Author name code: goossens ADS astronomy entries on 2022-09-14 author:"Goossens, Marcel" ------------------------------------------------------------------------ Title: Non-linear damping of kink waves through uniturbulence and its role in heating the wind Authors: van Doorsselaere, Tom; Li, Bo; Goossens, Marcel; Ruderman, Michael; Magyar, Norbert; Ismayilli, Rajab; Hnat, Bogdan Bibcode: 2022cosp...44.1346V Altcode: Numerical simulations have revealed a new type of turbulence of unidirectional waves in a plasma that is perpendicularly structured (Magyar et al. 2017), named uniturbulence. For this new type of turbulence, the transverse structuring modifies the upward propagating wave to have both Elsasser variables, leading to the well-known perpendicular cascade. In this talk, we discuss our analytical description of the non-linear evolution of kink waves in a cylindrical flux tube, which are prone to uniturbulence. We show that they lead to a non-linear cascade for both propagating and standing waves. We calculate explicit expressions for the wave pressure and energy cascade rate. We compare the damping times from our formula with the results of numerical simulations and observations. In both cases we find a reasonably good match. The comparison with the simulations show that the non-linear damping dominates in the high amplitude regime, while the low amplitude regime shows damping by resonant absorption. In the comparison with the observations, we find a power law inversely proportional to the amplitude $\eta^{-1}$ as an outer envelope for our Monte Carlo data points, which fits with the observed data points. These numerically tested and observationally verified damping rates may be used to implement extra heating in coronal models. That in turn allows for a comparison with in-situ data. Title: The properties of magnetoacoustic waves in magnetic flux tubes with background rotational flows Authors: Skirvin, Samuel; Fedun, Viktor; van Doorsselaere, Tom; Goossens, Marcel; Verth, Gary; Claes, Niels Bibcode: 2022cosp...44.2547S Altcode: Rotational flows are commonly observed features in structures within the lower solar atmosphere, for example in solar vortices and within intergranular lanes. It is to be expected that the presence of an equilibrium rotational flow inside a magnetic flux tube will modify the behaviour of propagating magnetoacoustic (MA) waves inside the structure. Using a previously developed numerical eigensolver, we obtain the eigenvalues for both the sausage and kink modes of the magnetic flux tube in the presence of a background rotational flow under photospheric conditions. The effect of both the amplitude of the rotational flow and the flow's radial structure are investigated. It is found that when the rotational flow is linear, the modified slow continuum, shifted due to the background flow, reduces to single-point values. However, in the case when the flow is non linear, the modified slow continuum now occupies a band of frequencies. The radial structure of the background rotational flow has important consequences for determining which wave modes are absorbed into the continua. Furthermore, we present for the first time 2D velocity field visualisations showing the resulting wave perturbations alongside incorporation of the additional background flow for both the sausage and kink modes. For both cases of linear and nonlinear background rotational flow, it is shown that the velocity fields with the additional background flow display different characteristics when compared to the perturbation alone, which may be useful for observers when interpreting high resolution data from e.g. DKIST. Finally, we present initial results investigating the nature of MA waves in rotating magnetic flux tubes with an additional vertical flow component, a configuration commonly seen in simulations of solar vortices. Title: Seismology in the presence of flow. Fast spatial damping of counterpropagating kink waves. Authors: Goossens, Marcel; Terradas, Jaume; Soler, Roberto Bibcode: 2022cosp...44.2500G Altcode: This presentation is concerned with the propagation of MHD waves in the presence of flows. An important theoretical finding is that counterstreaming MHD waves undergo fast spatial damping due to resonant absorption even when the flows are rather slow. The analysis deals with propagating waves in cylindrically symmetric 1-D plasma flux tubes with an axial magnetic field and an axial flow. The inhomogeneity in the radial direction causes resonant damping of the propagating kink waves. Analytic expressions are presented for the phase velocities and damping lengths of the forward and backward propagating kink waves in the thin tube and thin boundary approximations. The analytic expressions are confirmed by numerical simulations that go beyond the TT and TB approximations. Information on the phase velocities of the backward and forward propagating waves enables us to determine the internal and external Alfv\'{e}n velocities. This seismological method is applied to the observations by Morton et al. 2015. An important result is that the effect of flow on the damping depends on the propagation direction of the waves. For forward propagating waves the damