthal flux is transferred into the solar atmosphere during the emergence of the magnetic field. Title: Shock heating in the solar corona Authors: Bareford, Michael; Hood, A. Bibcode: 2013SPD....4420002B Altcode: We explore the process by which a coronal loop can become heated in response to an ideal magnetic field instability. A three-dimensional magnetohydrodynamic Lagrangian-remap code is used to simulate the evolution of a specific line-tied field configuration, which is based on a zero-net-current cylindrical loop model. The initial loop state is known to be linearly kink unstable. In addition, the field surrounding the loop is potential (the external field is parallel to the initial loop axis). The kink instability rapidly leads to the formation of slow mode shocks within the loop interior, where the pressure and sound speed are low compared to the loop boundary. We investigate how these shocks influence the heating process. In general, slow mode shocks act to release magnetic energy in the form of currents, which then give rise to steep velocity gradients at the loop boundary. It is this last feature that causes shock heating, represented in the code as artificial viscosity. Our model also incorporates thermal conduction, radiation and gravity; thus, we can forward model our results to show the appearance of the loop within the 171 Å passband used by the AIA instrument onboard the Solar Dynamics Observatory. Title: Erratum: "A Numerical Model of Standard to Blowout Jets" (2013, ApJL, 769, L21) Authors: Archontis, V.; Hood, A. W. Bibcode: 2013ApJ...770L..41A Altcode: No abstract at ADS Title: A Numerical Model of Standard to Blowout Jets Authors: Archontis, V.; Hood, A. W. Bibcode: 2013ApJ...769L..21A Altcode: We report on three-dimensional (3D) MHD simulations of the formation of jets produced during the emergence and eruption of solar magnetic fields. The interaction between an emerging and an ambient magnetic field in the solar atmosphere leads to (external) reconnection and the formation of "standard" jets with an inverse Y-shaped configuration. Eventually, low-atmosphere (internal) reconnection of sheared fieldlines in the emerging flux region produces an erupting magnetic flux rope and a reconnection jet underneath it. The erupting plasma blows out the ambient field and, moreover, it unwinds as it is ejected into the outer solar atmosphere. The fast emission of the cool material that erupts together with the hot outflows due to external/internal reconnection form a wider "blowout" jet. We show the transition from "standard" to "blowout" jets and report on their 3D structure. The physical plasma properties of the jets are consistent with observational studies. Title: Damping of kink waves by mode coupling. I. Analytical treatment Authors: Hood, A. W.; Ruderman, M.; Pascoe, D. J.; De Moortel, I.; Terradas, J.; Wright, A. N. Bibcode: 2013A&A...551A..39H Altcode:
Aims: We investigate the spatial damping of propagating kink waves in an inhomogeneous plasma. In the limit of a thin tube surrounded by a thin transition layer, an analytical formulation for kink waves driven in from the bottom boundary of the corona is presented.
Methods: The spatial form for the damping of the kink mode was investigated using various analytical approximations. When the density ratio between the internal density and the external density is not too large, a simple differential-integral equation was used. Approximate analytical solutions to this equation are presented.
Results: For the first time, the form of the spatial damping of the kink mode is shown analytically to be Gaussian in nature near the driven boundary. For several wavelengths, the amplitude of the kink mode is proportional to (1 + exp(-z2/Lg2))/2, where Lg2 = 16/ɛκ2k2. Although the actual value of 16 in Lg depends on the particular form of the driver, this form is very general and its dependence on the other parameters does not change. For large distances, the damping profile appears to be roughly linear exponential decay. This is shown analytically by a series expansion when the inhomogeneous layer width is small enough.

Appendix A is available in electronic form at http://www.aanda.org Title: Damping of kink waves by mode coupling. II. Parametric study and seismology Authors: Pascoe, D. J.; Hood, A. W.; De Moortel, I.; Wright, A. N. Bibcode: 2013A&A...551A..40P Altcode: Context. Recent observations of the corona reveal ubiquitous transverse velocity perturbations that undergo strong damping as they propagate. These can be understood in terms of propagating kink waves that undergo mode coupling in inhomogeneous regions.
Aims: The use of these propagating waves as a seismological tool for the investigation of the solar corona depends upon an accurate understanding of how the mode coupling behaviour is determined by local plasma parameters. Our previous work suggests the exponential spatial damping profile provides a poor description of the behaviour of strongly damped kink waves. We aim to investigate the spatial damping profile in detail and provide a guide to the approximations most suitable for performing seismological inversions.
Methods: We propose a general spatial damping profile based on analytical results that accounts for the initial Gaussian stage of damped kink waves as well as the asymptotic exponential stage considered by previous authors. The applicability of this profile is demonstrated by a full parametric study of the relevant physical parameters. The implication of this profile for seismological inversions is investigated.
Results: The Gaussian damping profile is found to be most suitable for application as a seismological tool for observations of oscillations in loops with a low density contrast. This profile also provides accurate estimates for data in which only a few wavelengths or periods are observed. Title: Coronal heating by the partial relaxation of twisted loops Authors: Bareford, M. R.; Hood, A. W.; Browning, P. K. Bibcode: 2013A&A...550A..40B Altcode: 2012arXiv1211.3855B Context. Relaxation theory offers a straightforward method for estimating the energy that is released when continual convective driving causes a magnetic field to become unstable. Thus, an upper limit to the heating caused by ensembles of nanoflaring coronal loops can be calculated and checked against the level of heating required to maintain observed coronal temperatures (T ≳ 106 K).
Aims: We present new results obtained from nonlinear magnetohydrodynamic (MHD) simulations of idealised coronal loops. All of the initial loop configurations discussed are known to be linearly kink unstable. The purpose of this work is to determine whether or not the simulation results agree with Taylor relaxation, which will require a modified version of relaxation theory applicable to unbounded field configurations. In addition, we show for two cases how the relaxation process unfolds.
Methods: A three-dimensional (3D) MHD Lagrangian-remap code is used to simulate the evolution of a line-tied cylindrical coronal loop model. This model comprises three concentric layers surrounded by a potential envelope; hence, being twisted locally, each loop configuration is distinguished by a piecewise-constant current profile, featuring three parameters. Initially, all configurations carry zero-net-current fields and are in ideally unstable equilibrium. The simulation results are compared with the predictions of helicity-conserving relaxation theory.
Results: For all simulations, the change in helicity is no more than 2% of the initial value; also, the numerical helicities match the analytically-determined values. Magnetic energy dissipation predominantly occurs via shock heating associated with magnetic reconnection in distributed current sheets. The energy release and final field profiles produced by the numerical simulations are in agreement with the predictions given by a new model of partial relaxation theory: the relaxed field is close to a linear force free state; however, the extent of the relaxation region is limited, while the loop undergoes some radial expansion.
Conclusions: The results presented here support the use of partial relaxation theory, specifically, when calculating the heating-event distributions produced by ensembles of kink-unstable loops. The energy release increases with relaxation radius; but, once the loop has expanded by more than 50%, further expansion yields little more energy. We conclude that the relaxation methodology may be used for coronal heating studies. Title: The Creation of Outflowing Plasma in the Corona at Emerging Flux Regions: Comparing Observations and Simulations Authors: Harra, L. K.; Archontis, V.; Pedram, E.; Hood, A. W.; Shelton, D. L.; van Driel-Gesztelyi, L. Bibcode: 2012SoPh..278...47H Altcode: In this paper we analyse the flux emergence that occurred in the following polarity area of an active region on 1 - 2 December 2006. Observations have revealed the existence of fast outflows at the edge of the emerging flux region. We have performed 3-D numerical simulations to study the mechanisms responsible for these flows. The results indicate that these outflows are reconnection jets or pressure-driven outflows, depending on the relative orientation of the magnetic fields in contact (i.e. the emerging flux and the active region's field which is favourable for reconnection on the west side and nearly parallel with the pre-existing field on the east side of the emerging flux). In the observations, the flows are larger on the west side until late in the flux emergence, when the reverse is true. The simulations show that the flows are faster on the west side, but do not show the east flows increasing with time. There is an asymmetry in the expansion of the emerging flux region, which is also seen in the observations. The west side of the emerging flux region expands faster into the corona than the other side. In the simulations, efficient magnetic reconnection occurs on the west side, with new loops being created containing strong downflows that are clearly seen in the observations. On the other side, the simulations show strong compression as the dominant mechanism for the generation of flows. There is evidence of these flows in the observations, but the flows are stronger than the simulations predict at the later stages. There could be additional small-angle reconnection that adds to the flows from the compression, as well as reconnection occurring in larger loops that lie across the whole active region. Title: 3D MHD Flux Emergence Experiments: Idealised Models and Coronal Interactions Authors: Hood, A. W.; Archontis, V.; MacTaggart, D. Bibcode: 2012SoPh..278....3H Altcode: 2011arXiv1103.3685H This paper reviews some of the many 3D numerical experiments of the emergence of magnetic fields from the solar interior and the subsequent interaction with the pre-existing coronal magnetic field. The models described here are idealised, in the sense that the internal energy equation only involves the adiabatic, Ohmic and viscous shock heating terms. However, provided the main aim is to investigate the dynamical evolution, this is adequate. Many interesting observational phenomena are explained by these models in a self-consistent manner. Title: On Signatures of Twisted Magnetic Flux Tube Emergence Authors: Vargas Domínguez, S.; MacTaggart, D.; Green, L.; van Driel-Gesztelyi, L.; Hood, A. W. Bibcode: 2012SoPh..278...33V Altcode: 2011arXiv1105.0758V Recent studies of NOAA active region 10953, by Okamoto et al. (Astrophys. J. Lett.673, 215, 2008; Astrophys. J.697, 913, 2009), have interpreted photospheric observations of changing widths of the polarities and reversal of the horizontal magnetic field component as signatures of the emergence of a twisted flux tube within the active region and along its internal polarity inversion line (PIL). A filament is observed along the PIL and the active region is assumed to have an arcade structure. To investigate this scenario, MacTaggart and Hood (Astrophys. J. Lett.716, 219, 2010) constructed a dynamic flux emergence model of a twisted cylinder emerging into an overlying arcade. The photospheric signatures observed by Okamoto et al. (2008, 2009) are present in the model although their underlying physical mechanisms differ. The model also produces two additional signatures that can be verified by the observations. The first is an increase in the unsigned magnetic flux in the photosphere at either side of the PIL. The second is the behaviour of characteristic photospheric flow profiles associated with twisted flux tube emergence. We look for these two signatures in AR 10953 and find negative results for the emergence of a twisted flux tube along the PIL. Instead, we interpret the photospheric behaviour along the PIL to be indicative of photospheric magnetic cancellation driven by flows from the dominant sunspot. Although we argue against flux emergence within this particular region, the work demonstrates the important relationship between theory and observations for the successful discovery and interpretation of signatures of flux emergence. Title: Spatial damping of propagating kink waves due to mode coupling Authors: Pascoe, D. J.; Hood, A. W.; de Moortel, I.; Wright, A. N. Bibcode: 2012A&A...539A..37P Altcode:
Aims: We investigate the damping process for propagating transverse velocity oscillations, observed to be ubiquitous in the solar corona, due to mode coupling.
Methods: We perform 3D numerical simulations of footpoint-driven transverse waves propagating in a low β coronal plasma with a cylindrical density structure. Mode coupling in an inhomogeneous layer leads to the coupling of the kink mode to the Alfvén mode, observed as the decay of the transverse kink oscillations.
Results: We consider the spatial damping profile and find a Gaussian damping profile of the form exp(-z2/Lg2) to be the most congruent with our numerical data, rather than the exponential damping profile of the form exp(- z/Ld) used in normal mode analysis. Our results highlight that the nature of the driver itself will have a substantial influence on observed propagating kink waves.
Conclusions: Our study suggests that this modified damping profile should be taken into account when using coronal seismology to infer local plasma properties from observed damped oscillations. Title: What can we learn from propagating Alfvenic waves? Authors: Pascoe, D. J.; De Moortel, I.; Hood, A. W.; Wright, A. N. Bibcode: 2012decs.confE..24P Altcode: Observations have revealed ubiquitous transverse velocity perturbation waves propagating in the solar corona. We perform 3D numerical simulations of footpoint-driven transverse waves propagating in a low beta plasma. When density structuring is present, mode coupling in inhomogeneous regions leads to the coupling of the kink mode to the Alfvén mode. The frequency-dependent decay of the propagating kink wave is observed as energy is transferred to the local Alfvén mode. Modest changes in density are capable of efficiently converting energy from the driving footpoint motion to localised Alfvén modes. Thus, realistic transverse footpoint motions will deposit energy to (azimuthal) Alfvén modes in the corona. Mode coupling is investigated in detail for propagating kink modes as an explanation for the observed wave damping and as a possible seismological tool. The observed strong damping of the Doppler shift oscillations indicates the presence of wide inhomogeneous layers at the edges of the loops. Our simulations (backed up by analytical calculations) show that in this regime, the traditional exp(-z/L) damping rate no longer applies. Hence, care has to be taken when seismologically inferring damping lengths from the observed oscillations. In addition, taking into account line-of-sight integration of multiple loops supporting transverse oscillations, we show that the energy budget present in the 3D coronal volume could be substantially higher than the energy budget derived from the observed Doppler shift oscillations. 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: Coronal Kink Instability With Parallel Thermal Conduction Authors: Botha, Gert J. J.; Arber, Tony D.; Hood, Alan W.; Srivastava, A. K. Bibcode: 2012csem.conf....7B Altcode: Thermal conduction along magnetic field lines plays an important role in the evolution of the kink instability in coronal loops. In the nonlinear phase of the instability, local heating occurs due to reconnection, so that the plasma reaches high temperatures. To study the effect of parallel thermal conduction in this process, the 3D nonlinear magnetohydrodynamic (MHD) equations are solved for an initially unstable equilibrium. The initial state is a cylindrical loop with zero net current. Parallel thermal conduction reduces the local temperature, which leads to temperatures that are an order of magnitude lower than those obtained without thermal conduction. This process is important on the timescale of fast MHD phenomena; it reduces the kinetic energy released by an order of magnitude. The impact of this process on observational signatures is presented. Synthetic observables are generated that include spatial and temporal averaging to account for the resolution and exposure times of TRACE images. It was found that the inclusion of parallel thermal conductivity does not have as large an impact on observables as the order of magnitude reduction in the maximum temperature would suggest. The reason is that response functions sample a broad range of temperatures, so that the net effect of parallel thermal conduction is a blurring of internal features of the loop structure. Title: Magnetic activity on the Sun Authors: Hood, A. Bibcode: 2012hell.conf....2H Altcode: After a long period with very little magnetic activity, the Sun has started a new cycle. This rise in activity means it is an excellent time to study the Sun, particularly given the outstanding satellite and ground based instruments that are tracking solar phenomena with higher spectral, space and time resolution. I will discuss some of the recent observations of dynamic activity such as solar flares, Coronal Mass Ejections, prominence eruptions, outflows and jets. Most of the indicators of magnetic activity owe their existence to the emergence of new magnetic fields from the solar interior. This emergence occurs on scales from granulation to full blown active regions. Recent simulations are highlighting the important physical processes responsible, from convection driven emergence to magnetic buoyancy emergence. Finally, the interesting problem of why the solar corona is so hot will be discussed. Ideas for coronal heating will be mentioned and some recent simulations presented. What is clear is that magnetic complexity very quickly develops from relatively simple magnetic structures. Title: Magnetic flux emergence: a precursor of solar plasma expulsion Authors: Archontis, V.; Hood, A. W. Bibcode: 2012A&A...537A..62A Altcode:
Aims: We model the emergence of magnetized plasma from the top of the convection zone to the lower corona. We investigate the eruption of coronal flux ropes above emerging flux regions.
Methods: We performed three-dimensional numerical experiments in which the time-dependent and resistive equations of MHD are solved self-consistently, using the Lare3D code.
Results: A subphotospheric magnetic flux tube rises from the convectively unstable layer into the solar surface, followed by the formation and eruption of a new flux rope into the corona. Firstly, we examined the case where the corona is field-free. The expansion of the emerging field forms an envelope sheath that surrounds the newly formed flux rope. The erupting ropes are confined by the envelope field. The eruptions are driven by the gradient of the gas pressure and the tension of fieldlines that reconnect within the emerging flux region. The amount of the initial twist of the emerging field and the dense plasma that is lifted up, determine the height-time profile of the erupting ropes. Secondly, we examined the case of emergence into a pre-existing magnetic field in the upper solar atmosphere. A variety of different ambient field configurations was used in the experiments. External reconnection between the emerging and the pre-existing field may result in the removal of sufficient flux from the interacting fields and the full ejection of the flux ropes.
Conclusions: The results indicate that the relative contact angle of the interacting flux systems and their field strengths are crucial parameters that ultimately affect the evolution of the eruption of the rope into the higher solar atmosphere. One important result is that for any contact angle that favors reconnection, ejective eruptions occur earlier when the ambient field is relatively strong. In many cases, the erupting plasma adopts an S-like configuration. The sigmoidal structure accelerates during the fast eruption of the rope. The acceleration is enhanced by the external and internal reconnection of fieldlines during the rising motion of the rope. A key result is that in the reconnection-favored cases, the flux ropes experience ejective eruptions when the envelope flux is reduced (owing to removal by external reconnection) below that of the erupting flux rope. If the envelope flux stays higher than the erupting flux, the magnetic flux rope remains confined by the envelope field. Title: Magnetohydrodynamics dynamical relaxation of coronal magnetic fields. II. 2D magnetic X-points Authors: Fuentes-Fernández, J.; Parnell, C. E.; Hood, A. W. Bibcode: 2011A&A...536A..32F Altcode: 2011arXiv1110.5253F Context. Magnetic neutral points are potential locations for energy conversion in the solar corona. 2D X-points have been widely studied in the past, but only a few of those studies have taken finite plasma beta effects into consideration, and none of them look at the dynamical evolution of the system. At the moment there exists no description of the formation of a non-force-free equilibrium around a two-dimensional X-point.
Aims: Our aim is to provide a valid magnetohydrostatic equilibrium from the collapse of a 2D X-point in the presence of a finite plasma pressure, in which the current density is not simply concentrated in an infinitesimally thin, one-dimensional current sheet, as found in force-free solutions. In particular, we wish to determine if a finite pressure current sheet will still involve a singular current, and if so, what is the nature of the singularity.
Methods: We use a full MHD code, with the resistivity set to zero, so that reconnection is not allowed, to run a series of experiments in which an X-point is perturbed and then is allowed to relax towards an equilibrium, via real, viscous damping forces. Changes to the magnitude of the perturbation and the initial plasma pressure are investigated systematically.
Results: The final state found in our experiments is a "quasi-static" equilibrium where the viscous relaxation has completely ended, but the peak current density at the null increases very slowly following an asymptotic regime towards an infinite time singularity. Using a high grid resolution allows us to resolve the current structures in this state both in width and length. In comparison with the well known pressureless studies, the system does not evolve towards a thin current sheet, but concentrates the current at the null and the separatrices. The growth rate of the singularity is found to be tD, with 0 < D < 1. This rate depends directly on the initial plasma pressure, and decreases as the pressure is increased. At the end of our study, we present an analytical description of the system in a quasi-static non-singular equilibrium at a given time, in which a finite thick current layer has formed at the null. The dynamical evolution of the system and the dependence of the final state on the initial plasma and magnetic quantities is discussed, as are the energetic consequences. Title: Solar magnetic fields Authors: Hood, Alan W.; Hughes, David W. Bibcode: 2011PEPI..187...78H Altcode: 2011arXiv1107.0908H This review provides an introduction to the generation and evolution of the Sun's magnetic field, summarising both observational evidence and theoretical models. The eleven year solar cycle, which is well known from a variety of observed quantities, strongly supports the idea of a large-scale solar dynamo. Current theoretical ideas on the location and mechanism of this dynamo are presented. The solar cycle influences the behaviour of the global coronal magnetic field and it is the eruptions of this field that can impact on the Earth's environment. These global coronal variations can be modelled to a surprising degree of accuracy. Recent high resolution observations of the Sun's magnetic field in quiet regions, away from sunspots, show that there is a continual evolution of a small-scale magnetic field, presumably produced by small-scale dynamo action in the solar interior. Sunspots, a natural consequence of the large-scale dynamo, emerge, evolve and disperse over a period of several days. Numerical simulations can help to determine the physical processes governing the emergence of sunspots. We discuss the interaction of these emerging fields with the pre-existing coronal field, resulting in a variety of dynamic phenomena. Title: Review Article: MHD Wave Propagation Near Coronal Null Points of Magnetic Fields Authors: McLaughlin, J. A.; Hood, A. W.; de Moortel, I. Bibcode: 2011SSRv..158..205M Altcode: 2010SSRv..tmp..174M; 2010arXiv1004.5568M; 2010SSRv..tmp..157M We present a comprehensive review of MHD wave behaviour in the neighbourhood of coronal null points: locations where the magnetic field, and hence the local Alfvén speed, is zero. The behaviour of all three MHD wave modes, i.e. the Alfvén wave and the fast and slow magnetoacoustic waves, has been investigated in the neighbourhood of 2D, 2.5D and (to a certain extent) 3D magnetic null points, for a variety of assumptions, configurations and geometries. In general, it is found that the fast magnetoacoustic wave behaviour is dictated by the Alfvén-speed profile. In a β=0 plasma, the fast wave is focused towards the null point by a refraction effect and all the wave energy, and thus current density, accumulates close to the null point. Thus, null points will be locations for preferential heating by fast waves. Independently, the Alfvén wave is found to propagate along magnetic fieldlines and is confined to the fieldlines it is generated on. As the wave approaches the null point, it spreads out due to the diverging fieldlines. Eventually, the Alfvén wave accumulates along the separatrices (in 2D) or along the spine or fan-plane (in 3D). Hence, Alfvén wave energy will be preferentially dissipated at these locations. It is clear that the magnetic field plays a fundamental role in the propagation and properties of MHD waves in the neighbourhood of coronal null points. This topic is a fundamental plasma process and results so far have also lead to critical insights into reconnection, mode-coupling, quasi-periodic pulsations and phase-mixing. Title: Phase mixing of nonlinear visco-resistive Alfvén waves Authors: McLaughlin, J. A.; de Moortel, I.; Hood, A. W. Bibcode: 2011A&A...527A.149M Altcode: 2011arXiv1101.5945M
Aims: We investigate the behaviour of nonlinear, nonideal Alfvén wave propagation within an inhomogeneous magnetic environment.
Methods: The governing MHD equations are solved in 1D and 2D using both analytical techniques and numerical simulations.
Results: We find clear evidence for the ponderomotive effect and visco-resistive heating. The ponderomotive effect generates a longitudinal component to the transverse Alfvén wave, with a frequency twice that of the driving frequency. Analytical work shows the addition of resistive heating. This leads to a substantial increase in the local temperature and thus gas pressure of the plasma, resulting in material being pushed along the magnetic field. In 2D, our system exhibits phase mixing and we observe an evolution in the location of the maximum heating, i.e. we find a drifting of the heating layer.
Conclusions: Considering Alfvén wave propagation in 2D with an inhomogeneous density gradient, we find that the equilibrium density profile is significantly modified by both the flow of density due to visco-resistive heating and the nonlinear response to the localised heating through phase mixing. Title: Thermal conduction effects on the kink instability in coronal loops Authors: Botha, G. J. J.; Arber, T. D.; Hood, A. W. Bibcode: 2011A&A...525A..96B Altcode: Context. Heating of the solar corona by nanoflares, which are small transient events in which stored magnetic energy is dissipated by magnetic reconnection, may occur as the result of the nonlinear phase of the kink instability (Hood et al. 2009). Because of the high temperatures reached through these reconnection events, thermal conduction cannot be ignored in the evolution of the kink instability.
Aims: To study the effect of thermal conduction on the nonlinear evolution of the kink instability of a coronal loop. To assess the efficiency of loop heating and the role of thermal conduction, both during the kink instability and for the long time evolution of the loop.
Methods: Numerically solve the 3D nonlinear magnetohydrodynamic equations to simulate the evolution of a coronal loop that is initially in an unstable equilibrium. The initial state has zero net current. A comparison is made of the time evolution of the loop with thermal conduction and without thermal conduction.
Results: Thermal conduction along magnetic field lines reduces the local temperature. This leads to temperatures that are an order of magnitude lower than those obtained in the absence of thermal conductivity. Consequently, different spectral lines are activated with and without the inclusion of thermal conduction, which have consequences for observations of solar corona loops. The conduction process is also important on the timescale of the fast magnetohydrodynamic phenomena. It reduces the kinetic energy released by an order of magnitude.
Conclusions: Thermal conduction plays an essential role in the kink instability of coronal loops and cannot be ignored in the forward modelling of such loops. Title: Ionosphere-Magnetosphere Waves Authors: Russell, A. J.; Wright, A. N.; Streltsov, A. V.; Hood, A. W. Bibcode: 2010AGUFMSM24B..06R Altcode: Feedback between the coupled ionosphere and low-altitude magnetosphere gives rise to 'ionosphere-magnetosphere' waves. Understanding these waves and their properties is extremely valuable for interpretation of coupled magnetosphere-ionosphere dynamics, and provides insight, for example, into widening of downward current channels via E-region depletion and the origin of small-scale Alfven waves in large-scale current systems. Here, we present simulations that show the properties of these waves, and analytic results that describe them. Title: Periodic Spectral Line Asymmetries in Solar Coronal Structures from Slow Magnetoacoustic Waves Authors: Verwichte, E.; Marsh, M.; Foullon, C.; Van Doorsselaere, T.; De Moortel, I.; Hood, A. W.; Nakariakov, V. M. Bibcode: 2010ApJ...724L.194V Altcode: Recent spectral observations of upward moving quasi-periodic intensity perturbations in solar coronal structures have shown evidence of periodic line asymmetries near their footpoints. These observations challenge the established interpretation of the intensity perturbations in terms of propagating slow magnetoacoustic waves. We show that slow waves inherently have a bias toward enhancement of emission in the blue wing of the emission line due to in-phase behavior of velocity and density perturbations. We demonstrate that slow waves cause line asymmetries when the emission line is averaged over an oscillation period or when a quasi-static plasma component in the line of sight is included. Therefore, we conclude that slow magnetoacoustic waves remain a valid explanation for the observed quasi-periodic intensity perturbations. Title: Trend of photospheric magnetic helicity flux in active regions generating halo coronal mass ejections Authors: Smyrli, A.; Zuccarello, F.; Romano, P.; Zuccarello, F. P.; Guglielmino, S. L.; Spadaro, D.; Hood, A. W.; Mackay, D. Bibcode: 2010A&A...521A..56S Altcode: Context. Coronal mass ejections (CMEs) are very energetic events (~ 1032 erg) initiated in the solar atmosphere, resulting in the expulsion of magnetized plasma clouds that propagate into interplanetary space. It has been proposed that CMEs can play an important role in shedding magnetic helicity, avoiding its endless accumulation in the corona.
Aims: The aim of this work is to investigate the behavior of magnetic helicity accumulation in sites where the initiation of CMEs occurred to determine whether and how changes in magnetic helicity accumulation are temporally correlated with CME occurrence.
Methods: We used MDI/SOHO line-of-sight magnetograms to calculate magnetic flux evolution and magnetic helicity injection in 10 active regions that gave rise to halo CMEs observed during the period 2000 February to 2003 June.
Results: The magnetic helicity injection does not have a unique trend in the events analyzed: in 40% of the cases it shows a large sudden and abrupt change that is temporally correlated with a CME occurrence, while in the other cases it shows a steady monotonic trend, with a slight change in magnetic helicity at CME occurrence.
Conclusions: The results obtained from the sample of events that we have analyzed indicate that major changes in magnetic helicity flux are observed in active regions characterized by emergence of new magnetic flux and/or generating halo CMEs associated with X-class flares or filament eruptions. In some of the analyzed cases the changes in magnetic helicity flux follow the CME events and can be attributed to a process of restoring a torque balance between the subphotospheric and the coronal domain of the flux tubes.

Appendix is only available in electronic form at http://www.aanda.org Title: Magnetic reconnection in the solar atmosphere: from proposal to paradigm Authors: Cargill, Peter; Parnell, Clare; Browning, Philippa; de Moortel, Ineke; Hood, Alan Bibcode: 2010A&G....51c..31C Altcode: MEETING REPORT On 13 November 2009, the RAS hosted a discussion meeting to commemorate the formal retirement of Prof. Eric Priest. Here Peter Cargill, Clare Parnell, Philippa Browning, Ineke de Moortel and Alan Hood examine how magnetic reconnection has evolved over the past 50 years from an important but controversial proposal, to a general paradigm. Title: Simulating the "Sliding Doors" Effect Through Magnetic Flux Emergence Authors: MacTaggart, David; Hood, Alan W. Bibcode: 2010ApJ...716L.219M Altcode: Recent Hinode photospheric vector magnetogram observations have shown that the opposite polarities of a long arcade structure move apart and then come together. In addition to this "sliding doors" effect, orientations of horizontal magnetic fields along the polarity inversion line on the photosphere evolve from a normal-polarity configuration to an inverse one. To explain this behavior, a simple model by Okamoto et al. suggested that it is the result of the emergence of a twisted flux rope. Here, we model this scenario using a three-dimensional megnatohydrodynamic simulation of a twisted flux rope emerging into a pre-existing overlying arcade. We construct magnetograms from the simulation and compare them with the observations. The model produces the two signatures mentioned above. However, the cause of the "sliding doors" effect differs from the previous model. Title: Flux emergence and coronal eruption Authors: Archontis, V.; Hood, A. W. Bibcode: 2010A&A...514A..56A Altcode: 2010arXiv1003.2333A
Aims: Our aim is to study the photospheric flux distribution of a twisted flux tube that emerges from the solar interior. We also report on the eruption of a new flux rope when the emerging tube rises into a pre-existing magnetic field in the corona.
Methods: To study the evolution, we use 3D numerical simulations by solving the time-dependent and resistive MHD equations. We qualitatively compare our numerical results with MDI magnetograms of emerging flux at the solar surface.
Results: We find that the photospheric magnetic flux distribution consists of two regions of opposite polarities and elongated magnetic tails on the two sides of the polarity inversion line (PIL), depending on the azimuthal nature of the emerging field lines and the initial field strength of the rising tube. Their shape is progressively deformed due to plasma motions towards the PIL. Our results are in qualitative agreement with observational studies of magnetic flux emergence in active regions (ARs). Moreover, if the initial twist of the emerging tube is small, the photospheric magnetic field develops an undulating shape and does not possess tails. In all cases, we find that a new flux rope is formed above the original axis of the emerging tube that may erupt into the corona, depending on the strength of the ambient field. Title: Magnetohydrodynamics dynamical relaxation of coronal magnetic fields . I. Parallel untwisted magnetic fields in 2D Authors: Fuentes-Fernández, J.; Parnell, C. E.; Hood, A. W. Bibcode: 2010A&A...514A..90F Altcode: 2011arXiv1110.5258F Context. For the last thirty years, most of the studies on the relaxation of stressed magnetic fields in the solar environment have only considered the Lorentz force, neglecting plasma contributions, and therefore, limiting every equilibrium to that of a force-free field.
Aims: Here we begin a study of the non-resistive evolution of finite beta plasmas and their relaxation to magnetohydrostatic states, where magnetic forces are balanced by plasma-pressure gradients, by using a simple 2D scenario involving a hydromagnetic disturbance to a uniform magnetic field. The final equilibrium state is predicted as a function of the initial disturbances, with aims to demonstrate what happens to the plasma during the relaxation process and to see what effects it has on the final equilibrium state.
Methods: A set of numerical experiments are run using a full MHD code, with the relaxation driven by magnetoacoustic waves damped by viscous effects. The numerical results are compared with analytical calculations made within the linear regime, in which the whole process must remain adiabatic. Particular attention is paid to the thermodynamic behaviour of the plasma during the relaxation.
Results: The analytical predictions for the final non force-free equilibrium depend only on the initial perturbations and the total pressure of the system. It is found that these predictions hold surprisingly well even for amplitudes of the perturbation far outside the linear regime.
Conclusions: Including the effects of a finite plasma beta in relaxation experiments leads to significant differences from the force-free case. Title: Self-consistent ionospheric plasma density modifications by field-aligned currents: Steady state solutions Authors: Russell, A. J. B.; Wright, A. N.; Hood, A. W. Bibcode: 2010JGRA..115.4216R Altcode: 2010JGRA..11504216R The magnetosphere and ionosphere are coupled by field-aligned currents that remove or deposit E-region electrons. Changes in electron number density modify ionospheric reflectivity, hence altering the magnetospheric current. Thus, self-consistent solutions are nontrivial. In this paper, we present 1-D steady states that self-consistently model modifications of ionospheric plasma density by field-aligned currents. These are used to investigate the width broadening and minimum plasma density of E-region plasma density cavities and the origin of small-scale features observed in downward current channels. A plasma density cavity forms and broadens if the maximum initial current density j$\parallel$0 exceeds jc = αne2he/(1 + 1/β), where α is the recombination coefficient, ne is the equilibrium E-region number density in the absence of currents, h is the E-region thickness, and β = $\SigmaP0/\Sigma_{A is the initial ratio of Pedersen to magnetospheric Alfvén conductivities. If a plasma density cavity forms, its final width increases monotonically with $\cal{W = 2B0/μ0VAαne2he, where B0 is the background magnetic field strength and VA is the magnetospheric Alfvén speed. The minimum E-region number density, and the finest length scale present in the steady state, both scale as 1/β. For typical ionospheric parameters and j$\parallel$0 = 5 μAm-2, the fine scale is comparable to or less than 6λe for β $\gtrsim$ 2, where λe is the electron inertial length. This suggests that electron inertial effects may become significant and introduce small-scale features, following the production of a single fine scale by depletion and broadening. Title: Coronal Heating Authors: Hood, Alan William Bibcode: 2010LNP...793..109H Altcode: The Sun is, of course, the only star we can see in detail and the recent space missions and advances in ground based telescopes means that we can now analyse it in more detail than ever before. Looking at smaller lengthscales and with higher time and spectral resolution, it has become clear that there are many phenomena that are still not clearly understood. Title: Propagating magneto-hydrodynamic waves in a cooling homogenous coronal plasma Authors: Morton, R. J.; Hood, A. W.; Erdélyi, R. Bibcode: 2010A&A...512A..23M Altcode:
Aims: We present an investigation into how the cooling of the background plasma influences the propagation of slow and fast MHD wave modes supported by an unbounded, homogenous plasma. Previous investigations have suggested that the cooling of the plasma and a reduction in density could lead to the damping of fast magneto-acoustic oscillations. We aim to investigate whether cooling of the background plasma at a constant density may be responsible for the damping of slow and fast modes.
Methods: The plasma is assumed homogeneous and the background temperature (pressure) is decreasing with time. The temperature change is assumed to be due to optically thin radiation. A special case of the radiative function is chosen to allow an analytical assessment of the effects of cooling on magneto-acoustic MHD modes and ensures the temperature evolution of the background plasma due to this radiation also matches the observed cooling profile of coronal loops.
Results: A time-dependent dispersion relation is obtained on the slow timescale of cooling and full time-dependent solutions are found. Leading order equations for the amplitude of the waves are obtained and solved analytically for the slow and fast MHD modes. The cooling of the plasma is found to cause the frequency of the magneto-acoustic modes to decrease with time. The slow modes are found to experience a greater change in frequency than the fast modes. More importantly, the radiative losses also provide a significant damping of the slow mode and a small damping of the component of the fast mode perpendicular to the magnetic field. The damping of the slow mode is found to be strong within typical lifetimes of oscillations observed in coronal structures. Cooling could have important consequences and needs to be assessed when trying to determine what mechanism is responsible for the observed damping of coronal oscillations. Title: Trend of photospheric helicity flux in active regions generating halo CMEs Authors: Smyrli, Aimilia; Zuccarello, Francesco; Zuccarello, Francesca; Romano, Paolo; Guglielmino, Salvatore Luigi; Spadaro, Daniele; Hood, Alan; Mackay, Duncan Bibcode: 2010cosp...38.1860S Altcode: 2010cosp.meet.1860S Coronal Mass Ejections (CMEs) are very energetic events initiated in the solar atmosphere, re-sulting in the expulsion of magnetized plasma clouds that propagate into interplanetary space. It has been proposed that CMEs can play an important role in shedding magnetic helicity, avoiding its endless accumulation in the corona. We therefore investigated the behavior of magnetic helicity accumulation in sites where the initiation of CMEs occurred, in order to de-termine whether and how changes in magnetic helicity accumulation are temporally correlated with CME occurrence. After identifying the active regions (AR) where the CMEs were ini-tiated by means of a double cross-check based on the flaring-eruptive activity and the use of SOHO/EIT difference images, we used MDI magnetograms to calculate magnetic flux evolu-tion, magnetic helicity injection rate and magnetic helicity injection in 10 active regions that gave rise to 12 halo CMEs observed during the period February 2000 -June 2003. No unique behavior in magnetic helicity injection accompanying halo CME occurrence is found. In fact, in some cases there is an abrupt change in helicity injection timely correlated with the CME event, while in some others no significant variation is recorded. However, our analysis show that the most significant changes in magnetic flux and magnetic helicity injection are associated with impulsive CMEs rather than gradual CMEs. Moreover, the most significant changes in mag-netic helicity are observed when X-class flares or eruptive filaments occur, while the occurrence of flares of class C or M seems not to affect significantly the magnetic helicity accumulation. Title: Formation of Ellerman bombs due to 3D flux emergence Authors: Archontis, V.; Hood, A. W. Bibcode: 2009A&A...508.1469A Altcode: Aims. We investigate the emergence of a “sea-serpent” magnetic field into the outer solar atmosphere and the connection between undulating fieldlines and formation of Ellerman bombs.
Methods: We perform 3D numerical experiments solving the time-dependent and resistive MHD equations.
Results: A sub-photospheric magnetic flux sheet develops undulations due to the Parker instability. It rises from the convectively unstable sub-photospheric layer and emerges into the highly stratified atmosphere through successive reconnection events along the undulating system. Brightenings with the characteristics of Ellerman bombs are produced due to reconnection, which occurs during the emergence of the field. At an advanced stage of the evolution of the system, the resistive emergence leads to the formation of long, arch-like magnetic fields that expand into the corona. The enhancement of the magnetic field at the low atmosphere and episodes of emergence of new magnetic flux are also discussed.
Title: Multiple eruptions from magnetic flux emergence Authors: MacTaggart, D.; Hood, A. W. Bibcode: 2009A&A...508..445M Altcode: 2009arXiv0910.2616M Aims. In this paper we study the effects of a toroidal magnetic flux tube emerging into a magnetized corona, with an emphasis on large-scale eruptions. The orientation of the fields is such that the two flux systems are almost antiparallel when they meet.
Methods: We follow the dynamic evolution of the system by solving the 3D MHD equations using a Lagrangian remap scheme.
Results: Multiple eruptions are found to occur. The physics of the trigger mechanisms is discussed and related to well-known eruption models.
Title: On the emergence of toroidal flux tubes: general dynamics and comparisons with the cylinder model Authors: MacTaggart, D.; Hood, A. W. Bibcode: 2009A&A...507..995M Altcode: 2009arXiv0909.3987M Aims: In this paper we study the dynamics of toroidal flux tubes emerging from the solar interior, through the photosphere and into the corona. Many previous theoretical studies of flux emergence use a twisted cylindrical tube in the solar interior as the initial condition. Important insights can be gained from this model, however, it does have shortcomings. The axis of the tube never fully emerges as dense plasma becomes trapped in magnetic dips and restrains its ascent. Also, since the entire tube is buoyant, the main photospheric footpoints (sunspots) continually drift apart. These problems make it difficult to produce a convincing sunspot pair. We aim to address these problems by considering a different initial condition, namely a toroidal flux tube.
Methods: We perform numerical experiments and solve the 3D MHD equations. The dynamics are investigated through a range of initial field strengths and twists.
Results: The experiments demonstrate that the emergence of toroidal flux tubes is highly dynamic and exhibits a rich variety of behaviour. In answer to the aims, however, if the initial field strength is strong enough, the axis of the tube can fully emerge. Also, the sunspot pair does not continually drift apart. Instead, its maximum separation is the diameter of the original toroidal tube. Title: Coronal heating by magnetic reconnection in loops with zero net current Authors: Hood, A. W.; Browning, P. K.; van der Linden, R. A. M. Bibcode: 2009A&A...506..913H Altcode: Context: The paper is concerned with heating of the solar corona by nanoflares: a superposition of small transient events in which stored magnetic energy is dissipated by magnetic reconnection. It is proposed that heating occurs in the nonlinear phase of an ideal kink instability, where magnetic reconnection leads to relaxation to a state of minimum magnetic energy.
Aims: The aim is to investigate the nonlinear aspects of magnetic relaxation on a current loop with zero net axial current. The dynamical processes leading to the establishment of a relaxed state are explored. The efficiency of loop heating is investigated.
Methods: A 3D magnetohydrodynamic numerical code is used to simulate the evolution of coronal loops which are initially in ideally unstable equilibrium. The initial states have zero net current. The results are interpreted by comparison both with linear stability analysis and with helicity-conserving relaxation theory.
Results: The disturbance due to the unstable mode is strongly radially confined when the loop carries zero net current. Strong current sheets are still formed in the nonlinear phase with dissipation of magnetic energy by fast reconnection. The nonlinear development consists first of reconnection in a large scale current sheet, which forms near the quasi-resonant surface of the equilibrium field. Subsequently, the current sheet extends and then fragments, leading to multiple reconnections and effective relaxation to a constant α field.
Conclusions: Magnetic reconnection is triggered in the nonlinear phase of kink instability in loops with zero net current. Initially, reconnection occurs in a single current sheet, which then fragments into multiple reconnection sites, allowing almost full relaxation to the minimum energy state. The loop is heated to high temperatures throughout its volume. Title: The emergence of toroidal flux tubes from beneath the solar photosphere Authors: Hood, A. W.; Archontis, V.; Galsgaard, K.; Moreno-Insertis, F. Bibcode: 2009A&A...503..999H Altcode: Context: Models of flux emergence frequently use a twisted cylindrical loop as the initial starting configuration and ignore the coupling between the radiation field and plasma. In these models, the axis of the original tube never emerges through the photosphere. Without the axis emerging, it is very difficult to form a realistic sunspot.
Aims: The aim is to use a toroidal flux loop, placed beneath the solar photosphere and study whether the axis of the system emerges fully into the atmosphere. The toroidal curvature means that the plasma can drain more effectively than in a straight cylindrical tube.
Methods: Three-dimensional magnetohydrodynamic numerical simulations of an emerging magnetic flux tube are presented for an initial toroidal loop model. The simulations use a Lagrangian-Remap code that is particularly suited to dealing with shocks and strong current sheets.
Results: The evolution of the toroidal loop is followed and the characteristics of the emergence process are compared with the traditional cylindrical loops. The flux sources seen at the photosphere are more circular, and there are less shearing motions in the upper photosphere. When the initial magnetic field strength is relatively weak the evolution of the system is similar to the cylindrical loop case, with the formation of a new flux rope above the photosphere. A striking result is that for large values of field strength the axial field of the toroidal loop emerges fully into the corona. This is reported for the first time in experiments of flux emergence in a highly stratified atmosphere that do not solve self-consistently the radiation transfer problem. In addition, the new flux rope forms below the original axis of the toroidal tube when the field strength is sufficiently strong. Title: Can magnetic breakout be achieved from multiple flux emergence? Authors: MacTaggart, D.; Hood, A. W. Bibcode: 2009A&A...501..761M Altcode: Aims: We study the breakout model using multiple flux emergence to produce the magnetic configuration and the trigger. We do not impose any artificial motions on the boundaries. Once the original flux tube configuration is chosen the system is left to evolve itself.
Methods: We perform non-linear simulations in 2.5D by solving the compressible and resistive MHD equations using a Lagrangian remap, shock capturing code (Lare2D). To produce a quadrupolar configuration from flux emergence we build on previous work where the interaction of two flux tubes forms the required quadrupole. Instead of imposing a shearing flow, a third flux tube is then allowed to emerge up through the central arcade.
Results: Breakout is not achieved in any of the experiments. This is due to the interaction of the third tube with the quadrupole and the effect of the plasma β being O(1) at the photosphere and β ⪆ O(1) in the solar interior. When β is of these orders, flows generated in the plasma can influence the magnetic field and so photospheric footpoints do not remain fixed. Title: On the Structure and Evolution of Complexity in Sigmoids: A Flux Emergence Model Authors: Archontis, V.; Hood, A. W.; Savcheva, A.; Golub, L.; Deluca, E. Bibcode: 2009ApJ...691.1276A Altcode: Sigmoids are structures with a forward or inverse S-shape, generally observed in the solar corona in soft X-ray emission. It is believed that the appearance of a sigmoid in an active region is an important factor in eruptive activity. The association of sigmoids with dynamic phenomena such as flares and coronal mass ejections (CMEs) make the study of sigmoids important. Recent observations of a coronal sigmoid, obtained with the X-Ray Telescope (XRT) on board Hinode, showed the formation and eruption phase with high spatial resolution. These observations revealed that the topological structure of the sigmoid is complex: it consists of many differently oriented loops that all together form two opposite J-like bundles or an overall S-shaped structure. A series of theoretical and numerical models have been proposed, over the past years, to explain the nature of sigmoids but there is no explanation on how the aforementioned complexity in sigmoids is built up. In this paper, we present a flux emergence model that leads to the formation of a sigmoid, whose structure and evolution of complexity are in good qualitative agreement with the recent observations. For the initial state of the experiment a twisted flux tube is placed below the photosphere. A density deficit along the axis of the tube makes the system buoyant in the middle and it adopts an Ω-shape as it rises toward the outer atmosphere. During the evolution of the system, expanding field lines that touch the photosphere at bald-patches (BPs) form two seperatrix surfaces where dissipation is enhanced and current sheets are formed. Originally, each of the BP seperatrix surfaces has a J-like shape. Each one of the J's consist of reconnected field lines with different shapes and different relative orientation. The further dynamical evolution of the emerging flux tube results in the occurrence of many sites that resemble rotational discontinuities. Thus, additional current layers are formed inside the rising magnetized volume increasing the complexity of the system. The reconnected field lines along these layers form an overall S-shaped structure. The reconnection process continues to occur leading to the formation of another current concentration in the middle of the sigmoid where a flaring episode occurs. This central brightening is accompanied by the eruption of a flux rope from the central area of the sigmoid and the appearance of "post-flare" loops underneath the current structure. Title: MHD Mode Conversion around a 2D Magnetic Null Point Authors: McDougall, A. M. D.; Hood, A. W. Bibcode: 2009AIPC.1094..752M Altcode: 2009arXiv0907.1541M; 2009csss...15..752M Mode conversion occurs when a wave passes through a region where the sound and Alfvén speeds are equal. At this point there is a resonance, which allows some of the incident wave to be converted into a different mode. We study this phenomenon in the vicinity of a two-dimensional, coronal null point. As a wave approaches the null it passes from low- to high-β plasma, allowing conversion to take place. We simulate this numerically by sending in a slow magnetoacoustic wave from the upper boundary; as this passes through the conversion layer a fast wave can clearly be seen propagating ahead. Numerical simulations combined with an analytical WKB investigation allow us to determine and track both the incident and converted waves throughout the domain. Title: Nonlinear fast magnetoacoustic wave propagation in the neighbourhood of a 2D magnetic X-point: oscillatory reconnection Authors: McLaughlin, J. A.; De Moortel, I.; Hood, A. W.; Brady, C. S. Bibcode: 2009A&A...493..227M Altcode: 2009arXiv0901.1781M Context: This paper extends the models of Craig & McClymont (1991, ApJ, 371, L41) and McLaughlin & Hood (2004, A&A, 420, 1129) to include finite β and nonlinear effects.
Aims: We investigate the nature of nonlinear fast magnetoacoustic waves about a 2D magnetic X-point.
Methods: We solve the compressible and resistive MHD equations using a Lagrangian remap, shock capturing code (Arber et al. 2001, J. Comp. Phys., 171, 151) and consider an initial condition in {v}×{B} \cdot {hat{z}} (a natural variable of the system).
Results: We observe the formation of both fast and slow oblique magnetic shocks. The nonlinear wave deforms the X-point into a “cusp-like” point which in turn collapses to a current sheet. The system then evolves through a series of horizontal and vertical current sheets, with associated changes in connectivity, i.e. the system exhibits oscillatory reconnection. Our final state is non-potential (but in force balance) due to asymmetric heating from the shocks. Larger amplitudes in our initial condition correspond to larger values of the final current density left in the system.
Conclusions: The inclusion of nonlinear terms introduces several new features to the system that were absent from the linear regime.

A movie is available in electronic form at http://www.aanda.org Title: Forward modelling to determine the observational signatures of propagating slow waves for TRACE, SoHO/CDS, and Hinode/EIS Authors: Owen, N. R.; De Moortel, I.; Hood, A. W. Bibcode: 2009A&A...494..339O Altcode: Context: The propagation and damping of slow MHD waves in the solar atmosphere are investigated by numerical simulations and forward modelling, with particular emphasis placed on waves with periodicities of the order of five minutes.
Aims: We extend a coronal model by adding an equilibrium temperature gradient allowing study of wave propagation from the transition region to the corona.
Methods: A 1D model is used that includes gravitational stratification and damping by thermal conduction, optically thin radiation, and compressive viscosity. Forward modelling of the simulation results, for both uniform and non-uniform equilibrium temperature profiles, is undertaken to establish the observational consequences of the physical processes involved for TRACE, SoHO/CDS, and Hinode/EIS.
Results: The presence of thermal conduction causes a phase shift between the wave velocity, energy, and density. This shift may be observable by comparing Doppler velocity and intensity observations. Phase shifts are also seen between intensity observations by different instruments and between different spectral lines. This is an observational effect that arises due to the forward modelling process in which observations are synthesised, but it is not seen in the simulation results. Oscillations from the transition region are found to dominate the coronal emission for TRACE 171 Å by nearly two orders of magnitude. 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: 3D MHD Coronal Oscillations about a Magnetic Null Point: Application of WKB Theory Authors: McLaughlin, J. A.; Ferguson, J. S. L.; Hood, A. W. Bibcode: 2008SoPh..251..563M Altcode: 2007arXiv0712.1731M; 2008SoPh..tmp....8M This paper is a demonstration of how the WKB approximation can be used to help solve the linearised 3D MHD equations. Using Charpit's method and a Runge - Kutta numerical scheme, we have demonstrated this technique for a potential 3D magnetic null point, B=[x,εy,−(ε+1)z]. Under our cold-plasma assumption, we have considered two types of wave propagation: fast magnetoacoustic and Alfvén waves. We find that the fast magnetoacoustic wave experiences refraction towards the magnetic null point and that the effect of this refraction depends upon the Alfvén speed profile. The wave and thus the wave energy accumulate at the null point. We have found that current buildup is exponential and the exponent is dependent upon ε. Thus, for the fast wave there is preferential heating at the null point. For the Alfvén wave, we find that the wave propagates along the field lines. For an Alfvén wave generated along the fan plane, the wave accumulates along the spine. For an Alfvén wave generated across the spine, the value of ε determines where the wave accumulation will occur: fan plane (ε=1), along the x-axis (0<ε<1) or along the y-axis (ε>1). We have shown analytically that currents build up exponentially, leading to preferential heating in these areas. The work described here highlights the importance of understanding the magnetic topology of the coronal magnetic field for the location of wave heating. Title: Heating the corona by nanoflares: simulations of energy release triggered by a kink instability Authors: Browning, P. K.; Gerrard, C.; Hood, A. W.; Kevis, R.; van der Linden, R. A. M. Bibcode: 2008A&A...485..837B Altcode: Context: The heating of solar coronal plasma to millions of degrees is likely to be due to the superposition of many small energy-releasing events, known as nanoflares. Nanoflares dissipate magnetic energy through magnetic reconnection.
Aims: A model has been recently proposed in which nanoflare-like heating naturally arises, with a sequence of dissipation events of various magnitudes. It is proposed that heating is triggered by the onset of ideal instability, with energy release occurring in the nonlinear phase due to fast magnetic reconnection. The aim is to use numerical simulations to investigate this heating process.
Methods: Three-dimensional magnetohydrodynamic numerical simulations of energy release are presented for a cylindrical coronal loop model. Initial equilibrium magnetic-field profiles are chosen to be linearly unstable, with a two-layer parameterisation of the current profile. The results are compared with calculations of linear instability, with line-tying, which are extended to account for a potential field layer surrounding the loop. The energy release is also compared with predictions that the field relaxes to a state of minimum magnetic energy with conserved magnetic helicity (a constant α force-free field).
Results: The loop initially develops a helical kink, whose structure and growth rate are generally in accordance with linear stability theory, and subsequently a current sheet forms. During this phase, there is a burst of kinetic energy while the magnetic energy decays. A new relaxed equilibrium is established that corresponds quite closely to a constant α field. The fraction of stored magnetic energy released depends strongly on the initial current profile, which agrees with the predictions of relaxation theory.
Conclusions: Energy dissipation events in a coronal loop are triggered by the onset of ideal kink instability. Magnetic energy is dissipated, leading to large or small heating events according to the initial current profile. Title: MHD mode conversion in a stratified atmosphere Authors: McDougall, A. M. Dee; Hood, Alan W. Bibcode: 2008IAUS..247..296M Altcode: 2008arXiv0808.0145D Mode conversion in the region where the sound and Alfvén speeds are equal is a complex process, which has been studied both analytically and numerically, and has been seen in observations. In order to further the understanding of this process we set up a simple, one-dimensional model, and examine wave propagation through this system using a combination of analytical and numerical techniques. Simulations are carried out in a gravitationally stratified atmosphere with a uniform, vertical magnetic field for both isothermal and non-isothermal cases. For the non-isothermal case a temperature profile is chosen to mimic the steep temperature gradient encountered at the transition region. In all simulations, a slow wave is driven on the upper boundary, thus propagating down from low-β to high-β plasma across the mode-conversion region. In addition, a detailed analytical study is carried out where we predict the amplitude and phase of the transmitted and converted components of the incident wave as it passes through the mode-conversion region. A comparison of these analytical predictions with the numerical results shows good agreement, giving us confidence in both techniques. This knowledge may be used to help determine wave types observed and give insight into which modes may be involved in coronal heating. Title: Photospheric cancelling magnetic features and associated phenomena in a stratified solar atmosphere Authors: von Rekowski, B.; Hood, A. W. Bibcode: 2008MNRAS.385.1792V Altcode: 2008MNRAS.tmp..254V We present two-dimensional numerical magnetohydrodynamics (MHD) simulations of a photospheric cancelling magnetic feature (CMF) and the associated reconnection event in a stratified solar atmosphere. Both, reconnection phase and cancellation phase, are modelled in a self-consistent way. It is found that different quiet-Sun phenomena result from the CMF, which is driven by converging photospheric flows. The type of structure forming in the low solar atmosphere depends on the initial overall plasma density magnitude and on the heating and cooling mechanisms included. The arising phenomenon can be a bright structure such as an X-ray bright point, a small-scale filament or a mixture of both of them. Loop-like brightening in various parts of the magnetic structure is found in all cases. Title: Solar coronal heating by magnetic cancellation - III. Thermodynamics Authors: von Rekowski, B.; Hood, A. W. Bibcode: 2008MNRAS.384..972V Altcode: 2008MNRAS.tmp..118V We present two-dimensional numerical magnetohydrodynamics simulations of a coronal X-ray bright point (XBP) caused by a cancelling magnetic feature (CMF). Cancellation is driven by converging motions of two magnetic bipolar sources. These sources are initially disconnected from each other so that both, the CMF and the associated reconnection/heating event (i.e. the XBP), are modelled in a self-consistent way. In the initial state, there is no X-point but two separatrices are present. Hence, the reconnection/heating and the cancellation phases have not yet started. Our numerical experiments end shortly after the converging magnetic bipole has fully cancelled. By this time, reconnection in the inner domain has ceased and occurs only at the base. Solving the energy equation with various heating and cooling terms included, and considering different bottom boundary conditions, reveals that the unrealistically high temperatures produced by Ohmic heating are reduced to more moderate temperatures of 1.5-2 MK consistent with observations of XBPs, if thermal conduction is included and density and temperature are fixed at the base. Title: Emerging flux tubes from the solar interior into the atmosphere: effects of non-constant twist Authors: Murray, M. J.; Hood, A. W. Bibcode: 2008A&A...479..567M Altcode: Context: Observations of large-scale solar emergence events indicate that the magnetic field is already twisted prior to its emergence. However, the nature of twist of the pre-emergence field is largely unknown.
Aims: By testing two different twist profiles for subsurface magnetic flux tubes, we aim to identify any differences in the emergence process of the field and its atmospheric signatures that occur as a result of the twist. Given that differences do occur, future comparisons of these emergence results with observations should reveal specific properties of the twist of the subsurface magnetic field.
Methods: Using a 3D numerical MHD code, we consider a simple stratified model, comprising of one solar interior layer and three overlying atmospheric layers. We set a horizontal, twisted flux tube in the lowest layer and prescribe the central protion along the tube's length to be buoyant so that it will rise towards the surface. We test two different non-constant twist profiles for the tube and perform a parameter study for each profile, looking for differences and similarities during the rise, emergence and expansion stages of the tube's evolution.
Results: We find that, irrespective of the tube's twist profile, if the tube initially has a low tension force then it will experience greater expansion and consequential weakening of its field strength during the rise through the solar interior. Thus, upon reaching the solar surface it will fail to undergo a magnetic buoyancy instability and will not emerge into the atmosphere. For those tubes that do emerge into the atmosphere, there is little distinction between the atmospheric field and few indicators as to the initial twist profile of the tube. In general, tubes with stronger tension forces have a faster growth rate of the magnetic buoyancy instability, while tubes with weaker tension forces expand to a greater degree in the horizontal direction post-emergence. Synthesised magnetograms at the solar surface do vary between the two tested twist profiles but only in cases with initially low tension forces.
Conclusions: Upon emergence, it appears that most of the specific details of the tube's initial twist are lost. The field must initially be sufficiently twisted such that it is able to undergo a magnetic buoyancy instability but such a level of twist subsequently results in the emerging flux having generic atmospheric characteristics. Only in cases with an initially low tension force is it possible to make some distiction post-emergence by considering magnetograms at the solar surface. Title: A Flux Emergence Model for Solar Eruptions Authors: Archontis, V.; Hood, A. W. Bibcode: 2008ApJ...674L.113A Altcode: 2008arXiv0801.1649A We have simulated the three-dimensional (3D) emergence and interaction of two twisted flux tubes, which rise from the interior into the outer atmosphere of the Sun. We present evidence for the multiple formation and eruption of flux ropes inside the emerging flux systems and hot arcade-like structures in between them. Their formation is due to internal reconnection, occurring between oppositely directed, highly stretched, and sheared field lines at photospheric heights. Most of the eruptions escape into the corona, but some are confined and fade away without leaving the low atmosphere. As these flux ropes erupt, new reconnected field lines accumulate around the main axis of the initial magnetic flux systems. We also show the complex 3D field-line geometry and the structure of the multiple current sheets, which form as a result of the reconnection between the emerging flux systems. 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: Coronal heating by nanoflares: a model based on Taylor relaxation following kink instability Authors: van der Linden, Ronald; Browning, Philippa; Hood, Alan Bibcode: 2008cosp...37.3285V Altcode: 2008cosp.meet.3285V In this work we present progress on a recently proposed model in which coronal heating is generated by nanoflares, with a sequence of dissipation events of various magnitudes according to the initial current profile. In this model it was proposed that heating is triggered by the onset of ideal instability, with energy release occurring in the nonlinear phase due to fast magnetic reconnection. As a proof of principle, the model was applied to a simplified representation of coronal loops consisting of two regions of constant-alpha force-free magnetic fields joined together at an interface. By adding an evolutionary scenario, the field evolves until it reaches the stability threshold, after which a kink instability sets in with resistive dissipation of the magnetic energy. The distribution of nanoflares energies can be obtained in a straightforward way by using the Taylor relaxation principle, whereby the field evolves to the lowest energy state under the constraint of conservation of helicity (a constant-alpha field). This heating process has also been verified for a number of cases using numerical simulations. These studies showed that the loop initially develops a helical kink, whose structure and growth rate are generally in accordance with linear stability theory, and subsequently a current sheet forms, which leads to a burst of kinetic energy whilst magnetic energy decays. A new relaxed equilibrium is established which corresponds quite closely to a constant-alpha field. The fraction of stored magnetic energy released depends strongly on the initial current profile, and this is in agreement with the predictions of relaxation theory. It is discussed how observational data of loop structure and footpoint motions could be used to apply this model so as to generate a nanoflare distribution. Title: Preface: A Topical Issue in Honor of Professor Bernard Roberts Authors: Ballester, J. L.; Erdélyi, R.; Hood, A. W.; Leibacher, J. W.; Nakariakov, V. M. Bibcode: 2007SoPh..246....1B Altcode: No abstract at ADS Title: A New Look at Mode Conversion in a Stratified Isothermal Atmosphere Authors: McDougall, A. M. D.; Hood, A. W. Bibcode: 2007SoPh..246..259M Altcode: 2007arXiv0707.0830M Recent numerical investigations of wave propagation near coronal magnetic null points (McLaughlin and Hood: Astron. Astrophys.459, 641, 2006) have indicated how a fast MHD wave partially converts into a slow MHD wave as the disturbance passes from a low-β plasma to a high-β plasma. This is a complex process and a clear understanding of the conversion mechanism requires the detailed investigation of a simpler model. An investigation of mode conversion in a stratified, isothermal atmosphere with a uniform, vertical magnetic field is carried out, both numerically and analytically. In contrast to previous investigations of upward-propagating waves (Zhugzhda and Dzhalilov: Astron. Astrophys.112, 16, 1982a; Cally: Astrophys. J.548, 473, 2001), this paper studies the downward propagation of waves from a low-β to high-β environment. A simple expression for the amplitude of the transmitted wave is compared with the numerical solution. Title: Ionospheric depletion in auroral downward currents Authors: Cran-McGreehin, Alexandra P.; Wright, Andrew N.; Hood, Alan W. Bibcode: 2007JGRA..11210309C Altcode: The auroral downward field-aligned current is mainly carried by electrons of ionospheric origin accelerated into the magnetosphere along the Earth's high-latitude field lines. The ionosphere is a finite source of electrons: Thus, if a current is to continue to flow, it is natural to assume that the current region must broaden to access more current carriers. In this paper, we present an Alfvén wave model of magnetosphere-ionosphere interaction to describe the evolution of ionospheric E region number density under the influence of a downward current. The behavior of the system falls into two regimes depending upon whether the quantity ? = j?0/αene2h is greater or less than unity (where j?0 is initial current density, α is the recombination coefficient, ne is background E region number density, and h is E region height): If the current density is smaller than a critical current density, jc = αene2h (i.e., ? < 1), then the E region only depletes within the original current region, and there is sufficient photoionization to feed the current to the magnetosphere; if the required current density is larger than jc (i.e., ? > 1), then the current region is forced to broaden in order to access sufficient electrons. On the dayside, where a typical E region number density is ∼1011 m-3, broadening only occurs for very strong current densities ∼10 μA m-2; on the nightside, however, where E region number densities can fall by a factor of 10, broadening occurs for any current density greater than ∼0.1 μA m-2. From this model, we derive expressions for the final depletion width (generally ∼1-10 times the width of the original current region) and for the characteristic timescale of depletion (typically ∼10-100 s). Title: The Effect of the Relative Orientation between the Coronal Field and New Emerging Flux. I. Global Properties Authors: Galsgaard, K.; Archontis, V.; Moreno-Insertis, F.; Hood, A. W. Bibcode: 2007ApJ...666..516G Altcode: 2007arXiv0705.1097G The emergence of magnetic flux from the convection zone into the corona is an important process for the dynamical evolution of the coronal magnetic field. In this paper we extend our previous numerical investigations, by looking at the process of flux interaction as an initially twisted flux tube emerges into a plane-parallel, coronal magnetic field. Significant differences are found in the dynamical appearance and evolution of the emergence process depending on the relative orientation between the rising flux system and any preexisting coronal field. When the flux systems are nearly antiparallel, the experiments show substantial reconnection and demonstrate clear signatures of a high-temperature plasma located in the high-velocity outflow regions extending from the reconnection region. However, the cases that have a more parallel orientation of the flux systems show very limited reconnection and none of the associated features. Despite the very different amount of reconnection between the two flux systems, it is found that the emerging flux that is still connected to the original tube reaches the same height as a function of time. As a compensation for the loss of tube flux, a clear difference is found in the extent of the emerging loop in the direction perpendicular to the main axis of the initial flux tube. Increasing amounts of magnetic reconnection decrease the volume, which confines the remaining tube flux. Title: Simple emergence structures from complex magnetic fields Authors: Murray, M. J.; Hood, A. W. Bibcode: 2007A&A...470..709M Altcode: Context: There has been suggestions that the initial subsurface magnetic field in flux emergence models is too organised. Thus, it may be that the results they yield are very specific and cannot be applied to the generic flux emergence process occurring on the Sun.
Aims: We will demonstrate that the interaction of two flux tubes can increase the complexity of the solar interior's magnetic field. However, the subsequent emergence of this complex field results in the atmospheric flux having a simple and generic structural form.
Methods: Using a numerical 3D MHD code, we consider the evolution of two flux tubes within a vertically stratified domain, representing the upper layers of the solar interior through to the corona. The flux tubes are initially situated in the solar interior, one tube lying directly above the other. By choosing the lower tube to be buoyant, whilst the upper tube is in mechanical equilibrium with its surroundings, we encourage the interaction of the two tubes within the solar interior. Thus, we will create a more complex magnetic field lying just below the photospheric surface than would be generated with a single flux tube model. By studying the subsequent emergence and structure of the resulting atmospheric field we will be able to identify if there are any significant changes due to the increased complexity of the field below the surface.
Results: The reconnection process modifies the topology of the subsurface magnetic field as indicated by the results of previous simulations. Since reconnection is occurring in a high plasma-β region, where the sound speed is greater than the Alfvén speed, we observe no significant jets and also find no significant heating. When this reconnected field comes to the surface it is complex but the emergence occurs in much the same manner as for a single flux tube and, therefore, produces very little change in the atmospheric field. This strongly indicates that the results of previous emergence simulations are valid for both simple and complex subsurface fields. Title: Emergence and interaction of twisted flux tubes in the Sun Authors: Archontis, V.; Hood, A. W.; Brady, C. Bibcode: 2007A&A...466..367A Altcode: Aims: We present results from numerical simulations that study the interaction of a pair of twisted, buoyant magnetic flux tubes, which rise from the solar interior into the outer atmosphere of the Sun. The aim of our new model is to reproduce some of the dynamic solar phenomena in a self-consistent manner.
Methods: We perform non-linear simulations in 2.5D numerical experiments by solving the compressible and resistive MHD equations using a Lagrangian remap, shock capturing code (Lare2D). For some aspects of the problem, we consider the evolution of the system using both uniform and locally enhanced resistivity.
Results: The two flux tubes start to rise at the same time but from a different height below the photosphere. The leading (first) tube, which is originally located nearer to the surface, rises and eventually expands above the photosphere forming a magnetized atmosphere for the upcoming system (second tube). Current sheets, high-velocity reconnection jets, plasmoids, loop brightnenings and arcade flare-like structures are formed, for the first time in such numerical experiments, self-consistently by the emergence, expansion and the dynamical interaction between the two emerging flux systems. Title: 3D simulations identifying the effects of varying the twist and field strength of an emerging flux tube Authors: Murray, M. J.; Hood, A. W.; Moreno-Insertis, F.; Galsgaard, K.; Archontis, V. Bibcode: 2006A&A...460..909M Altcode: Aims.We investigate the effects of varying the magnetic field strength and the twist of a flux tube as it rises through the solar interior and emerges into the atmosphere.
Methods: .Using a 3D numerical MHD code, we consider a simple stratified model, comprising of one solar interior layer and three overlying atmospheric layers. We set a horizontal, twisted flux tube in the lowest layer. The specific balance of forces chosen results in the tube being fully buoyant and the temperature is decreased in the ends of the tube to encourage the formation of an Ω-shape along the tube's length. We vary the magnetic field strength and twist independently of each other so as to give clear results of the individual effects of each parameter.
Results: .We find a self-similar evolution in the rise and emergence of the flux tube when the magnetic field strength of the tube is modified. During the rise through the solar interior, the height of the crest and axis, the velocity of the crest and axis, and the decrease in the magnetic field strength of the axis of the tube are directly dependent upon the initial magnetic field strength given to the tube. No such self-similarity is evident when the twist of the flux tube is changed, due to the complex interaction of the tension force on the rise of the tube. For low magnetic field strength and twist values, we find that the tube cannot fully emerge into the atmosphere once it reaches the top of the interior since the buoyancy instability criterion cannot be fulfilled. For those tubes that do advance into the atmosphere, when the magnetic field strength has been modified, we find further self-similar behaviour in the amount of tube flux transported into the atmosphere. For the tubes that do emerge, the variation in the twist results in the buoyancy instability, and subsequent emergence, occurring at different locations along the tube's length.
Title: MHD mode coupling in the neighbourhood of a 2D null point Authors: McLaughlin, J. A.; Hood, A. W. Bibcode: 2006A&A...459..641M Altcode: 2007arXiv0712.2402M Context: .At this time there does not exist a robust set of rules connecting low and high β waves across the β ≈ 1 layer. The work here contributes specifically to what happens when a low β fast wave crosses the β ≈ 1 layer and transforms into high β fast and slow waves.
Aims: .The nature of fast and slow magnetoacoustic waves is investigated in a finite β plasma in the neighbourhood of a two-dimensional null point.
Methods: .The linearised equations are solved in both polar and cartesian forms with a two-step Lax-Wendroff numerical scheme. Analytical work (e.g. small β expansion and WKB approximation) also complement the work.
Results: .It is found that when a finite gas pressure is included in magnetic equilibrium containing an X-type null point, a fast wave is attracted towards the null by a refraction effect and that a slow wave is generated as the wave crosses the β ≈ 1 layer. Current accumulation occurs close to the null and along nearby separatrices. The fast wave can now pass through the origin due to the non-zero sound speed, an effect not previously seen in related papers but clear seen for larger values of β. Some of the energy can now leave the region of the null point and there is again generation of a slow wave component (we find that the fraction of the incident wave converted to a slow wave is proportional to β). We conclude that there are two competing phenomena; the refraction effect (due to the variable Alfvén speed) and the contribution from the non-zero sound speed.
Conclusions: .These experiments illustrate the importance of the magnetic topology and of the location of the β ≈ 1 layer in the system. Title: Three-dimensional Plasmoid Evolution in the Solar Atmosphere Authors: Archontis, V.; Galsgaard, K.; Moreno-Insertis, F.; Hood, A. W. Bibcode: 2006ApJ...645L.161A Altcode: We present clear evidence of the formation of three-dimensional (3D) plasmoids in the current sheet between two magnetic flux systems in a 3D numerical experiment of flux emergence into the solar atmosphere and study their properties and time evolution. Plasmoids are most likely the result of resistive tearing mode instabilities. They adopt the shape of a solenoid contained within the current sheet: the solenoid is tightly wound when the field in the two flux systems is close to antiparallel. The plasmoids are expelled to the sides of the sheet as a result of a reconnection imbalance between the two x-lines on their sides. We show the complex, 3D field line geometry in various plasmoids: individual plasmoid field lines have external linkages to the flux system on either side of the current sheet; we also find field lines that go through a few plasmoids in succession, probably indicating that the field line has resulted from multiple reconnection events. Title: Magnetohydrodynamics wave propagation in the neighbourhood of two dipoles Authors: McLaughlin, J. A.; Hood, A. W. Bibcode: 2006A&A...452..603M Altcode: 2007arXiv0712.1784M Context: .This paper is the third in a series of investigations by the authors.
Aims: .The nature of fast magnetoacoustic and Alfvén waves is investigated in a 2D β=0 plasma in the neighbourhood of two dipoles.
Methods: .We use both numerical simulations (two-step Lax-Wendroff scheme) and analytical techniques (WKB approximation).
Results: .It is found that the propagation of the linear fast wave is dictated by the Alfvén speed profile and that close to the null, the wave is attracted to the neutral point. However, it is also found that in this magnetic configuration some of the wave can escape the refraction effect; this had not been seen in previous investigations by the authors. The wave split occurs near the regions of very high Alfvén speed (found near the loci of the two dipoles). Also, for the set-up investigated it was found that 40% of the wave energy accumulates at the null. Ohmic dissipation will then extract the wave energy at this point. The Alfvén wave behaves in a different manner in that part of the wave accumulates along the separatrices and part escapes. Hence, the current density will accumulate at this part of the topology and this is where wave heating will occur.
Conclusions: .The phenomenon of wave accumulation at a specific place is a feature of both wave types, as is the result that a fraction of the wave can now escape the numerical box when propagating in this magnetic configuration. Title: Flux emergence and interaction with a coronal field: 3D MHD simulations Authors: Archontis, V.; Moreno-Insertis, F.; Galsgaard, K.; Hood, A. W. Bibcode: 2006IAUS..233...53A Altcode: The dynamic process of magnetic flux emergence from the solar interior to the outer atmosphere may well be related with eruptive phenomena and intense events of the Solar activity. However, the physics of the emergence is not still well understood. Thus, we have performed 3D MHD simulations to study the rising motion of a twisted flux tube from the convection zone of the Sun and its interaction with a preexisting coronal magnetic field. The results show that the reconnection process depends criticaly on the initial relative orientation between the two magnetic flux systems into contact. On the other hand, the overal process of emergence depends mostly on the dynamics of the sub-photospheric plasma. Title: The Three-dimensional Interaction between Emerging Magnetic Flux and a Large-Scale Coronal Field: Reconnection, Current Sheets, and Jets Authors: Archontis, V.; Moreno-Insertis, F.; Galsgaard, K.; Hood, A. W. Bibcode: 2005ApJ...635.1299A Altcode: Using MHD numerical experiments in three dimensions, we study the emergence of a bipolar magnetic region from the solar interior into a model corona containing a large-scale, horizontal magnetic field. An arch-shaped concentrated current sheet is formed at the interface between the rising magnetized plasma and the ambient coronal field. Three-dimensional reconnection takes place along the current sheet, so that the corona and the photosphere become magnetically connected, a process repeatedly observed in recent satellite missions. We show the structure and evolution of the current sheet and how it changes in time from a simple tangential discontinuity to a rotational discontinuity with no null surface. We find clear indications that individual reconnection events in this three-dimensional environment in the advanced stage are not one-off events, but instead take place in a continuous fashion, with each field line changing connectivity during a finite time interval. We also show that many individual field lines of the rising tube undergo multiple processes of reconnection at different points in the corona, thus creating photospheric pockets for the coronal field. We calculate global measures for the amount of subphotospheric flux that becomes linked to the corona during the experiment and find that most of the original subphotospheric flux becomes connected to coronal field lines. The ejection of plasma from the reconnection site gives rise to high-speed and high-temperature jets. The acceleration mechanism for those jets is akin to that found in previous two-dimensional models, but the geometry of the jets bears a clear three-dimensional imprint, having a curved-sheet appearance with a sharp interface to the overlying coronal magnetic field system. Temperatures and velocities of the jets in the simulations are commensurate with those measured in soft X-rays by the Yohkoh satellite. Title: a Model of Nanoflare Energies Based on Relaxation Theory Authors: Browning, P. K.; van der Linden, R.; Gerrard, C.; Kevis, R.; Hood, A. Bibcode: 2005ESASP.600E..82B Altcode: 2005dysu.confE..82B; 2005ESPM...11...82B No abstract at ADS Title: Magnetic Flux Emergence and its Interaction with AN Existing Coronal Field Authors: Galsgaard, K.; Moreno-Insertis, F.; Archontis, V.; Hood, A. Bibcode: 2005ESASP.596E..27G Altcode: 2005ccmf.confE..27G No abstract at ADS Title: Magnetic Flux Emergence and its Interaction with AN Existing Coronal Field Authors: Galsgaard, K.; Moreno-Insertis, F.; Archontis, V.; Hood, A. Bibcode: 2005ESASP.596E..55G Altcode: 2005ccmf.confE..55G No abstract at ADS Title: MHD wave propagation in the neighbourhood of two null points Authors: McLaughlin, J. A.; Hood, A. W. Bibcode: 2005A&A...435..313M Altcode: 2007arXiv0712.1809M The nature of fast magnetoacoustic and Alfvén waves is investigated in a zero β plasma in the neighbourhood of a pair of two-dimensional null points. This gives an indication of wave propagation in the low β solar corona, for a more complicated magnetic configuration than that looked at by McLaughlin & Hood (2004, A&A, 420, 1129). It is found that the fast wave is attracted to the null points and that the front of the wave slows down as it approaches the null point pair. Here, the wave splits and part of the wave accumulates at one null and the rest at the other. Current density will then accumulate at these points and ohmic dissipation will then extract the energy in the wave at these points. This suggests locations where wave heating will occur in the corona. The Alfvén wave behaves in a different manner in that the wave accumulates along the separatrices. Hence, the current density will accumulate at this part of the topology and this is where wave heating will occur. However, the phenomenon of wave accumulation at a specific place is a feature of both wave types, and illustrates the importance of studying the topology of the corona when considering MHD wave propagation. 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: Phase mixing of Alfvén pulses and wavetrains propagating in coronal holes Authors: Hood, A. W.; Brooks, S. J.; Wright, A. N. Bibcode: 2005RSPSA.461..237H Altcode: The propagation of Alfvén pulses into an inhomogeneous model of a solar coronal hole is investigated. The algebraic damping of single and bi-polar pulses remains for the leading and trailing pulses as the number of pulses is increased but the decay of the internal pulses returns to the exponential damping of an infinite wavetrain when three pulses or more are present. Thus, wavetrains with most of their energy residing in internal oscillations will be dominated by efficient exponential damping. In contrast, short wavetrains with most of their energy in the leading and trailing pulses will suffer less efficient algebraic damping. The implications of both the damping of these disturbances to the heating of coronal holes and the nonlinear wave pressure to the acceleration of the solar wind are discussed. Title: A Three-dimensional Study of Reconnection, Current Sheets, and Jets Resulting from Magnetic Flux Emergence in the Sun Authors: Galsgaard, K.; Moreno-Insertis, F.; Archontis, V.; Hood, A. Bibcode: 2005ApJ...618L.153G Altcode: 2004astro.ph.10057G We present the results of a set of three-dimensional numerical simulations of magnetic flux emergence from below the photosphere and into the corona. The corona includes a uniform and horizontal magnetic field as a model for a preexisting large-scale coronal magnetic system. Cases with different relative orientations of the upcoming and coronal fields are studied. Upon contact, a concentrated current sheet with the shape of an arch is formed at the interface that marks the positions of maximum jump in the field vector between the two systems. Relative angles above 90° yield abundant magnetic reconnection and plasma heating. The reconnection is seen to be intrinsically three-dimensional in nature and to be accompanied by marked local heating. It generates collimated high-speed outflows only a short distance from the reconnection site, and these propagate along the ambient magnetic field lines as jets. As a result of the reconnection, magnetic field lines from the magnetized plasma below the surface end up connecting to coronal field lines, thus causing a profound change in the connectivity of the magnetic regions in the corona. The experiments presented here yield a number of features repeatedly observed with the TRACE and Yohkoh satellites, such as the establishment of connectivity between emergent and preexisting active regions, local heating, and high-velocity outflows. Title: Flux Emergence from the Solar Interior Into a Uniformly Magnetized Corona Authors: Moreno-Insertis, F.; Galsgaard, K.; Archontis, V.; Hood, A. Bibcode: 2004ESASP.575..216M Altcode: 2004soho...15..216M No abstract at ADS Title: Preferential Heating in the Neighbourhood of a Two-Dimensional Null Point Authors: McLaughlin, J. A.; Hood, A. W. Bibcode: 2004ESASP.575...74M Altcode: 2004soho...15...74M No abstract at ADS Title: Coronal Heating by Nanoflares: a Reconnection Model Authors: Browning, P. K.; van der Linden, R.; Gerrard, C.; Kevis, R.; Hood, A. Bibcode: 2004ESASP.575..210B Altcode: 2004soho...15..210B 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: 3D MHD Simulations on Magnetic Flux Emergence Authors: Archontis, V.; Moreno-Insertis, F.; Galsgaard, K.; Hood, A. Bibcode: 2004ESASP.575..342A Altcode: 2004soho...15..342A No abstract at ADS Title: Emergence of magnetic flux from the convection zone into the corona Authors: Archontis, V.; Moreno-Insertis, F.; Galsgaard, K.; Hood, A.; O'Shea, E. Bibcode: 2004A&A...426.1047A Altcode: Numerical experiments of the emergence of magnetic flux from the uppermost layers of the solar interior to the photosphere and its further eruption into the low atmosphere and corona are carried out. We use idealized models for the initial stratification and magnetic field distribution below the photosphere similar to those used for multidimensional flux emergence experiments in the literature. The energy equation is adiabatic except for the inclusion of ohmic and viscous dissipation terms, which, however, become important only at interfaces and reconnection sites. Three-dimensional experiments for the eruption of magnetic flux both into an unmagnetized corona and into a corona with a preexisting ambient horizontal field are presented. The shocks preceding the rising plasma present the classical structure of nonlinear Lamb waves. The expansion of the matter when rising into the atmosphere takes place preferentially in the horizontal directions: a flattened (or oval) low plasma-β ball ensues, in which the field lines describe loops in the corona with increasing inclination away from the vertical as one goes toward the sides of the structure. Magnetograms and velocity field distributions on horizontal planes are presented simultaneously for the solar interior and various levels in the atmosphere. Since the background pressure and density drop over many orders of magnitude with increasing height, the adiabatic expansion of the rising plasma yields very low temperatures. To avoid this, the entropy of the rising fluid elements should be increased to the high values of the original atmosphere via heating mechanisms not included in the present numerical experiments. The eruption of magnetic flux into a corona with a preexisting magnetic field pointing in the horizontal direction yields a clear case of essentially three-dimensional reconnection when the upcoming and ambient field systems come into contact. The coronal ambient field is chosen at time t=0 perpendicular to the direction of the tube axis and thus, given the twist of the magnetic tube, almost anti-parallel to the field lines at the upper boundary of the rising plasma ball. A thin, dome-shaped current layer is formed at the interface between the two flux systems, in which ohmic dissipation and heating are taking place. The reconnection proceeds by merging successive layers on both sides of the reconnection site; however, this occurs not only at the cusp of the interface, but, also, gradually along its sides in the direction transverse to the ambient magnetic field. The topology of the magnetic field in the atmosphere is thereby modified: the reconnected field lines typically are part of the flanks of the tube below the photosphere but then join the ambient field system in the corona and reach the boundaries of the domain as horizontal field lines. Title: The damping of slow MHD waves in solar coronal magnetic fields. III. The effect of mode coupling Authors: De Moortel, I.; Hood, A. W.; Gerrard, C. L.; Brooks, S. J. Bibcode: 2004A&A...425..741D Altcode: The properties of slow MHD waves in a two dimensional model are investigated, in a low-beta plasma. Including a horizontal density variation causes ``phase mixing'' and coupling between slow and fast MHD waves. The effects of different density profiles, different driving frequencies, different values for the viscosity coefficient and plasma beta (<1) are studied. Using numerical simulations, it was found that the behaviour of the perturbed velocity was strongly dependent on the values of the parameters. From analytical approximations, a strong interaction with the fundamental, normal modes of the system was found to play an important role. The coupling to the fast wave proved to be an inefficient way to extract energy from the driven slow wave and is unlikely to be responsible for the rapid damping of propagating slow MHD waves, observed by TRACE. The ``phase mixing'' of the slow waves due to the (horizontal) density inhomogeneity does cause a significant amount of damping, but is again unlikely to be sufficiently strong to explain the rapid observed damping. Title: Current build-up as a result of the kink instability in a loop Authors: Gerrard, C. L.; Hood, A. W. Bibcode: 2004SoPh..223..143G Altcode: The kink instability may be responsible for compact loop flares since the instability is triggered once the twist in a coronal loop exceeds a critical value. During the non-linear evolution of the instability a large current builds up, reconnection can occur and the magnetic energy released due to reconnection may explain the rapid heating of the flare. However, there has been some debate over the nature of the current concentration and, in particular, whether the current saturates or whether it is a current sheet, and what influences these possible states. In this paper we consider two similar equilibria having a twist function which rises to a peak and then falls off. One is steeper than the other allowing us to investigate whether the steepness of the peak has any effect on the nature of the current. For each profile, we run the code on five different grid resolutions and see how the maximum of the current scales with grid resolution. We also look for behavior in the x-component of the velocity which might be similar to the step-function behavior associated with singularities in the linear kink instability. For both profiles we find that the current scales almost linearly with resolution and that vx drops steeply at the position of the current concentration. This suggests that, for these particular profiles, there are indications of current sheet formation and that the steepness in the peak of the twist does not affect the nature of the current. Title: Wavelet Analysis: the effect of varying basic wavelet parameters Authors: De Moortel, I.; Munday, S. A.; Hood, A. W. Bibcode: 2004SoPh..222..203D Altcode: The most commonly used methods to analyse (observed) quasi-periodic signals are standard techniques such as Fourier and wavelet analysis. Whereas a Fourier transform provides information on the dominant frequencies, wavelet analysis has the added advantage of providing the time localisation of the various frequency components. The usefulness and robustness of wavelet analysis is investigated by varying the different parameters which characterise the `mother' wavelet. We examine the effect of varying these parameters on the temporal and frequency resolution and the damping profile, which can be obtained from the wavelet transform. Additionally, the effect of a changing periodicity on the wavelet transform is investigated. Both simple harmonic functions and intensity oscillations observed by TRACE are used to demonstrate the various advantages and disadvantages of the different methods. In general, using the Paul wavelet or a smaller value of the wavelet parameter k provides a better time resolution, whereas the Morlet wavelet or a larger value of k improves the frequency resolution. Overall, our results indicate that great care is needed when using a wavelet analysis and that all the possible factors that could affect the transform should be taken into consideration. Title: Effect of photospheric twisting motions on a confined toroidal loop Authors: Gerrard, C. L.; Hood, A. W.; Brown, D. S. Bibcode: 2004SoPh..222...79G Altcode: In this paper we investigate the effect of twisting motions at the photosphere on a curved loop confined by overlying field lines. We find that the twisting motions form a twisted loop along which a current builds up. However, the toroidal curvature of the loop appears to have a stabilising effect as there is no sign of the kink instability for a twist of 3.4 π whereas in a straight cylinder for the same twist profile the critical twist is approximately 2.5 π. When we include resistivity in the simulation there are indications that reconnection occurs and releases a substantial proportion of the free magnetic energy. Title: MHD wave propagation in the neighbourhood of a two-dimensional null point Authors: McLaughlin, J. A.; Hood, A. W. Bibcode: 2004A&A...420.1129M Altcode: 2007arXiv0712.1792M The nature of fast magnetoacoustic and Alfvén waves is investigated in a zero β plasma. This gives an indication of wave propagation in the low β solar corona. It is found that for a two-dimensional null point, the fast wave is attracted to that point and the front of the wave slows down as it approaches the null point, causing the current density to accumulate there and rise rapidly. Ohmic dissipation will extract the energy in the wave at this point. This illustrates that null points play an important role in the rapid dissipation of fast magnetoacoustic waves and suggests the location where wave heating will occur in the corona. The Alfvén wave behaves in a different manner in that the wave energy is dissipated along the separatrices. For Alfvén waves that are decoupled from fast waves, the value of the plasma β is unimportant. However, the phenomenon of dissipating the majority of the wave energy at a specific place is a feature of both wave types. Title: Observations and theory of slow waves in coronal loops Authors: De Moortel, I.; Hood, A. W. Bibcode: 2004AAS...204.9502D Altcode: 2004BAAS...36..826D High cadence TRACE observations show that outward propagating intensity disturbances are a common feature in large, quiescent coronal loops, close to active regions. An overview is given of measured parameters of such longitudinal oscillations in coronal loops. The observed oscillations are interpreted as propagating slow magneto-acoustic waves and are unlikely to be flare-driven. A theoretical model of slow magneto-acoustic waves, incorporating the effects of gravitational stratification, the magnetic field geometry, thermal conduction and compressive viscosity is presented to explain the very short observed damping lengths. The results of these numerical simulations are compared with the TRACE observations. Preliminary results indicate that thermal conduction and the magnetic field geometry play an important role. Title: The damping of slow MHD waves in solar coronal magnetic fields. II. The effect of gravitational stratification and field line divergence Authors: De Moortel, I.; Hood, A. W. Bibcode: 2004A&A...415..705D Altcode: This paper continues the study of De Moortel & Hood (\cite{Moortelh03}) into the propagation of slow MHD waves in the solar corona. Firstly, the damping due to optically thin radiation is investigated and compared to the effect of thermal conduction. In a second stage, gravitational stratification is included in the model and it is found that this increases the damping length significantly. Finally, the effect of different magnetic field geometries on the damping of the slow waves is investigated. As a first approximation, a purely radial magnetic field is considered and although the amplitudes of the perturbations decrease due to the divergence of the field, the effect is small compared to the effect of thermal conduction. A more realistic local geometry, estimated from the observations, is investigated and it is demonstrated that a general area divergence can cause a significant, additional, decrease of the amplitudes of the perturbations. The results of numerical simulations, incorporating the effects of gravitational stratification, the magnetic field geometry and thermal conduction are compared with TRACE observations of propagating waves in coronal loops. It is found that a combination of thermal conduction and (general) area divergence yields detection lengths that are in good agreement with observed values. Title: Time-Frequency Analysis of Quasi-Periodic Signals Authors: De Moortel, I.; Munday, S.; Hood, A. W. Bibcode: 2004ESASP.547..501D Altcode: 2004soho...13..501D In recent years, the analysis of quasi-periodic signals observed by satellites such as SOHO and TRACE has become increasingly important. So far, mostly standard methods have been used, such as Fourier analysis to identify the dominant frequencies and wavelet analysis to provide the time localisation of the various frequency components. We compare the temporal and frequency resolution of different `time-frequency' methods. In particular, the usefulness and robustness of wavelet analysis is investigated by varying the different parameters which characterise the `mother' wavelet. Both simple harmonic functions and intensity oscillations observed by TRACE are used to demonstrate the various advantages and disadvantages of the different methods. Title: Evidence for Wave Dissipation through EUV Emission Line Narrowing Authors: Harrison, R. A.; Hood, A. W.; Pike, C. D. Bibcode: 2004ESASP.547..229H Altcode: 2004soho...13..229H Using long-duration observations over closed-field, quiet Sun regions above the solar equator, evidence has been found for the narrowing of coronal emission lines with increasing altitude. This is interpreted as evidence for wave dissipation in the quiet Sun corona. Title: MHD Waves in the Neighbourhood of a 2D X-Type Neutral Point Authors: McLaughlin, J. A.; Hood, A. W. Bibcode: 2004ESASP.547..537M Altcode: 2004soho...13..537M A linear, fast magnetoacoustic wave is generated at a boundary and travels towards an magnetic X-type neutral point. Due to refraction, the wave wraps itself around the null point, causing a large current to accumulate there. Simulations show that the current build up is exponential in time. The numerical simulations are in good agreement with analytic work based on a WKB solution obtained by the method of characteristics. Title: Observations and Theory of Longitudinal Waves in Coronal Loops Authors: De Moortel, I.; Hood, A. W.; De Pontieu, B. Bibcode: 2004ESASP.547..427D Altcode: 2004soho...13..427D High cadence TRACE observations show that outward propagating intensity disturbances are a common feature in large, quiescent coronal loops, close to active regions. An overview is given of measured parameters of such longitudinal oscillations in coronal loops. The observed oscillations are interpreted as propagating slow magnetoacoustic waves and are unlikely to be flare-driven. A basic magnetic field extrapolation is used to estimate the local geometry of the magnetic field. A theoretical model of slow magneto-acoustic waves, incorporating the effects of gravitational stratification, the magnetic field geometry, thermal conduction and compressive viscosity is presented to explain the very short observed damping lengths. The results of these numerical simulations are compared with the TRACE observations. Preliminary results indicate that the magnetic field geometry plays an important role. Title: A Quantitative Method to Optimise Magnetic Field Line Fitting of Observed Coronal Loops Authors: Carcedo, L.; Brown, D. S.; Hood, A. W.; Neukirch, T.; Wiegelmann, T. Bibcode: 2003SoPh..218...29C Altcode: Many authors use magnetic-field models to extrapolate the field in the solar corona from magnetic data in the photosphere. The accuracy of such extrapolations is usually judged qualitatively by eye, where a less judgemental quantitative approach would be more desirable. In this paper, a robust method for obtaining the best fit between a theoretical magnetic field and intensity observations of coronal loops on the solar disk will be presented. The method will be applied to Yohkoh data using a linear force-free field as an illustration. Any other theoretical model for the magnetic field can be used, provided there is enough freedom in the model to optimize the fit. Title: The damping of slow MHD waves in solar coronal magnetic fields Authors: De Moortel, I.; Hood, A. W. Bibcode: 2003A&A...408..755D Altcode: A theoretical description of slow MHD wave propagation in the solar corona is presented. Two different damping mechanisms, namely thermal conduction and compressive viscosity, are included and discussed in detail. We revise the properties of the ``thermal'' mode, which is excited when thermal conduction is included. The thermal mode is purely decaying in the case of standing waves, but is oscillatory and decaying in the case of driven waves. When thermal conduction is dominant, the waves propagate largely undamped, at the slower, isothermal sound speed. This implies that there is a minimum damping time (or length) that can be obtained by thermal conduction alone. The results of numerical simulations are compared with TRACE observations of propagating waves, driven by boundary motions, and standing waves observed by SUMER/SOHO, excited by an initial impulse. For typical coronal conditions, thermal conduction appears to be the dominant damping mechanism. Title: Determination of coronal loop properties from trace observations Authors: De Moortel, I.; Parnell, C. E.; Hood, A. W. Bibcode: 2003SoPh..215...69D Altcode: In this paper, we determine the temperature profile along the footpoints of large coronal loops observed by TRACE in both the 171 Å and 195 Å passbands. The temperature along the lower part of these coronal loops only shows small variations and can probably be considered to be isothermal. Using the obtained temperature profile T(s) and an estimate of the column depth along the loop, we then determine the pressure along the lower part of the observed coronal loops and hence the value of the pressure scale length. The obtained scale lengths correspond in order-of-magnitude with the theoretically predicted gravitational scale height. We show that the differences between the observed and predicted scale heights are unlikely to be caused by (significant) flows along the loops but could possibly be a consequence of the inclination of the loops. This implies that the quasi-periodic intensity oscillations observed in the loops are most probably caused by compressive waves propagating upward at the coronal sound speed. Title: Hydrodynamic Simulations of Longitudinal Intensity Oscillations Observed in Coronal Loops by TRACE Authors: Tanner, S. E.; Klimchuk, J. A.; Hood, A. W.; De Moortel, I. Bibcode: 2003SPD....34.0406T Altcode: 2003BAAS...35..811T Propagating intensity disturbances are often observed by TRACE in large coronal loops located at the perimeters of active regions (e.g., De Moortel et al., 2002, Solar Phys., 209, 61). On average, the disturbances have periods of 280 s, propagation speeds of 120 km s-1, intensity amplitudes of 4%, and surprisingly small damping (detection) lengths of 9000 km. In addition, there is a positive correlation between damping length and period. The preliminary interpretation of these disturbances is that they are rapidly dissipating slow magneto-acoustic waves.

To investigate this interpretation more rigorously, we have performed a series of detailed coronal loop simulations using our 1D hydrodynamic code, ARGOS. We generate waves in the loop by imposing a spatially localized oscillating force at the loop footpoint, using a range of different oscillation periods. We here report on the results of our study and, in particular, whether the damping lengths have the properties observed by TRACE.

This work was supported by NASA and ONR. Title: Kink unstable coronal loops: current sheets, current saturation and magnetic reconnection Authors: Gerrard, C. L.; Hood, A. W. Bibcode: 2003SoPh..214..151G Altcode: The kink instability in a coronal loop is a possible explanation of a compact loop flare as it may cause a current sheet to form allowing reconnection to take place and release the free magnetic energy stored in the loop. However, current sheets do not form in all cases. Ali and Sneyd (2001) investigated three different classes of equilibrium (determined by the form of the twist) using a magneto-frictional code. They searched for the equilibria to which the loop might evolve once it had become unstable to the kink instability. They found indications of current-sheet formation for only one class of equilibrium studied. However, as they pointed out, since their code searched for equilibria they were unable to say for certain that the loop would evolve in this way. In this paper we have considered the same three classes of equilibria but have used a code which follows the non-linear 3D MHD (magnetohydrodynamic) evolution of the loop. We have investigated whether or not there are indications of current-sheet formation. In the cases where there is evidence of this we have found that reconnection does occur and releases sufficient magnetic energy to explain a compact loop flare. Title: Field-aligned electron acceleration in Alfvén waves Authors: Wright, Andrew N.; Hood, Alan W. Bibcode: 2003JGRA..108.1135W Altcode: The field-aligned current of standing Alfvén waves is mainly carried by electrons travelling parallel to the magnetic field. During the upward current phase, magnetospheric electrons travel downward to the ionosphere. In large-amplitude Alfvén waves, where current densities reach a few μAm-2 above the ionosphere, the electrons achieve energies of the order of keV. This problem has been addressed recently in terms of two-fluid theory. The present paper builds on these studies by employing a distribution function formulation. When the electron motion is dominated by the parallel velocity component, we find the B/n curve is central to interpreting the solution: B/n has a peak (i.e., d(B/n)/dℓ = 0, where ℓ is path length along the field line) below which ionospheric electrons are trapped. Above the peak we find the parallel electric field is balanced by the convective plasma acceleration, as suggested by [1999] and has a value of the order of mV/m for ∼1 RE above the B/n peak. The maximum E∥ occurs where d2(B2/n2)/dℓ2 = 0 and is located a couple of density scale heights beyond the B/n peak. Title: MHD simulations of sunspot rotation and the coronal consequences Authors: Gerrard, C. L.; Brown, D. S.; Mellor, C.; Arber, T. D.; Hood, A. W. Bibcode: 2003SoPh..213...39G Altcode: A simplified magnetic configuration is used to model some aspects of observations of a rotating sunspot and its overlying coronal loops. In the observations a large sunspot rotates over a few days and two smaller pores spiral into it. The coronal loops become sigmoidal in shape and flares are seen in Yohkoh/SXT and GOES. We have modeled the sunspot, one of the pores and the loops connecting these to a diffuse region of plasma of the opposite polarity. Two sets of MHD simulations are considered: (i) rotation of the sunspot and pore alone and (ii) rotation of the sunspot with inflow of the pore. Rotation alone can trigger the ideal kink instability in the loops but only for a rotation that is much greater than the observed value. There is no build-up of current which is needed for magnetic reconnection to occur. However, when inflow is included a strong build-up of current is seen as the pore merges with the sunspot. Comparing these results from the simulations with the observations, we find that the observed merging of the pores coincides with the timing of the flare. Therefore, we suggest that the merging of the pores with the large sunspot may be responsible for the flaring. Title: Thermal conduction damping of longitudinal waves in coronal loops Authors: De Moortel, I.; Hood, A. W. Bibcode: 2003PADEU..13..127D Altcode: High cadence TRACE observations show that outward propagating intensity disturbances are a common feature in large coronal loops. An overview is given of measured parameters of such longitudinal waves in coronal loops. We found that loops that are situated above sunspot regions display intensity oscillations with periods centred around 3 minutes, whereas oscillations in `non-sunspot' loops show periods centred around 5 minutes. The observed longitudinal waves are interpreted as propagating slow magneto-acoustic waves and we show that the disturbances are not flare-driven but are most likely caused by an underlying driver exciting the loop footpoints. We found that (slightly enhanced) thermal conduction could account for the observed damping lengths. Title: An overview of longitudinal oscillations in coronal loops Authors: De Moortel, I.; Hood, A. W.; Ireland, J.; Walsh, R. W. Bibcode: 2002ESASP.506..509D Altcode: 2002svco.conf..509D; 2002ESPM...10..509D High cadence TRACE observations show that outward propagating intensity disturbances are a common feature in large, quiescent coronal loops. An overview is given of geometric and physical parameters of such propagating disturbances observed in 38 coronal loops. We found that loops that are situated above sunspot regions display intensity oscillations with periods centred around 3 minutes, whereas oscillations in 'non-sunspot' loops show periods centred around 5 minutes. The observed longitudinal oscillations are interpreted as propagating slow magneto-acoustic waves and we show that the disturbances are not flare-driven but are most likely caused by an underlying driver exciting the loop footpoints. We present a simple theoretical model to explain the observed features. Title: Magnetic structure of transition region blinkers Authors: Bewsher, D.; Parnell, C. E.; Brown, D. S.; Hood, A. W. Bibcode: 2002ESASP.505..239B Altcode: 2002IAUCo.188..239B; 2002solm.conf..239B Analysis of the photospheric magnetic field has shown that the majority of blinkers, small-scale intensity enhancements seen in the transition region, occur above single fragments. We investigate the relationship between the strength of these single magnetic fragments or the ratio of any mixed magnetic fields beneath blinkers and blinker characteristics. In all cases, no correlation is found between the strength of the magnetic field and the blinker properties. We suggest, therefore, that blinkers are not caused by reconnection and that other mechanisms should be explored further. Title: Magnetic reconnection throughout the solar atmosphere Authors: Hood, A. W.; Galsgaard, K.; Parnell, C. E. Bibcode: 2002ESASP.505..285H Altcode: 2002solm.conf..285H; 2002IAUCo.188..285H Magnetic reconnection is responsible for many different solar phenomena and it is the release of magnetic energy through reconnection that is believed to (i) drive flares, (ii) generate CMEs, (III) heat the corona and (iv) generate MHD waves. In basic models of 2D magnetic reconnection, the particular choise of boundary conditions influences the form of reconnection obtained. Reconnection in 3D can occur with and without null points. Numerical experiments have attempted to investigate different types of reconnection but a basic understanding of reconnection at 3D magnetic null points is essential in understanding these fumdamental processes. The structure of magnetic regions depends on features such as the magnetic skeleton, the mull points, the spine and fan plane. Numerical simulations are important but, at present, are unable to fully resolve the reconnection region. Recent analytical and numerical results of 3D reconnection will be presented. Applications of reconnection in the solar atmosphere will be discussed also. Title: Observational evidence of underlying driving of longitudinal oscillations in coronal loops Authors: De Moortel, I.; Ireland, J.; Hood, A. W.; Walsh, R. W. Bibcode: 2002ESASP.505..211D Altcode: 2002IAUCo.188..211D; 2002solm.conf..211D We give an overview of both geometric and physical parameters of propagating disturbances in coronal loops, using high cadence TRACE data (JOP83 & JOP144). The majority of these outward propagating oscillations are found in the footpoints of large diffuse coronal loop structures, close to active regions. The disturbances travel outward with a propagation speed v = 122±43 km s-1. The variations in intensity are estimated to be of the order of 4.1±1.5%, compared to the background brightness and are found to be damped very quickly, within 8.9±4.4 Mm along the loop. Using a wavelet analysis, periods in the 282±93 seconds range are obtained. However, it was found that loops that are situated above sunspot regions display intensity oscillations with a period smaller than 200 seconds, whereas oscillations in 'non-sunspot' loops show periods larger than 200 seconds. This result provides evidence that the underlying oscillations can propagate through the transition region and into the corona. We conclude that the observed longitudinal oscillations are not flare-driven but are most likely caused by an underlying driver exciting the loop footpoints. Title: Coronal heating by the phase mixing of individual pulses propagating in coronal holes Authors: Hood, A. W.; Brooks, S. J.; Wright, A. N. Bibcode: 2002RSPSA.458.2307H Altcode: 2002RSPSA.458.2307W No abstract at ADS Title: Off-limb EUV line profiles and the search for wave activity in the low corona Authors: Harrison, R. A.; Hood, A. W.; Pike, C. D. Bibcode: 2002A&A...392..319H Altcode: Two extreme-ultraviolet (EUV) observations are used to examine the off-limb characteristics of emission line widths of the million K Mg X 625 Å line. To obtain sufficient statistical accuracy, the observations were made over long periods of time and a pixel summing technique is used. The observations are made above the western limb, for quiet corona. The most significant result is the discovery of emission line narrowing as a function of altitude and intensity at altitudes above 50 000 km. The results are compared to past observations, which suggest that emission line broadening, at lower altitudes, is due to the outward propagation of undamped Alfvén waves, in open field regions with decreasing density with altitude. The narrowing at higher altitudes, determined by the current study is interpreted as further evidence for coronal wave activity, but in closed field regions, and most likely the first evidence of the dissipation of Alfvén waves in the corona. An additional result of this work is the identification of a significant line broadening across a narrow region on the limb, which may be due to flows in low-lying loop systems. Title: Longitudinal intensity oscillations in coronal loops observed with TRACE II. Discussion of Measured Parameters Authors: De Moortel, I.; Hood, A. W.; Ireland, J.; Walsh, R. W. Bibcode: 2002SoPh..209...89D Altcode: In this paper, we give a detailed discussion of the parameters of longitudinal oscillations in coronal loops, described in Paper I. We found a surprising absence of correlations between the measured variables, with the exception of a relation between the estimated damping length and the period of the intensity variations. Only for 2 out of the 38 cases presented in Paper I did we find a significant perturbation in the 195 Å TRACE data. The loops supporting the propagating disturbances were typically stable, quiescent loops and the total luminosity of the analyzed structures generally varied by no more than 10%. The observed density oscillations are unlikely to be flare-driven and are probably caused by an underlying driver exciting the loop footpoints. It was demonstrated that the rapid damping of the perturbations could not simply be explained as a consequence of the decreasing intensity along the loops. However, we found that (slightly enhanced) thermal conduction alone could account for the observed damping lengths and wavelengths, and, additionally, explain the correlation between propagation period and damping length. Title: Longitudinal intensity oscillations in coronal loops observed with TRACE I. Overview of Measured Parameters Authors: De Moortel, I.; Ireland, J.; Walsh, R. W.; Hood, A. W. Bibcode: 2002SoPh..209...61D Altcode: In this paper we aim to give a comprehensive overview of geometric and physical properties of longitudinal oscillations in large coronal loops. The 38 examples of propagating disturbances were obtained from the analysis of high cadence, 171 Å TRACE data (JOP 83 and JOP 144). The majority of these outward propagating oscillations are found in the footpoints of large diffuse coronal loop structures, close to active regions. The disturbances travel outward with a propagation speed of the order of v≈122±43 km s−1. The variations in intensity are estimated to be roughly 4.1±1.5% of the background loop brightness. The propagating disturbances are found to be damped very quickly and are typically only detected in the first 8.9±4.4 Mm along the loop. Using a wavelet analysis, periods of the order of 282±93 s are found and the energy flux was estimated as 342±126 erg cm−2 s−1. We found highly filamentary behavior in the lower part of the coronal loops and showed that the intensity oscillations can be present for several consecutive hours, with a more or less constant period. It is evident that the longitudinal oscillations are a widespread, regularly occurring coronal phenomena. A companion paper is devoted to the interpretation and discussion of the results. Title: The triggering of MHD instabilities through photospheric footpoint motions Authors: Gerrard, C. L.; Arber, T. D.; Hood, A. W. Bibcode: 2002A&A...387..687G Altcode: The results of 3D numerical simulations modelling the twisting of a coronal loop due to photospheric vortex motions are presented. The simulations are carried out using an initial purely axial field and an initial equilibrium configuration with twist, Phi = L Btheta / r Bz < Phicrit. The non-linear and resistive evolutions of the instability are followed. The magnetic field is twisted by the boundary motions into a loop which initially has boundary layers near the photospheric boundaries as has been suggested by previous work. The boundary motions increase the twist in the loop until it becomes unstable. For both cases the boundary twisting triggers the kink instability. In both cases a helical current structure wraps itself around the kinked central current. This current scales linearly with grid resolution indicating current sheet formation. For the cases studied 35-40% of the free magnetic energy is released. This is sufficient to explain the energy released in a compact loop flare. Title: The detection of 3 & 5 min period oscillations in coronal loops Authors: De Moortel, I.; Ireland, J.; Hood, A. W.; Walsh, R. W. Bibcode: 2002A&A...387L..13D Altcode: High cadence, 171 Alfvén A, TRACE observations show that outward propagating intensity disturbances are a common feature in large, quiescent coronal loops. These oscillations are interpreted as propagating slow magneto-acoustic waves. Using a wavelet analysis, we found periods of the order of 282 +/- 93 s. However, a careful study of the location of the footpoints revealed a distinct separation between those loops that support oscillations with periods smaller than 200 s and periods larger than 200 s. It was found that loops that are situated above sunspot regions display intensity oscillations with a period of the order of 172 +/- 32 s, whereas oscillations in ``non-sunspot'' loops show periods of the order of 321 +/- 74 s. We conclude that the observed longitudinal oscillations are not flare-driven but are most likely caused by an underlying driver exciting the loop footpoints. This result suggests that the underlying oscillations can propagate through the transition region and into the corona. 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: Coronal seismology through wavelet analysis Authors: De Moortel, I.; Hood, A. W.; Ireland, J. Bibcode: 2002A&A...381..311D Altcode: This paper expands on the suggestion of De Moortel & Hood (\cite{DeMoortel00}) that it will be possible to infer coronal plasma properties by making a detailed study of the wavelet transform of observed oscillations. TRACE observations, taken on 14 July 1998, of a flare-excited, decaying coronal loop oscillation are used to illustrate the possible applications of wavelet analysis. It is found that a decay exponent n ~ 2 gives the best fit to the double logarithm of the wavelet power, thus suggesting an e-varepsilon t^2 damping profile for the observed oscillation. Additional examples of transversal loop oscillations, observed by TRACE on 25 October 1999 and 21 March 2001, are analysed and a damping profile of the form e-varepsilon t^n, with n ~ 0.5 and n ~ 3 respectively, is suggested. It is demonstrated that an e-varepsilon t^n damping profile of a decaying oscillation survives the wavelet transform, and that the value of both the decay coefficient varepsilon and the exponent n can be extracted by taking a double logarithm of the normalised wavelet power at a given scale. By calculating the wavelet power analytically, it is shown that a sufficient number of oscillations have to be present in the analysed time series to be able to extract the period of the time series and to determine correct values for both the damping coefficient and the decay exponent from the wavelet transform. Title: Numerical simulations of kink instability in line-tied coronal Loops Authors: Gerrard, C. L.; Arber, T. D.; Hood, A. W.; Van der Linden, R. A. M. Bibcode: 2001A&A...373.1089G Altcode: The results from numerical simulations carried out using a new shock-capturing, Lagrangian-remap, 3D MHD code, Lare3d are presented. We study the evolution of the m=1 kink mode instability in a photospherically line-tied coronal loop that has no net axial current. During the non-linear evolution of the kink instability, large current concentrations develop in the neighbourhood of the infinite length mode rational surface. We investigate whether this strong current saturates at a finite value or whether scaling indicates current sheet formation. In particular, we consider the effect of the shear, defined by r phi ' / phi where phi = L Btheta / r Bz is the fieldline twist of the loop, on the current concentration. We also include a non-uniform resistivity in the simulations and observe the amount of free magnetic energy released by magnetic reconnection. Title: Transition Region Blinkers Authors: Parnell, C. E.; Bewsher, D.; Harrison, R. A.; Hood, A. W. Bibcode: 2001IAUS..203..359P Altcode: Blinkers are small bright emission events observed best in the O V transition region line that occur above the supergranular network. They were first observed using SoHO/CDS data and were identified manually by Harrison (1997). They are believed to be density enhancements, but how they are created and what their properties are is not well known. We have developed the first program to automatically identify blinkers and their characteristics. The evolution of the magnetic field observed by SoHO/MDI below these blinkers has then be analysed to determine what magnetic field configuration is required for a blinker to occur. Also, the coronal emission above has been investigated using SoHO/CDS and TRACE data to determine the relation between blinkers, x-ray bright points and nanoflares. All three of these events are known to occur at the network, but as yet the relation between them is not understood. Putting together the results from these multi-wave length studies we have been able to determine a model for how blinkers occur and what their effect is on the transition region around and the corona above. Title: Do Power Frequency Magnetic Fields Affect Human Heart Rate and Brain Function? (invited) Authors: Hood, A. W.; Sait, M. L.; Stough, C. K.; Shardey, V. K. Bibcode: 2001aprs.conf..262H Altcode: No abstract at ADS Title: Wavelet analysis and the determination of coronal plasma properties Authors: De Moortel, I.; Hood, A. W. Bibcode: 2000A&A...363..269D Altcode: The usefulness of wavelet analysis is demonstrated by considering analytical expressions for phase mixed Alfvén waves in different physical circumstances. The wavelet analysis is briefly introduced, using the complex-valued Morlet wavelet, consisting of a plane wave modulated by a Gaussian, as the basic wavelet. The time and scale resolution of the wavelet transform are then discussed in more detail, by working out the transform of simple harmonic functions analytically. As an illustration of the power of wavelet analysis, phase mixed Alfvén waves are investigated. A comparison is made between a truly finite harmonic wave and an Alfvén wave, dissipated by phase mixing and, using the wavelet transform, it is demonstrated that it is possible to distinguish between these two `finite' signals. It is also possible to extract the value of the dissipation coefficient from the wavelet transform. When considering phase mixing of Alfvén waves in a gravitationally stratified atmosphere, the lengthening of the wavelengths is clearly evident in the transform, which provides an independent estimate of the value of the pressure scale height. In a radially diverging atmosphere, the shortening of the wavelengths is also apparent in the wavelet transform, showing how the Alfvén speed varies along the loop and thus providing information on the coronal density and magnetic field. When applying wavelet analysis to observed wave-like oscillations, it should be possible to infer properties of the coronal plasma by making a detailed study of the wavelet transform. Title: Magnetohydrodynamic Instabilities Authors: Hood, A. Bibcode: 2000eaa..bookE2222H Altcode: Magnetohydrodynamic (MHD) stability theory determines whether a given PLASMA equilibrium configuration will either remain unchanged or evolve dynamically, in response to a general initial disturbance. If there is an initial disturbance whose amplitude subsequently grows in time, then the plasma is unstable, otherwise the plasma is stable. In addition, if the initial destabilizing disturbance has ... Title: Non-linear kink instabilities in line-tied coronal loops Authors: Gerrard, C. L.; Arber, T. D.; Hood, A. W.; van der Linden, R. A. M. Bibcode: 2000AIPC..537..248G Altcode: 2000wdss.conf..248G Photospheric line-tying has a stabilizing effect that allows magnetic energy to build up in coronal loops until critical conditions are reached and the loop becomes unstable to the m=1 kink instability [1]. Recent research has concentrated on the non-linear evolution of instabilities in line-tied coronal loops. There are suggestions [2-5] that current sheets form during the non-linear evolution of the kink instability. We present 3D MHD simulations of the non-linear evolution of MHD instabilities in line-tied coronal loops. These simulations are carried out on a multi-processor cluster at St Andrews using a new 3D MHD Lagrangian remap code (Lare3d) which we shall discuss briefly. Results are presented for loops with different shear profiles to test the conditions for current sheet formation. We begin by presenting the test case of the Gold-Hoyle field, and compare our results with previous results [1,6]. New results for equilibria with no net axial current are presented and the formation of current sheets discussed. . Title: Phase mixing of Alfvén waves in an open and stratified atmosphere Authors: De Moortel, I.; Hood, A. W.; Arber, T. D. Bibcode: 2000AIPC..537..224D Altcode: 2000wdss.conf..224D Phase mixing was introduced by Heyvaerts and Priest [1] as a mechanism for heating plasma in open magnetic field regions. Here we include a stratified density and a diverging background magnetic field. We present numerical and WKB solutions to describe the effect of stratification and divergence on phase mixing of Alfvén waves. It is shown that the decrease in density lengthens the oscillation wavelengths and thereby reduces the generation of transverse gradients. However, the divergence of the field lines shortens the wavelengths and thus enhances the generation of gradients. Furthermore we found that in a stratified atmosphere, ohmic heating is spread out over a greater height range whereas viscous heating is not strongly influenced by the stratification. A wavelet analysis indicated that the wavelet transform could provide us with information about the medium the waves are traveling through. . Title: Phase mixing of Alfvén waves in a stratified and radially diverging, open atmosphere Authors: De Moortel, I.; Hood, A. W.; Arber, T. D. Bibcode: 2000A&A...354..334D Altcode: Phase mixing was proposed by Heyvaerts and Priest (1983) as a mechanism for heating the plasma in open magnetic field regions of coronal holes. Here the basic model is modified to include a gravitationally stratified density and a diverging background magnetic field. We present WKB solutions and use a numerical code to describe the effect of dissipation, stratification and divergence on phase mixing of Alfvén\ waves. It is shown that the wavelengths of an Alfvén\ wave is shortened as it propagates outwards which enhances the generation of gradients. Therefore, the convection of wave energy into heating the plasma occurs at lower heights than in a uniform model. The combined effect of a stratified density and a radially diverging background magnetic field on phase mixing of Alfvén\ waves depends strongly on the particular geometry of the configuration. Depending on the value of the pressure scale height, phase mixing can either be more or less efficient than in the uniform case. Title: Commission 10: Solar Activity: (Activite Solaire) Authors: Ai, G.; Benz, A.; Dere, K. P.; Engvold, O.; Gopalswamy, N.; Hammer, R.; Hood, A.; Jackson, B. V.; Kim, I.; Marten, P. C.; Poletto, G.; Rozelot, J. P.; Sanchez, A. J.; Shibata, K.; van Driel-Geztelyi, L. Bibcode: 2000IAUTA..24...67A Altcode: No abstract at ADS Title: A Phenomenological Model of Coronal Mass Ejection Authors: Kuznetsov, V. D.; Hood, A. W. Bibcode: 2000AdSpR..26..539K Altcode: A model of coronal mass ejection (CME) is proposed, that is based on the break of equilibrium of twisted magnetic tubes (loops) emerging from the photosphere into the corona. Under the assumption of mass and axial flux conservation in the tube, a phenomenological model describes the loss of equilibrium as a result of a pressure increase in the tube due to its warming and additional magnetic heating when the twist increases in the expanding tube. A fast expansion of the tube to a new equilibrium radius will reduce the density inside the tube and, due to an additional buoyancy force, the tube will be ejected into the corona. The conditions are determined under which a pressure decrease inside a tube, due to the plasma outflow through its ends removes the onset of the eruptive instability. The upward motion of mass and the onset of the eruptive instability are related in the following way: the loops that lose a large amount of mass are not susceptible to an eruptive instability but the loops that lose only a small amount of mass experience an eruptive instability that leads to an ejection of the loop Title: Phase Mixing of Alfvén Waves in an Open and Stratified Atmosphere Authors: De Moortel, I.; Hood, A. W.; Arber, T. D. Bibcode: 1999ESASP.448..257D Altcode: 1999ESPM....9..257D; 1999mfsp.conf..257D No abstract at ADS Title: A complete coronal loop stability analysis in ideal magnetohydrodynamics. II. Force-free cylindrical equilibria Authors: van der Linden, R. A. M.; Hood, A. W. Bibcode: 1999A&A...346..303V Altcode: A WKB method to determine approximations to the critical length for the onset of ideal MHD instabilities with high poloidal mode numbers m in one-dimensional force-free cylindrical models of line-tied coronal loops is presented, extending the work of Hood et al. (\cite{wkb}) and Van der Linden & Hood (\cite{vh98}). Qualitatively, the procedure is similar to the one used in these two papers and pioneered by Connor et al. (\cite{CHT}). It is found, however, that the scalings for sheared force-free equilibria are different from those in the other cases, so that significant modifications to the method are necessary. The WKB method developed only requires solving a simple ordinary differential equation rather than the original set of complicated two-dimensional partial differential equations. For all force-free sheared equilibria we find that for large m the marginal stability length behaves like lc~ ml0+l2/m compared to lc~ ml0+l1 for the unsheared case investigated in Hood et al. (\cite{wkb}). Thus, it appears that in the force-free (or nearly force-free) case the m=1 mode is always the first to become unstable. The WKB results are complemented with numerical solutions of the full equations and for sufficiently large values of the wave number m excellent agreement is found. The combination of the results and methods described in this paper, together with those in Van der Linden & Hood (\cite{vh98}) provide all the tools necessary to perform a complete stability assessment of any one-dimensional cylindrically-symmetric equilibrium model for a coronal loop. Title: Phase mixing of Alfvén waves in a stratified and open atmosphere Authors: De Moortel, I.; Hood, A. W.; Ireland, J.; Arber, T. D. Bibcode: 1999A&A...346..641D Altcode: Phase mixing was introduced by Heyvaerts and Priest (1983) as a mechanism for heating the plasma in the open magnetic field regions of coronal holes. Here the basic process is modified to include a stratified atmosphere in which the density decreases with height. We present an analytical solution in the case of zero dissipation and use a numerical code in the non-zero dissipation case to describe the effect of stratification on phase mixing. The exponential damping behaviour derived by Heyvaerts and Priest is largely confirmed in the non stratified limit. However, it is shown that the decrease in density lengthens the oscillation wavelengths and thereby reduces the generation of transverse gradients. Furthermore we found that in a stratified atmosphere the perturbed magnetic field and velocity behave quite differently depending on whether we consider resistivity or viscosity. Ohmic heating is spread out over a greater height range in a stratified medium whereas viscous heating is not strongly influenced by the stratification. Title: Working Group 2 Report: Energy Input, Heating, and Solar Wind Acceleration in Coronal Holes Authors: Hood, A. W. Bibcode: 1999SSRv...87...79H Altcode: Theories and observations of energy input, heating and acceleration mechanisms in the low corona were presented and discussed. The main topics of discussion were large-scale solar wind simulations, theoretical heating mechanisms, observational constraints, confronting theory with observations and observational issues. Title: On the magnetoacoustic waves in a current sheet. Authors: Boddie, D.; Roberts, B.; Hood, A. W.; van der Linden, R. Bibcode: 1999joso.proc..139B Altcode: Magnetoacoustic waves in a structured medium can exist as hybrid waves, exhibiting the properties of both surface and body waves (Smith et al., 1997). Such hybrid waves may occur within a structured medium in which the parameters describing the physical properties of the medium are defined to be continuous functions. The dispersive behaviour of hybrid waves in a current sheet with this property is explored and compared to that in a slab model. Title: A complete solar coronal loop stability analysis in ideal magnetohydrodynamics. I. Non-force-free cylindrical equilibria Authors: van der Linden, R. A. M.; Hood, A. W. Bibcode: 1998A&A...339..887V Altcode: A procedure is introduced to perform a complete ideal MHD stability analysis of one-dimensional cylindrical equilibrium models for coronal loops, including the important effect of line-tying. The stability is completely determined by calculating the critical (marginally stable) length for the onset of ideal MHD instabilities for every azimuthal wave number m. The analysis consists of the combination of a WKB method to determine the critical length of intermediate to high (infinite) values of m with a numerical code (using bicubic finite elements) for the low to intermediate values of m. As before it is found that for large enough m the critical length can be expressed as lc=l0+l1/m. It is also demonstrated that in general either the m=1 or the m->infty mode has the shortest critical length, the former being the first to become unstable for nearly force-free magnetic fields, the latter for strongly non-force-free fields. Therefore, a stability analysis of these two modes will normally suffice, with perhaps a need for some more numerical calculations near the point where the modes cross over. The combination of these two tools provides a complete stability assessment. Title: The Effect of Resistivity on the Formation of Prominence Fine-Scale Structure Authors: Ireland, R. C.; Van Der Linden, R. A. M.; Hood, A. W. Bibcode: 1998SoPh..179..115I Altcode: The normal mode spectrum for the linearized MHD equations is investigated for a simple cylindrical equilibrium. This spectrum is examined for zero and non-zero scalar resistivity. Particular attention is paid to the thermal sub-spectrum. It is shown that when resistivity is included, a `dissipative' layer forms at the location of the singularity associated with the thermal continuum. For the most unstable `quasi-continuum modes', the thickness of this dissipative layer is proportional to the 1/4 power of the magnetic Reynolds number. This generates length scales that are of the same order of magnitude as those reported for the fine-scale structure seen in prominences. It is therefore concluded that dissipation due to resistivity may be relevant for the formation of prominence fine-scale structure. Title: MHD models of coronal plumes Authors: Del Zanna, L.; Hood, A.; Velli, M.; von Steiger, R. Bibcode: 1998ESASP.421..359D Altcode: 1998sjcp.conf..359D No abstract at ADS Title: The effect of spatially dependent heating on the thermal equilibria of coronal loops. Authors: Mendoza-Briceno, C. A.; Hood, A. W. Bibcode: 1997A&A...325..791M Altcode: The thermal equilibria along a symmetric coronal loop with constant cross-sectional area is investigated in the absence of gravity. A coronal heating function that depends on distance along the loop is considered and the effects of varying the values of the parameters involved in the governing equations are studied. It is found that there is a critical decay length of the heating below which a hot coronal loop does not exist. It is suggested that thermal non-equilibrium occurs, allowing the existence of catastrophic cooling and it is shown that prominence-type equilibria are possible. A study of the stability of the equilibrium up to a second order approximation is presented, and it is found that the response of the structure not only depends on the amplitude of the disturbance, but also on whether the disturbance increases or decreases the equilibrium temperature. Title: Heating of coronal loops by phase-mixing. Authors: Hood, A. W.; Gonzalez-Delgado, D.; Ireland, J. Bibcode: 1997A&A...324...11H Altcode: A simple, self similar solution for the heating of coronal loops is presented. It is shown that the Heyvaerts-Priest model gives a good description of phase mixing in a certain class of coronal loops. In addition, under typical coronal conditions the ohmic heating, due to phase mixing, can provide magnetic energy on a timescale comparable with the coronal radiative time. Thus, it is possible that phase mixing can maintain a hot coronal loop for large Lundquist number. If the photospheric motions continually excite coronal loops, then phase mixing could contribute to a background level of coronal heating for very large Lundquist number. Title: Discrete Random Heating Events in Coronal Loops Authors: Walsh, R. W.; Bell, G. E.; Hood, A. W. Bibcode: 1997SoPh..171...81W Altcode: The response of the coronal plasma in a magnetic loop to the release of discrete, random amounts of energy quanta over fixed time intervals is investigated. Nanoflare heating (1024 erg per event) with event lifetimes on a scale of 1-20 s are shown to be able to maintain a coronal loop at typical coronal temperatures, ≈ 2 x 106 K (Parker, 1988; Kopp and Poletto, 1993). Microflare events (1027 erg) observed by Porter et al. (1995) with a lifetime of approximately 1 min are also investigated and it is found that the loop apex temperature varies by at most 40% from its initial static condition. However, larger energy events of the order of 1028 erg (Schmieder et al., 1994) occur too infrequently and the plasma cools to chromospheric values. The implications of time-dependent heating of the corona upon observations are also discussed. Title: Non-equilibrium of Magnetic Flux Tubes emerging into the Solar Corona Authors: Kuznetsov, V. D.; Hood, A. W. Bibcode: 1997SoPh..171...61K Altcode: A lack of equilibrium of twisted magnetic flux tubes emerging from the photosphere into the corona is considered. Assuming mass and flux conservation in the tube and an isothermal tube that is in thermal equilibrium with the surrounding plasma, it is shown that a sufficently rapid temperature increase through the transition zone may lead to the loss of magnetohydrostatic equilibrium of the emerging flux tube due to the enhancement of the plasma pressure inside the tube. The non-equilibrium leads to a rapid expansion of the tube to reach a new equilibrium state. The rise and expansion of the tube before and after the non-equilibrium are accompanied by an increase in the twist of the magnetic field. This may lead to the field exceeding the threshold for the onset of the kink instability and a subsequent explosive release of magnetic energy. Title: An MHD model for solar coronal plumes. Authors: Del Zanna, L.; Hood, A. W.; Longbottom, A. W. Bibcode: 1997A&A...318..963D Altcode: Solar coronal plumes are modelled by solving the steady, ideal, 2-D, magnetohydrodynamic (MHD) equations and assuming azimuthal symmetry around the plume axis. Since magnetic fields are believed to play an essential role in plume formation and structure, a self-consistent method of linearisation of the MHD equations with respect to the magnetic field has been considered here. This consists of three distinct steps: first a potential field is calculated as a deviation from the radial case due to a flux concentration at the plume base, then the other plasma quantities are worked out by solving a Bernoulli-like equation and finally the modifications to the zeroth order field are found. Free functions of the model are the radial field component at the coronal base, the density at the coronal base and the temperature, which is assumed to be constant along the field lines. This method allows one to reproduce basic features of coronal plumes such as the super-radial expansion close to their base. The results are compared with the observations. 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: Multiple-timescales analysis of ideal poloidal Alfvén waves Authors: Mann, Ian R.; Wright, Andrew N.; Hood, Alan W. Bibcode: 1997JGR...102.2381M Altcode: Time-dependent analytic solutions for the evolution of undriven ideal standing poloidal Alfvén waves are considered in a box model magnetosphere. Assuming an ``azimuthal'' variation of expiλy, where λ is large, we use the asymptotic method of multiple timescales to determine analytic solutions over the long timescale σ defined by σ=ɛt, where ɛ=1/λ. Our asymptotic poloidal Alfvén wave solutions (with λ>>kx,kz) accurately reproduce the undriven ideal wave polarization rotation from poloidal to toroidal in time determined numerically by Mann and Wright [1995]. Using the same asymptotic method, we further consider the evolution of radially localized large λ Alfvén waves. We find that undriven waves having kx,λ>>kz, oscillating in a radially inhomogeneous plasma remain incompressible to leading order and experience similar asymptotically toroidal behavior as t->∞. Consequently, undriven poloidal Alfvén waves and, in general, transversally localized large λ ideal Alfvén wave disturbances have a finite lifetime before they evolve into purely decoupled toroidal Alfvén waves. This polarization rotation may be apparent in waves driven by the drift-bounce resonance mechanism in situations where the wave evolution occurs more rapidly than ionospheric damping. This can be possible on the dayside of the magnetosphere, with the evolution more likely to be observable toward the end of a temporal wave packet when the driving mechanism is no longer operative. Title: Thermal evolution of a coronal condensation. Authors: Mendoza-Briceno, C. A.; Hood, A. W. Bibcode: 1997ASIC..494..117M Altcode: 1997topr.conf..117M The thermal evolution of coronal magnetic structures is studied under the assumption that the inertial terms are small. Assuming the coronal heating function is due to the damping of waves, then the amount of energy supplied to the loop will decay from the footpoint towards the summit. The effect of the decay length on the heating is investigated, and when this length is below a critical value a cool condensation forms. Different initial profiles are considered and either purely hot plasmas or cool condensations can be found depending on whether the initial profile is above or below a threshold value. Title: Phase-mixing poloidal alfvén wave polarisations Authors: Mann, I. R.; Wright, A. N.; Hood, A. W. Bibcode: 1997AdSpR..20..489M Altcode: Standing poloidal Alfvén waves are believed to be excited by drift-bounce resonance with energetic particle populations in the Earth's magnetosphere. Using a fully compressible ideal MHD model, in a cartesian geometry, we investigate the temporal evolution of localised poloidal Alfvén waves evolving in radially inhomogeneous magnetoplasmas. We find that the polarisation of these waves rotates from being poloidal to toroidal in time. This polarisation rotation is driven by the magnetic field gradients which develop as the wave fields phase mix in time. Asymptotically, in an ideal plasma, all the wave energy is deposited in the toroidal polarisation. We define the time taken for the toroidal and poloidal amplitudes to become equal as the ideal poloidal lifetime, tau = lambda(domega_A/dx)^-1 and verify the result numerically (where lambda is the azimuthal wavenumber, and x represents the radial direction). Further, by using the method of multiple timescales, we analytically determine the time dependent wave solutions and find excellent agreement with our numerical work. The finite lifetime of ideal poloidal Alfvén waves is important if the spatial and temporal features of both in-situ satellite and ground-based observations are to be fully understood. Title: Validity of the Isobaric Assumption to the Solar Corona Authors: Walsh, R. W.; Bell, G. E.; Hood, A. W. Bibcode: 1996SoPh..169...33W Altcode: Many coronal heating mechanisms have been suggested to balance the losses from this tenuous medium by radiation, conduction, and plasma mass flows. A previous paper (Walsh, Bell, and Hood, 1995) considered a time-dependent heating supply where the plasma evolved isobarically along the loop length. The validity of this assumption is investigated by including the inertial terms in the fluid equations making it necessary to track the sound waves propagating in a coronal loop structure due to changes in the heating rate with time. It is found that the temperature changes along the loop are mainly governed by the variations in the heating so that the thermal evolution can be approximated to a high degree by the simple isobaric case. A typical isobaric evolution of the plasma properties is reproduced when the acoustic time scale is short enough. However, the cooling of a hot temperature equilibrium to a cool one creates supersonic flows which are not allowed for in this model. Title: A steady flow model for quiescent prominences. Authors: Del Zanna, L.; Hood, A. W. Bibcode: 1996A&A...309..943D Altcode: The normal polarity prominence model of Hood & Anzer (1990) has been modified to include the effect of a steady flow along the magnetic field lines. We consider two isothermal regions that model the hot corona and the cool prominence, considered as a vertical sheet of dense material with infinite length and height but finite width. The magnetic field, pressure and density are assumed to be exponentially decaying in the vertical direction (the velocity is independent of the height in our model) and equations for the horizontal behaviour are determined. Invariance along the prominence direction is assumed, but the magnetic and velocity vectors retain all their components. The introduction of a field aligned flow results in the coronal magnetic field no longer being force free and a pressure deficit allows a siphon flow to occur. Substantial coronal velocities are possible but only sub-sonic (and hence in the low plasma β corona sub-Alfvenic) flows are considered and these are consistent with observations. Finally, we propose a simple model for the steady supply of material into a prominence to balance the observed draining motions. 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: The nonlinear MHD evolution of axisymmetric line-tied loops in the solar corona Authors: Longbottom, A. W.; Hood, A. W.; Rickard, G. J. Bibcode: 1996PPCF...38..193L Altcode: The nonlinear evolution of the m = 0 sausage mode in coronal loops (Gold and Hoyle 1960 Mon. Not. R. Astron. Soc. 120 89) is investigated using numerical simulations. For the ideal line-tied case the growth rate of the linear phase of the instability is successfully reproduced, and it is found that the nonlinear development leads to the formation of a new equilibrium with an embedded, curved, current concentration ( not, however, a current sheet). This new equilibrium is not symmetric about the centre of the loop. For periodic boundary conditions a similar evolution is found, but with the final equilibrium being symmetric in which a straight, radial current concentration (possibly a current sheet) is embedded. In the line-tied resistive case the field lines reconnect, leading to the ejection of a plasmoid and relaxation to a (different) equilibrium. Title: Plasma Flows due to Time Dependent Heating of the Solar Corona Authors: Walsh, R. W.; Bell, G. E.; Hood, A. W. Bibcode: 1996ApL&C..34..181W Altcode: No abstract at ADS Title: Normal Polarity, Quiescent Prominences: Static and Steady Flow Models Authors: Hood, Alan W.; Longbottom, Aaron W.; Del Zanna, Luca Bibcode: 1996ASPC...95..258H Altcode: 1996sdit.conf..258H No abstract at ADS Title: Steady Flows in Quiescent Prominences Authors: Del Zanna, L.; Hood, A. W. Bibcode: 1996ApL&C..34...95D Altcode: No abstract at ADS Title: Formation of Cool Condensation in a Magnetic Structure Authors: Mendoza, C. A.; Hood, A. W. Bibcode: 1996ApL&C..34..107M Altcode: No abstract at ADS Title: Time-Dependent Heating of the Solar Corona Authors: Walsh, R. W.; Bell, G. E.; Hood, A. W. Bibcode: 1995SoPh..161...83W Altcode: The problem of how the corona is heated is of central importance in solar physics research. Here it is assumed that the heating occurs in a regular time-dependent manner and the response of the plasma is investigated. If the magnetic field is strong then the dynamics reduces to a one-dimensional problem along the field. In addition if the radiative time in the corona is much longer than the sound travel time then the plasma evolvesisobarically. The frequency with which heat is deposited in the corona is investigated and it is shown that there is a critical frequency above which a hot corona can be maintained and below which the plasma temperature cools to chromospheric values. An evaluation of the isobaric assumption to the solar corona and the implications of time-dependent heating upon the forthcoming SOHO observations are also presented. Title: Magnetothermal instabilities in coronal arcades Authors: Ireland, R. C.; Hood, A. W.; Van Der Linden, R. A. M. Bibcode: 1995SoPh..160..303I Altcode: The normal mode spectrum for the linearized MHD equations is investigated for a plasma in a cylindrical equilibrium. The equations describing these normal modes are solved numerically using a finite element code. The ballooning equations that describe localized modes are manipulated and a dispersion relation derived. It is shown that as the axial wave numberk is increased, the fundamental thermal and Alfvén modes can coalesce to form overstable magnetothermal modes. The ratio between the magnetic and thermal terms is varied and the existence of the magnetothermal modes examined. The corresponding growth rates are predicted by a WKB solution to the ballooning equations. The existence of these magnetothermal modes may be significant in the eruption of prominences into solar flares. Title: On the importance of high-m instabilities in line-tied coronal magnetic fields. Authors: van der Linden, R. A. M.; Hood, A. W. Bibcode: 1995A&A...299..912V Altcode: It is shown that for the determination of the magnetohydrodynamical (MHD) stability of coronal magnetic fields, where the photospheric line-tying effect is a basic element of the physical description, it is important to consider modes of both low and high angular wave number m. In particular, when the equilibrium deviates from the force-free state, modes with high m may have higher growth rates than the m=1 (kink) mode. It is then possible that high-m modes become unstable when the field line length increases in the evolution of the equilibrium, while the m=1 mode remains stable. This is important because the high-m modes intrinsically lead to strong dissipation. This contrasts to the case of the one-dimensional infinite (i.e. not line-tied) cylinder, where it is sufficient to prove stability of the m=1 mode to guarantee stability for all modes m>1 (Newcomb 1960). In the line-tied case however, there exists no prior reason to only consider m=1 instabilities in coronal magnetic fields. Title: Current Sheet Models for Inverse Polarity Prominences in Twisted Flux Tubes Authors: Schonfelder, A. O.; Hood, A. W. Bibcode: 1995SoPh..157..223S Altcode: This paper treats the prominence model of Low (1993) to examine more complicated sheet currents than those used in the original model. Nonlinear force-free field solutions, in Cartesian coordinates, invariant in a given direction, are presented to show the possibility of an inverse-polarity prominence embedded in a large twisted flux tube. The force-free solution is matched to an external, unsheared, potential coronal magnetic field. These new solutions are mathematically interesting and allow an investigation of different profiles of the current intensity, magnetic field vector and mass density in the sheet. These prominence models show a general increase in magnetic field strength with height in agreement with observations. Other prominence properties are shown to match the observed values. Title: The magnetic structuring of the solar corona Authors: Hood, A. Bibcode: 1995HiA....10..296H Altcode: No abstract at ADS Title: The Effect of Magnetic Shear on the Magnetohydrodynamic Stability of a Prominence Model Authors: Longbottom, A. W.; Hood, A. W. Bibcode: 1994SoPh..155..267L Altcode: The Hood-Anzer prominence model (Hood and Anzer, 1990) is modified to include magnetic shear. The stability properties of the model are then assessed to see if significant magnetic shear can stabilize ideal MHD disturbances. It is shown that a strong shear gradient in the magnetic field near the base of the prominence provides a stabilizing effect and realistic prominence heights are indeed possible. Title: The Influence of Line-Tying on Coronal Perturbations in a Gravitationally Stratified Equilibrium Authors: van der Linden, R. A. M.; Hood, A. W.; Goedbloed, J. P. Bibcode: 1994SoPh..154...69V Altcode: We study the influence of gravitational stratification of the solar atmosphere on the stability of coronal magnetic structures. In particular we question whether the (presumably stabilizing) influence of the anchoring of the magnetic field lines in the solar photosphere (`line-tying') can be adequately modelled by either `rigid wall' or `flow-through' boundary conditions on the coronal perturbations, as is commonly done. Using the ideal MHD model without gravitational effects,inertial line-tying alone cannot lead to afull stabilization, as marginal stability cannot be crossed by including only the rapid density increase at the photospheric interface. Title: The Magnetohydrodynamic Stability of a Twisted Flux Tube Prominence Model Authors: Longbottom, A. W.; Hood, A. W. Bibcode: 1994SoPh..154...51L Altcode: The ideal MHD stability of the 2D twisted magnetic flux tube prominence model of Cartledge and Hood (1993) is investigated. The model includes a temperature profile that varies from realistic prominence values up to typical coronal values. The prominence is considered to be of finite-width and finite height. The stability properties of the prominence models are studied by using a method that generates a separate necessary condition and a sufficient condition. These conditions give bounds on the parameters that define marginal stability. In many cases these bounds are quite close so that further, more detailed, stability calculations are not necessary. A number of parameter regimes are examined, corresponding to different profiles of the prominence temperatures, densities, and magnetic field shear. It is found that the model admits realistic stable and unstable loop lengths for observed prominence parameters when the axial magnetic field component does not vanish. Title: WKB Estimates for the Onset of Ideal Magnetohydrodynamic Instabilities in Solar Coronal Loops Authors: Hood, A. W.; de Bruyne, P.; van der Linden, R. A. M.; Goossens, M. Bibcode: 1994SoPh..150...99H Altcode: A WKB approach, based on the method of Connor, Hastie, and Taylor (1979), is used to obtain simple estimates of the critical conditions for the onset of ideal MHD instabilities in line-tied solar coronal loops. The method is illustrated for the constant twist, Gold-Hoyle (1960) field, and the critical conditions are compared with previous and new numerical results. For the force-free case, the WKB estimate for the critical loop length reduces to . For the sufficiently non-force-free case the critical length can be expressed in the forml0 +l1/m. The results confirm the findings of De Bruyne and Hood (1992) that for force-free fields them = 1 mode is the first mode to become unstable but for the sufficiently strong non-force-free case this reverses with them → ∞ mode being excited first. Title: A Necessary Condition for the Stability of a Class of Three-dimensional Laminated Equilibria Authors: Longbottom, A. W.; Melville, J. P.; Hood, A. W. Bibcode: 1994ApJ...423..496L Altcode: A necessary condition is derived for the ideal magnetohydrodynamic stability of a class of three-dimensional laminated isothermal equilibria presented by Chou, Low, & Bhattacharjee (1993). The condition is derived by the use of a particular destabilizing trial function known as a 'ballooning mode.' This choice of trial function allows the necessary condition to be found by the solution of four coupled first-order ordinary differential equations that may be integrated along individual field lines. Here the boundary conditions model the line-tying effect of the dense photosphere. The necessary condition for stability together with the sufficient condition derived by Chou gives a bound on marginal stability, the tightness of the bound depending on the parameter regime. For the case of penumbral loops, considered by Chou, an approximate lower and upper bound on the critical value of the plasma beta for this model can be found. The upper bound on Beta, however, is smaller than that determined from observations. Title: The Stability of 2d Current Sheet Models of Prominences Authors: Longbottom, A. W.; Melville, J. P.; Hood, A. W. Bibcode: 1994SoPh..149...73L Altcode: A necessary and sufficient condition for the ideal magnetohydrodynamic stability of 2D current sheet models of prominences suspended in a potential coronal field with line-tying is developed using the energy method. This condition takes the form of two simple coupled second-order differential equations which may be integrated along a field line to find marginal stability. The two conditions (85) and (86) of Anzer (1969) are now only sufficient for stability. Two current sheet models are investigated and it is shown that for a potential coronal field allowing perturbed electric currents to flow, line-tying can completely stabilize the equilibria for realistic heights. Title: External and Internal Solutions for the Twisted, Flux Tube, Prominence Model Authors: Cartledge, N.; Hood, A. W. Bibcode: 1994scs..conf..345C Altcode: 1994IAUCo.144..345C The authors consider a model for the support of a prominence sheet in a twisted magnetic flux tube. 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: Line-tying in a gravitationally stratified atmosphere Authors: van der Linden, R. A. M.; Hood, A. W. Bibcode: 1994LNP...432..135V Altcode: 1994LNPM...11..135V We study the influence of the gravitational stratification of the photosphere on magnetic line-tying. It has been demonstrated (Goedbloed et al, 1991) that in ideal MHD with zero gravity, the anchoring of magnetic field lines in the dense photosphere (modelled as a jump in density) cannot completely remove any coronal MHD instability. Consequently, the commonly used rigid wall line-tying conditions have to break down close to marginal stability. We demonstrate, using the (localized) ballooning ordering, that when the effects of gravity are included, coronal modes can be completely stabilized by the density stratification. Therefore, the marginal stability points predicted using rigid wall conditions are still relevant. Title: Magnetic Field Structures for Inverse Polarity Prominences Authors: Schonfelder, A. O.; Hood, A. W.; Fiedler, R. A. S. Bibcode: 1994scs..conf..335S Altcode: 1994IAUCo.144..335S Results of numerical solutions to the equilibrium equation indicate that a fully developed prominence will possess an O-type, but not in general an X-type neutral point. Title: External and internal solutions for the twisted, flux-tube, prominence model Authors: Cartledge, N.; Hood, A. W. Bibcode: 1993SoPh..148..253C Altcode: In this paper the twisted flux-tube model for the support of a prominence sheet with constant axial current density, given by Ridgway, Priest, and Amari (1991), is considered. Title: The Stability of Two Classes of Solar Quiescent Prominences Authors: de Bruyne, P.; Hood, A. W. Bibcode: 1993SoPh..147...97D Altcode: The stability properties of two prominence models are investigated by considering bounds on the marginal stability conditions. It is shown that Low's (1981) model is unstable to localized disturbances and the Hood and Anzer (1990) model is only stable for sufficiently low prominences. The latter result may be modified by including magnetic shear. It is shown that magnetic shear stabilizes coronal loops against Rayleigh-Taylor instabilities and may help to stabilize prominence models as well. Title: The stability of line-tied coronal loops and an extended Suydam criterion Authors: Hood, A. W. Bibcode: 1993AdSpR..13i.105H Altcode: 1993AdSpR..13..105H The initiation of prominence eruptions and solar flares can be described in terms of an MHD instability. When the footpoint of a coronal magnetic structure is anchored in the dense photosphere, magnetic energy is slowly built up until critical conditions are exceeded and an instability is triggered. The significance of an extended Suydam criterion for testing line-tied magnetic fields is illustrated by comparing with numerical instability thresholds for a variety of different modes. It is shown that when the extended Suydam criterion predicts an instability, for a nearly force free field, then there exists a global instability with a lower threshold. When the gas pressure is significant localised modes are destabilised slightly before a global mode. Title: The Effect of Shear on Numerical Models of Quiescent Normal Polarity Prominences Authors: Fiedler, R. A. S.; Hood, A. W. Bibcode: 1993SoPh..146..297F Altcode: The equilibrium structure of normal-polarity, quiescent prominences is investigated and the influence of magnetic shear in response to a slow, shearing, photospheric velocity discussed. The results show that the overall field structure predicted by Fiedler and Hood (1992) is largely unaffected but that magnetic shear reduces the plasma beta and lengthens and flattens the magnetic field when viewed from the side. The flatness of the field suggests that the initial condensation can form and, when the mass is sufficient, deform the field slightly into the equilibrium structure calculated here. Thus, it is postulated that the field must be highly sheared for the radiation (or condensation) time to be less than the free-fall time along the field. A simple estimate predicts that the field must lie close to the polarity inversion line with an angle in agreement with observations. Hence, it is apparent that normal polarity prominences will always be observed with a highly sheared field. Title: Bounds on the Stability of 3-DIMENSIONAL Magnetic Equilibria in the Solar Corona Authors: Longbottom, A. W.; Melville, J. P.; Hood, A. W. Bibcode: 1993SoPh..146...93L Altcode: A necessary and a sufficient condition are derived for the ideal magnetohydrodynamic stability of any 3D magnetohydrostatic equilibrium using the energy method and incorporating photospheric line-tying. The theory is demonstrated by application to a simple class of theoretical 3D equilibria. The main thrust of the method is the formulation of the stability conditions as two sets of ordinary differential equations together with appropriate boundary conditions which may be numerically integrated along tied field lines one at a time. In the case of the shearless fields with non-negligible plasma pressure treated here the conditions for stability arenecessary and sufficient. The method employs as a trial function a destabilizing `ballooning' mode, of large wave number vector perpendicular to the equilibrium field lines. These modes may not be picked up in a solution of the full partial differential equations which arise from a direct treatment of the problem. 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: 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: 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: Solar plasmas. Authors: Hood, A. W. Bibcode: 1993ppic.conf..267H Altcode: Contents: 1. Introduction. 2. The internal structure of the Sun. 3. The atmosphere of the Sun. 4. Sunspots. 5. Solar wind. 6. Prominences. 7. Solar flares. 8. Magnetic reconnection. 9. Conclusions. Title: The Thermal Continuum in Coronal Loops - the Influence of Finite Resistivity on the Continuous Spectrum Authors: Ireland, R. C.; van der Linden, R. A. M.; Hood, A. W.; Goossens, M. Bibcode: 1992SoPh..142..265I Altcode: The normal mode spectrum for the linearized MHD equations is investigated for a cylindrical equilibrium. This spectrum is examined for zero perpendicular thermal conduction, with both zero and non-zero scalar resistivity. Particular attention is paid to the continuous branches of this spectrum, or continuous spectra. For zero resistivity there are three types of continuous spectra present, namely the Alfvén, slow, and thermal continua. It is shown that when dissipation due to resistivity is included, the slow and Alfvén continua are removed and that the thermal continuum is shifted to a different position (where the shift is independent of the exact value of resistivity). The `old' location of the thermal continuum is covered by a dense set of nearly singular discrete modes called a quasi-continuum. The quasi-continuum is investigated numerically, and the eigenfunctions are shown to have rapid spatial oscillating behaviour. These oscillations are confined to the most unstable part of the equilibrium based on the Field criterion, and may be the cause of fine structure in prominences. Title: Stability of Line-Tied 1-D Coronal Loops - Significance of an Extended Suydam Criterion Authors: de Bruyne, P.; Hood, A. W. Bibcode: 1992SoPh..142...87D Altcode: The stability of coronal magnetic loops is investigated with the influence of the dense photosphere (line-tying) included. The stability method, based on the Finite Fourier Series method developed by Einaudi and Van Hoven (1981, 1983), is applied to two different equilibria and the approximate critical conditions for the onset of different azimuthal instabilities are investigated. It is shown that, for nearly force-free loops, the extended Suydam criterion, obtained by De Bruyne and Hood (1989) for localized modes, predicts the existence of a global kink instability when a localized mode is just destabilized. For loops with substantial gas pressure gradients it is the localized modes that are destabilized first of all and the extended Suydam criterion gives the necessary and sufficient conditions for an instability. In this latter case, the instability threshold for the kink mode is quite close to the localized mode threshold. Finally, it is shown that the growth times of the instabilities are comparable to the Aflvén travel times along the loop when the extended Suydam criterion is violated. 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: Numerical Models of Quiescent Normal Polarity Prominences Authors: Fiedler, R. A. S.; Hood, A. W. Bibcode: 1992SoPh..141...75F Altcode: We present 2-D numerical models of quiescent solar prominences with normal magnetic polarity. These models represent an extension to the classical Kippenhahn-Schlüter model in that the prominence is treated as having finite width and height and the external coronal field is matched smoothly to the internal prominence field so that there are no current sheets at the prominence sides. Using typical prominence and coronal values we find solutions to the generalised Grad-Shafranov equation which illustrate the necessary magnetic support. We also discuss some extensions to the basic model. Title: The relevance of the ballooning approximation for magnetic, thermal, and coalesced magnetothermal instabilities Authors: van der Linden, R. A. M.; Goossens, M.; Hood, A. W. Bibcode: 1992SoPh..140..317V Altcode: Approximate solutions of the linearized non-adiabatic MHD equations, obtained using the ballooning method, are compared with `exact' numerical solutions of the full equations (including the effects of optically thin plasma radiation). It is shown that the standard ballooning method, developed within the framework of ideal linear MHD, can be generalized to non-ideal linear MHD. The localized (ballooning) spectrum has to be used with caution, but can give valuable (though limited) information on non-ideal stability. 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: 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: Instabilities in the solar corona Authors: Hood, A. W. Bibcode: 1992PPCF...34..411H Altcode: No abstract at ADS Title: The Evolution of Twisted Coronal Loops Authors: Robertson, J. A.; Hood, A. W.; Lothian, R. M. Bibcode: 1992SoPh..137..273R Altcode: The evolution of coronal loops in response to slow photospheric twisting motions is investigated using a variety of methods. Firstly, by solving the time-dependent equations it is shown that the field essentially evolves through a sequence of 2-D equilibria with no evidence of rapid dynamic evolution. Secondly, a sequence of 1-D equilibria are shown to provide a remarkably good approximation to the 2-D time-dependent results using a fraction of the computer time. Thus, a substantial investigation of parameter space is now possible. Finally, simple bounds on the 3-D stability of coronal loops are obtained. Exact stability bounds can be found by using these bounds to reduce the region of parameter space requiring further investigation. Twisting the loop too much shows that a 3-D instability must be triggered. Title: Loss of Equilibrium in Coronal Loops Authors: Lothian, R. M.; Hood, A. W. Bibcode: 1992SoPh..137..105L Altcode: The loss of equilibrium in coronal magnetic field structures is a possible source of energy for coronal heating and solar flares. We investigate whether such a loss of equilibrium occurs when a coronal loop is progressively twisted by photospheric motions. In studies of 2-D cylindrical equilibria, long loops have been found to be of constant cross-sectional area along most of their length, with axial variations being confined to narrow boundary layers. We use this information to develop a 1-D line-tied model, for a 2-D coronal loop. We specify the twist in terms of the azimuthal field and more physically, in terms of the photospheric footpoint displacement. In the former case we find a loss of equilibrium, but not in the latter. We also examine a twisted loop with a non-zero plasma pressure. The loss of equilibrium is only found at high-plasma β. It is conjectured that such high-β can occur in flare loops and prior to a prominence eruption. However, when the plasma evolves adiabatically, there is no loss of equilibrium. 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: Book-Review - Advances in Solar System Magnetohydrodynamics Authors: Priest, E. R.; Hood, A. W. Bibcode: 1991JBAA..101..300P Altcode: No abstract at ADS 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: Resistive Ballooning Line-Tied Boundary Conditions Authors: Hardie, I. S.; Hood, A. W.; Allen, H. R. Bibcode: 1991SoPh..133..313H Altcode: Ideal and resistive ballooning modes are investigated for different ratios of a two-layer stratified density region representing a model for the photospheric/coronal boundary. Construction of the ballooning equations using a WKB approach is justified by comparison between the values of the growth rate obtained using Hain-Lüst and ballooning equations together with a WKB integral relation. Different values of the density ratio, radius, and resistivity are considered. Sausage-type and kink-type instabilities are found. One of these, depending on the value of r remained unstable for large density ratios. The other instability tended to marginal stability as the density ratio was increased, and allowed parallel and perpendicular flows across the boundary. This is contrary to the predictions of both the `rigid-wall' and `flow-through' conditions. 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: 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: Effects of Line-Tying and Non-Uniformities on Thermal Instabilities and Slow MHD Modes (With 2 Figures) Authors: Hermans, D.; Hood, A. W.; Clifford, L.; Milne, A. Bibcode: 1991mcch.conf..405H Altcode: No abstract at ADS Title: Magnetohydrodynamics of Solar Flares Authors: Hood, A. W. Bibcode: 1991assm.conf..307H Altcode: No abstract at ADS Title: MHD of solar flares. Authors: Hood, A. W. Bibcode: 1991gamp.conf..307H Altcode: The author considers MHD models for the initial stages of solar flares. 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 ideal MHD stability of line-tied coronal loops: A truncated Fourier series approach Authors: de Bruyne, P.; Velli, M.; Hood, A. W. Bibcode: 1990CoPhC..59...55D Altcode: The stability behaviour of a line-tied cylindrically symmetric coronal loop is investigated using a general method presented by Velli, Einaudi and Hood. The plasma perturbation in the linearised equation of motion is expanded in a truncated Fourier series in the poloidal and axial directions, and the resulting system of ordinary differential equations for the radial displacement is solved as an eigenvalue problem. The eigenvalue, be it the critical loop length or the growth rate, is found to converge rapidly with the order of the truncation (approximately as N-2, where N is the number of terms in the Fourier series).

Results for the non-force-free uniform-twist field of Gold and Hoyle are presented and compared with a previous study based on the energy principle. The instability threshold for the m = 1 kink mode and the m = ∞ balloning mode are found to be of the same order of magnitude when substantial pressure gradients are present. Preliminary results for higher-m modes indicate that they yield instability thresholds comparable to the ballooning threshold for smaller gradients too. Title: Structure and stability of the solar corona. Authors: Hood, A. W. Bibcode: 1990CoPhR..12..177H Altcode: A review of the structure and stability of solar coronal plasmas is given. Firstly the structure of the corona is presented in two parts, namely models for coronal arcades and coronal loops. Each topic is dealt with using two different approaches. One approach is to solve the equilibrium equations directly and the other is to solve the time dependent equations with a slow photospheric motion described. In this latter approach, the plasma evolves through a sequence of approximate equilibria with dynamic behaviour occurring only when the photospheric field distribution is sufficiently complex. The evolution of coronal loops shows that the internal magnetic field tends to contract whereas the external field tends to expand. It is interesting to note that the simple twisting of a straight cylindrical field generates substantial structuring in the coronal field, with a strong current concentration on the magnetic axis. Secondly, the stability of the above equilibrium structures is discussed. Three-dimensional disturbances are considered and some of the numerical methods used are described. The main focus of attention is the ideal and resistive MHD stability properties of the magnetic field. General results are hard to come by but numerical results have suggested that all force-free coronal arcades are stable unless a magnetic island exists. Title: A Model for Quiescent Solar Prominences with Normal Polarity Authors: Hood, A. W.; Anzer, U. Bibcode: 1990SoPh..126..117H Altcode: A class of 2-D models of solar quiescent prominences, with normal polarity, is presented. These represent an extension to the Kippenhahn-Schlüter model for which the prominence configuration matches smoothly onto an external non-potential coronal solution of a constant α field. Using typical prominence values a model is constructed which also matches the coronal conditions. It is found that the magnetic field component along the prominence influences the internal structure of the prominence. A simple extension to the basic models is indicated as a means of taking a lower boundary of the prominence and eliminating parasitic polarities in the photosphere. Title: Ideal Kink Instabilities in Line-tied Coronal Loops: Growth Rates and Geometrical Properties Authors: Velli, M.; Einaudi, G.; Hood, A. W. Bibcode: 1990ApJ...350..428V Altcode: A detailed analysis of the ideal kink instability in line-tied cylindrically symmetric coronal loops is presented. Using a rapidly converging Fourier series expansion technique, the growth rate, as well as the eigenfunction, of ideal m = 1 kink modes is calculated for two topologically distinct models of force-free static MHD equilibria: one in which all the magnetic field lines are connected to the photosphere and one presenting a polarity inversion surface. The growth rates depend crucially on the loop length. Loops of the former type are found to be more unstable, and possess higher growth rates, than loops of the latter type, which are unstable to sausage-tearing modes and may also be unstable to m = 1 resistive kink modes. Applications of these results to the structure of coronal loops are presented. Title: Boundary Effects on the Magnetohydrodynamic Stability of a Resistive Plasma Authors: Velli, M.; Einaudi, G.; Hood, A. W. Bibcode: 1990ApJ...350..419V Altcode: A general method for studying the resistive MHD stability of plasma configurations where boundary effects are of crucial importance and can be expressed as additional constraints on a periodic system is presented and applied to the case of line-tied cylindrically symmetric coronal loops. The eigenvalue equations obtained are a generalization of the Freidberg and Hewett equations, to which they reduce when the loop length is made infinite. An application to tearing modes is described which shows that in a finite geometry, tearing takes place at the center of the configuration, corresponding to the vertex of coronal loops. Applications to other configurations of astrophysical interest are described. Title: Numerical Models of Quiescent Normal Polarity Prominences Authors: Fiedler, R. A. S.; Hood, A. W. Bibcode: 1990PDHO....7..152F Altcode: 1990ESPM....6..152F; 1990dysu.conf..152F Two dimensional numerical models of quiescent solar prominences with normal polarity are presented. These models provide an extension to the classical Kippenhahn-Schluter model in that the prominence is treated as having finite width and the external coronal field is matched smoothly. Using typical prominence and coronal values solutions to the Grad-Shafranov equation which provide the necessary support are found. Some extensions to the basic model are discussed. Title: Magnetohydrodynamic Stability of Line-Tied Prominence Magnetic Fields Authors: de Bruyne, P.; Hood, A. W. Bibcode: 1990LNP...363..270D Altcode: 1990doqp.coll..270D; 1990IAUCo.117..270D No abstract at ADS Title: Linear stability of line-tied coronal loops. Authors: de Bruyne, P.; Velli, M.; Hood, A. W. Bibcode: 1990PDHO....7..142D Altcode: 1990dysu.conf..142D The ideal linear MHD stability of line-tied 1-D coronal loops is investigated. It is shown that an extended Suydam criterion, obtained from a local analysis, provides a necessary condition for stability of the global kink mode. Title: Loss of Equilibrium in Coronal Loops Authors: Lohian, R. M.; Hood, A. W. Bibcode: 1990ppsa.conf..243L Altcode: No abstract at ADS Title: A normal polarity quiescent prominence model. Authors: Hood, A. W.; Anzer, U. Bibcode: 1990PDHO....7..130H Altcode: 1990dysu.conf..130H A class of simple 2-D non-isothermal models for quiescent prominences with normal polarity are presented. These extended the Kippenhahn-Schlüter and Menzel models by smoothly matching the prominence region onto an external, force-free coronal field. In addition, the field component along the prominences is an integral part of the solution and modifies the internal structure. Title: A Model for Quiescent Solar Prominences with Normal Polarity Authors: Hood, A. W.; Anzer, U. Bibcode: 1990LNP...363..271H Altcode: 1990doqp.coll..271H; 1990IAUCo.117..271H No abstract at ADS Title: The Thermal Stability of a Planar Plasma in the Presence of a Line-Tied and Sheared Magnetic Field Authors: Hermans, D.; Hood, A. W.; Clifford, L. Bibcode: 1990PDHO....7..160H Altcode: 1990ESPM....6..160H; 1990dysu.conf..160H No abstract at ADS Title: The shape of twisted, line-tied coronal loops Authors: Browning, P. K.; Hood, A. W. Bibcode: 1989SoPh..124..271B Altcode: The magnetostatic equilibrium of a coronal loop in response to slow twisting of the photospheric footpoints is investigated. A numerical code is used to solve the full non-linear 2-D axisymmetric problem, extending earlier linearised models which assume weak twist and large aspect ratio. It is found that often the core of the loop tends to contract into a region of strong longitudinal field while the outer part expands. It is shown that, away from the photospheric footpoints, the equilibrium is very well approximated by a straight 1-D cylindrical model. This idea is used to develop a simple method for prescribing the footpoint angular displacement and calculating the equilibrium. 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: A formulation of non-ideal localized (or ballooning) modes in the solar corona Authors: Hood, A. W.; van der Linden, R.; Goossens, M. Bibcode: 1989SoPh..120..261H Altcode: The stability equations for localized (or ballooning) modes in the solar atmosphere are formulated. Dissipation due to viscosity, resistivity, and thermal conduction are included using the general forms due to Braginskii (1965). In addition, the effect of gravity, plasma radiation, and coronal heating are included. The resulting equations are one-dimensional and only involve derivatives along the equilibrium magnetic field. Thus, the stabilising influence of photospheric line-tying, which is normally neglected in most numerical simulations, can be studied in a simple manner. Two applications to sound wave propagation and thermal instabilities in a low-beta plasma are considered with a view to determining realistic coronal boundary conditions that model the lower, denser levels of the solar atmosphere in a simple manner. Title: Twisted Magnetic Flux Tubes - Effect of Small Twist Authors: Lothian, R. M.; Hood, A. W. Bibcode: 1989SoPh..122..227L Altcode: The shape of a magnetic flux tube is investigated when photospheric motion causes small twist at the magnetic footpoints. Using a Fourier-Bessel series expansion, the previous results of Zweibel and Boozer (1985) and Steinolfson and Tajima (1987), when the twist is small, are substantiated. A twisting motion that is restricted to a finite region is investigated. Inside the twisted region, the tube contracts, but in the outer region the field remains straight, except for a slight expansion at the outside of the loop near the footpoints. The amount of twist depends on the radial position and can in fact be larger in the contracted region with the twist decreasing as the tube expands. An axial boundary-layer region is present, as noted by the above authors, through which the field adjusts to the line-tied magnetic footpoint positions. An analysis of the boundary layer shows that the thickness remains constant as the loop-length is increased with the result that the main part of the loop has constant cross-sectional area and can be described by cylindrically-symmetric fields. This new 1-D model predicts the main behaviour of the loop without the need to solve the more complicated 2-D problem directly. It is speculated that the boundary layers will remain even when the twist becomes large and a simple example is presented. A detailed parametric study of different twist profiles shows how the central part of the loop responds. Title: Bounds on the Ideal Magnetohydrodynamic Stability of Line-Tied 2-D Coronal Magnetic Fields Authors: de Bruyne, P.; Hood, A. W. Bibcode: 1989SoPh..123..241D Altcode: A tractable method for investigating the linear stability of line-tied 2-D coronal magnetic fields is introduced. It is based on the Bernstein et al. (1958) energy principle and can be applied to non-isothermal equilibria with gravity, having a translational invariance. The perturbed potential energy integral is manipulated to produce either necessary conditions for stability to localized modes or sufficient conditions for stability to global modes. Each condition only requires the solution of a set of ordinary differential equations, integrated along the magnetic field lines. The tests are employed to two different classes of equilibria. A linear force-free field is shown to be completely stable, regardless of the shear. The role of pressure gradients, footpoint displacements, line-tying and stratification on an isothermal magneto-hydrostatic equilibrium is assessed. Title: Magnetic and Boundary Effects on Thermal Instabilities in Solar Magnetic Fields - Localized Modes in a Slab Geometry Authors: Cargill, P. J.; Hood, A. W. Bibcode: 1989SoPh..124..101C Altcode: The coupling of thermal and ideal MHD effects in a sheared magnetic field is investigated. A slab geometry is considered so that the Alfvén mode can be decoupled from the system. With the total perturbed pressure approximately zero, the fast mode is eliminated and a system of linearized equations describing magnetic effects on the slow mode and thermal mode is derived. These modes evolve independently on individual fieldlines. One of the main features of this approach is that the influence of the dense photosphere can be included. A variety of different conditions that simulate the photospheric boundary are presented and the different results are discussed. A choice of field geometry and boundary conditions is made which removes mode rational surfaces so that there are no regions in which parallel thermal conduction can be neglected. This provides a stabilizing mechanism for the thermal mode. Growth rates are reduced by 30-40% and there is complete stabilization for sufficiently short fieldlines. The influence of dynamic and thermal boundary conditions on the formation of prominences is discussed. Title: Resistive Tearing in Line-Tied Magnetic Fields - Slab Geometry Authors: Velli, M.; Hood, A. W. Bibcode: 1989SoPh..119..107V Altcode: The resistive tearing-mode instability of a current carrying plasma sheet is investigated including the stabilising photospheric line-tying boundary conditions. This end condition prohibits a single Fourier mode and so requires a series expansion in harmonics of the fundamental sheet excitation. Equilibria in which there exist field lines that do not connect to the photosphere are unstable provided the ratio of the sheet length to characteristic transverse scale is smaller than a critical value that depends on the equilibrium profile. Line-tying has a strong stabilising effect on the fundamental periodic mode. That tearing mode harmonic which develops close to the instability threshold, leads to a configuration with one X point and one 0 point. Its linear growth rate follows the usual constant-ψ scaling with resistivity γ ∼ S-3/5, where S is the magnetic Reynolds number. 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: Simple Tests for the Ideal Magnetohydrodynamic Stability of Line-Tied Coronal Magnetic Fields Authors: de Bruyne, P.; Hood, A. W. Bibcode: 1989SoPh..119...87D Altcode: Methods for investigating the stability of line-tied, cylindrically-symmetric magnetic fields are presented. The energy method is used and the perturbed potential energy integral is manipulated to produce simple tests that predict either stability to general coronal disturbances or instability to localized modes, both satisfying photospheric line-tying. Using these tests the maximum amount of magnetic energy, that can be stored in the coronal magnetic field prior to an instability, can be estimated. The tests are applied to four different classes of equilibria and results are obtained for both arcade and loop geometries. Title: A Model for Quiescent Solar Prominences with Normal Polarity Authors: Hood, A. W.; Anzer, U. Bibcode: 1989HvaOB..13..281H Altcode: No abstract at ADS Title: Can resistive kink instabilities drive simple loop flares? Authors: Velli, M.; Emaudi, G.; Hood, A. W. Bibcode: 1989sasf.confP.305V Altcode: 1988sasf.conf..305V; 1989IAUCo.104P.305V A detailed analysis of the kink instability in finite length (inertially line-tied), cylindrically symmetric coronal loops is presented. The correct line-tying boundary conditions within the framework of ideal and resistive magnetohydrodynamics are discussed, and the growth rates of unstable modes and corresponding eigenfunctions are calculated. Resistive kink modes are found to be unstable in configurations where the axial magnetic field undergoes an inversion, resistive effects being confined to a small region around the loop vertex. Title: MHD Stability of Line-Tied Prominence Magnetic Fields Authors: de Bruyne, P.; Hood, A. W. Bibcode: 1989HvaOB..13..269D Altcode: No abstract at ADS Title: Stability and eruption of prominences Authors: Hood, A. W. Bibcode: 1989ASSL..150..167H Altcode: 1988dsqs.work..167H; 1989dsqs.work..167H The application of stability theory to quiescent solar prominences is examined, reviewing the results of recent investigations. The governing equations for the primary MHD instabilities (kink-mode, sausage-mode, and Rayleigh-Taylor) are presented; normal-mode, energy-method, and nonequilibrium approaches to their solution are outlined; and particular attention is given to the effect of the dense photosphere, ballooning modes, coronal arcades, distributed current models and eruptive instability, localized modes and small-scale structure, and arcades containing a current sheet. Also discussed are the problem of thermal stability, resistive instabilities and tearing modes, the effect of line tying, and a simple model describing prominence eruption and coronal mass ejection. Title: On the MHD Stability of the M=1 Kink Mode in Finite Length Coronal Loops Authors: Velli, M.; Hood, A. W.; Einaudi, G. Bibcode: 1989ESASP.285..105V Altcode: 1989rsp..conf..105V A general method for studying the ideal and resistive MHD stability of plasma configurations with line-tying is presented, and applied to the case of the M=1 kink mode in coronal loops. The method consists in a truncated Fourier series approach applied to the linearized equations of motion, and is found to converge rapidly with the order of the truncation. Models of the boundary conditions at the corona-photosphere interface are discussed, and the growth rates of unstable modes are calculated for equilibrium profiles with an without a reversal in the field component connecting to the photosphere. The relevance of these modes to compact loop flares is assessed. 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: The Effects of Parallel and Perpendicular Viscosity on Resistive Ballooning Modes in Line-Tied Coronal Magnetic Fields Authors: van der Linden, R.; Goossens, M.; Hood, A. W. Bibcode: 1988SoPh..115..235V Altcode: The study of resistive ballooning instabilities in line-tied coronal magnetic fields is extended by including viscosity in the stability analysis. The equations that govern the resistive ballooning instabilities are derived and the effects of parallel and perpendicular viscosity are included using Braginskii's stress tensor. Numerical solutions to these equations are obtained under the rigid wall boundary conditions for arcades with cylindrically-symmetric magnetic fields. It is found that viscosity has a stabilizing effect on the resistive ballooning instabilities with perpendicular viscosity being more important by far than parallel viscosity. The strong stabilizing effect of perpendicular viscosity can lead to complete stabilization for realistic values of the equilibrium quantities. Title: Thermal Condensations in Coronal Magnetic Fields Authors: Hood, A.; Anzer, U. Bibcode: 1988SoPh..115...61H Altcode: Conditions under which cool condensations can form in the solar corona are investigated using the powerful phase plane method to analyse the energy and hydrostatic balance equations. The importance of the phase plane approach is that the conclusions deduced are not sensitive to the actual choice of boundary conditions adopted which only determine the actual contour. The importance of heating variations and area divergence are studied as well as the influence of gravity for their effect on the formation of cool condensations. The cool temperature at which optically thin radiation and heating balance is important and the links with other cool solutions are mentioned. Title: Stability and eruption of prominences. Authors: Hood, A. Bibcode: 1988dssp.conf..147H Altcode: The stability of coronal magnetic fields is investigated including the strong stabilising effect of photospheric line tying. Several possible eruptive mechanisms are considered. Conditions for global stability and instability are investigated. Locallised MHD modes, while unlikely to disrupt the prominence, could provide an explanation for the fine scale structure. The evolution of the prominence field to a nonequilibrium (or catastrophe) point suggests that an eruption will occur when no neighbouring equilibrium exists. Title: Resistive Ballooning Modes in Line-Tied Coronal Fields - Part Two Authors: Velli, M.; Hood, A. W. Bibcode: 1987SoPh..109..351V Altcode: The resistive stability of coronal loops to perturbations with short wavelength across the magnetic field is analysed, taking full account of the line tying effect due to the presence of the photosphere. The results presented are similar to those previously obtained for arcades: configurations with a pressure profile decreasing with distance from the loop axis at some point are found to be always unstable, the growth rate γ increasing monotonically with the wavenumber (n) and scaling approximately as γ ∼ (n2Dr)1/3 in the limit of large n. Title: The stability of line tied force-free cylindrical arcades: Is an active region filament a requirement for a two-ribbon flare? Authors: Hood, A.; Anzer, U. Bibcode: 1987SoPh..111..333H Altcode: The MHD stability of force-free, cylindrical arcades is investigated, including the stabilising effect of photospheric line tying. It is found that a wide variety of fields are stable. This suggests that either a departure from a force free equilibrium or suppression of line tying is necessary if a two-ribbon flare is to be triggered. It is postulated that in both circumstances, the existence of an active region filament is an essential preflare requirement for a two-ribbon flare. Title: The effects of viscosity on resistive ballooning modes in line-tied coronal magnetic fields. Authors: Vanderlinden, R.; Goossens, M.; Hood, A. W. Bibcode: 1987ESASP.275..109V Altcode: 1987sspp.symp..109V The study of resistive ballooning instabilities in line-tied coronal magnetic fields is extended by including viscosity in the stability analysis. The equations that govern the resistive ballooning instabilities are derived and the effects of viscosity are included using Braginskii's stress tensor. Numerical solutions to the equations are obtained under the rigid wall boundary conditions for arcades with cylindrically symmetric magnetic fields. The stabilizing influences of parallel and perpendicular viscosity are investigated. Perpendicular viscosity is more important and can lead to complete stabilization. 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: Stability and Eruption of Prominences Authors: Hood, A. W. Bibcode: 1987dssp.work..147H Altcode: 1987ASSL..150..147H No abstract at ADS Title: Stability of Magnetic Arcades Authors: Anzer, U.; Hood, A. W. Bibcode: 1987rfsm.conf..248A Altcode: The authors conclude that sheared force-free arcades cannot become unstable and produce solar flares. They therefore predict that two-ribbon flares must always be associated with extended solar prominences. 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 stability of coronal and prominence magnetic fields. Authors: Hood, A. W. Bibcode: 1986NASCP2442..457H Altcode: 1986copp.nasa..457H The magnetic fields in prominences and active regions (coronal arcades) may be susceptible to a variety of instabilities. Ideal MHD instabilities are the fastest growing and criteria for checking stability are complicated by the line tying effect of the dense photosphere. The significance of the localised instabilities is not yet fully understood. The nonlinear coupling of these modes may give rise to an explosive instability, with the modes coupling to longer wavelengths, (Mondt and Weiland, 1985). On the other hand, if the modes saturate early, then the main effect of the instability may be an enhancement of transport coefficients. Nonetheless, the author gives an equation which provides a simple test for the stability of cylindrical magnetic fields. Title: The Magnetohydrodynamic Stability of Coronal Arcades. III. Sheared Equilibrium Fields Authors: Cargill, P. J.; Hood, A. W.; Migliuolo, S. Bibcode: 1986ApJ...309..402C Altcode: The ideal magnetohydrodynamic stability of solar coronal arcades where all the field lines are tied to the photosphere is examined. Two sets of photospheric boundary conditions are examined, and the first detailed quantitative comparison is presented. It is found that conditions where all components of the perturbation vanish at the photosphere are significantly more stable to interchange modes than those for which a displacement along the field lines is allowed there. Much stronger radial pressure gradients are needed to destabilize the former case. It is also found that three sample force-free fields are stable to all perturbations which were imposed. These results outline a pressing need for a more precise treatment of the transition region/corona boundary in stability problems. Title: Resistive Ballooning Modes in Line-Tied Coronal Fields - Part One - Arcades Authors: Velli, M.; Hood, A. W. Bibcode: 1986SoPh..106..353V Altcode: The stability of coronal arcades to localized resistive interchange modes in the ballooning ordering, including photospheric line tying, is investigated. It is found that the anchoring of magnetic footpoints in the photosphere is not sufficient to stabilise ballooning modes, once resistivity is taken into account. All configurations with a pressure profile decreasing from the arcade axis at some point are unstable, a purely growing mode being excited. The dependence of the growth rate γ on the parameter Rm−1 ∼ k2η, where η is the resistivity and k the wavenumber in a direction perpendicular to the equilibrium field, can be described by a power law with varying index: for small values of k2 and an ideally stable field one finds γ ∼ Rm−1. As k2 is increased or marginal stability is approached one finds γ ∼ Rm−1/3. T implications of these localised instabilities to the temporal evolution and overall energy balance of arcade structures in the solar corona is discussed. 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: Photospheric Line-Tying Conditions for the Magnetohydrodynamic Stability of Coronal Magnetic Fields Authors: Hood, A. W. Bibcode: 1986SoPh..105..307H Altcode: Using the localised, ballooning ordering, the effect of a density stratification on the ideal MHD stability of magnetic fields is investigated. It is found that, when the photospheric density is very much greater than the coronal value, the line tying conditons are best simulated by assuming that all coronal disturbances vanish at the photospheric boundary. This is commonly known as the rigid wall conditions. Title: Ballooning Instabilities in the Solar Corona - Conditions for Stability Authors: Hood, A. W. Bibcode: 1986SoPh..103..329H Altcode: A method for analysing the stability of cylindrical loops and arcades to ballooning modes is presented. Using a WKB method, simple tests for instability (or stability to localised modes) are obtained for the two commonly used, line tying, conditions. In addition, when instabilities are present, the physical growth rate and the radial structure of the least stable can be computed from the solution of a 4th order system of ordinary differential equations. The detailed analysis for a particular field is presented in an Appendix. 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: 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: MHD instabilities. Authors: Hood, A. W. Bibcode: 1985ssmf.conf...80H Altcode: Contents: Equilibrium solutions. Physical description of MHD instabilities. Linearised MHD equations. Normal modes method. Energy (or variational) method. The Rayleigh-Taylor instability. The sharp pinch - normal modes. General cylindrical pinch - energy method. Necessary and sufficient conditions - Newcomb's analysis. Resistive instabilities - tearing modes. Applications of MHD instabilities. Title: Activation of Solar Flares Authors: Cargill, P. J.; Migliuolo, S.; Hood, A. W. Bibcode: 1984ESASP.207...57C Altcode: 1984plap.rept...57C The physics of the activation of two-ribbon solar flares via the MHD instability of coronal arcades is presented. The destabilization of a preflare magnetic field is necessary in order for a rapid energy release, characteristic of the impulsive phase of the flare, to occur. The authors examine the stability of a number of configurations and discuss the physical consequences and relative importance of varying pressure profiles and different sets of boundary conditions (involving field-line tying). Interchange modes, driven unstable by pressure gradients, are candidates for instability. Shearless vs. sheared equilibria are also discussed. Title: Magnetohydrodynamic stability of line-tied coronal arcades. II - Shearless magnetic fields Authors: Migliuolo, S.; Cargill, P. J.; Hood, A. W. Bibcode: 1984ApJ...281..413M Altcode: The stability of 'shearless' arcades is investigated using normal mode equations. It is found that all such equilibria are unstable to modes with very short wavelengths in the z-direction, provided the current channel is sufficiently localized in space. These unstable modes are pressure-driven interchange modes and obey lateral force balance. The algebraic minimization of the energy integral of Zweibel (1981) does describe the most unstable modes for such equilibria and does not contradict the formal minimization of Newcomb (1960). Line-tying plays no role in the stability of these shearless arcades, apart from eliminating mode rational surfaces. The unstable modes are described by interchange instabilities, and current channels that are more sharply localized in space yield larger growth rates. The role of shear as trigger for solar flares is discussed. 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: An energy method for the stability of solar magneto hydrostatic atmospheres Authors: Hood, A. W. Bibcode: 1984GApFD..28..223H Altcode: The energy method of Bernstein et al. (1958) was used by Schindler et al. (1983) to derive a useful form of the linearised potential energy for coronal arcades. The basic state magnetic field and plasma are assumed to be in magnetohydrostatic equilibrium and independent of variations along the length of the arcade. A sufficient condition for stability is derived and is applied to two particular magnetic structures. When the axial field component vanishes, this condition becomes necessary and suficient. Title: The stability of magnetic fields relevant to two-ribbon flares Authors: Hood, A. W. Bibcode: 1984AdSpR...4g..49H Altcode: 1984AdSpR...4...49H The preflare structure, prior to two-ribbon flares, is thought to consist of magnetic field arcades. As a first approximation, the magnetic field is assumed to be invariant along the length of the arcade. The ideal MHD stability of such structures is studied using the energy method. The dense photosphere is simulated by line-typing the magnetic field and a discussion of boundary conditions is presented. Using the energy method, sufficient conditions for stability are obtained for certain magnetohydrostatic fields that also include the effect of gravity. Under certain circumstances, these conditions become necessary and sufficient. Some comments on resistive effects are mentioned. Title: The Stability of Magnetohydrostatic Atmospheres Authors: Hood, A. W. Bibcode: 1983SoPh...89..235H Altcode: Using the analysis of Schindler et al. (1983) and Hood (1983), the `local' stability of Zweibel (1981) is extended to include the previously neglected magnetic tension terms. A particular magnetohydrostatic field is shown to be stable if the parameter, 2βH, is small enough. This is in contradiction to the previous `local' analysis. Title: Magnetic stability of coronal arcades relevant to two-ribbon flares. Authors: Hood, A. W. Bibcode: 1983SoPh...87..279H Altcode: The dense photosphere provides an extremely efficient mechanism, called line-tying, for stabilising solar coronal magnetic fields. In this paper, we study the ideal magnetohydrodynamic (MHD) stability of cylindrically symmetric arcades, the field structure thought to be present prior to the onset of a large two-ribbon flare. It is found that, when the axis of symmetry lies on the photosphere, a wide range of force-free fields are completely stable to all possible perturbations. However, replacing the axial magnetic field by an equivalent gas pressure will produce a localised instability. Instability, the mechanism for the release of energy for a flare, will also occur if the symmetry axis, assumed to coincide with an active-region filament, is too high above the photosphere to benefit from its stabilising influence. 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: 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: 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: 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: 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: Solar coronal loops Authors: Hood, Alan W. Bibcode: 1980PhDT.......165H Altcode: In the past few years it has been realised that loop structures are an important feature of the solar corona. Presumably, these structures outline the local magnetic field and in this thesis some theoretical aspects of solar coronal loops are considered. The starting point is to model the static equilibrium, in a 1 - D structure, and determine the temperature and density by solving the energy balance equation. The basic state is determined by two dimensionless parameters, namely the ratio of optically thin radiation to thermal conduction, and the ratio of mechanical heating to radiation, An important result is that when critical values of the parameters are exceeded thermal non-equilibrium- ensues and the loop rapidly cools from coronal temperatures 10. 6K to below10. 5K. A simple 2 - D model extends this work and results provide a possibleexplanation for several loop features. The thermal stability of coronal .loops is investigated by developing 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 conductive flux is large enough that it lies on the upper- of two equilibrium branches. Solar coronal loops are observed to be remarkably stable structures. A magneto hydrodynamic 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. Two-ribbon flares follow the eruption of an active region filament, which may lie along a magnetic flux tube. It is suggested that the eruption is caused by the kink instability, which sets in when the amount of magnetic twist in the flux tube exceeds a critical value. Occasionally active region loops may become unstable and give rise to small loop flares, which may also be a result of the kink instability. A more realistic model of an active region filament, that takes account of the overlying magnetic field, shows that instability may occur if either the twist or the height of the filament exceed critical values. Finally, the possibility that a solar flare is triggered by thermal non-equilibrium, instead of by magnetic instability, is investigated. This 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 temperature about 10. 4K and gradually increases theheating or decreases the loop pressure (or decreases the loop length), ultimately critical conditions are reached beyond which no cool equilibrium exists. The plasma rapidly heats up to a new quasi-equilibrium at typically 10. 7 K. Duringsuch a thermal flaring, any magnetic disruption or particle acceleration is of secondary importance. Title: Thermal equilibrium and non equilibrium in coronal loops. Authors: Hood, A. W. Bibcode: 1980AnPh....5..447H Altcode: 1980mhda.conf..447H No abstract at ADS 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: 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: Geochemical study of the Uinta Basin: formation of petroleum from the Green River formation Authors: Tissot, B.; Deroo, G.; Hood, A. Bibcode: 1978GeCoA..42.1469T Altcode: Kerogen from the Green River formation is rich in lipid material and contains predominantly aliphatic chains, with subordinate saturated cyclic material. Compositional differences due to the environment of deposition are observed in the extractable hydrocarbons. The influence of microbial degradation during deposition of organic matter is intense in the stratigraphically lowest zone and decreases toward younger beds, where fossil molecules derived from higher plants, algae and other planktonic organisms and bacteria are abundant. The great depth of the oil generation stage may be explained by a combination of (a) a relatively low geothermal gradient, and (b) a high oil generation threshold. The lower part of the formation has reached the principal stage of oil generation and is responsible for most of the crude oils produced in the Uinta Basin.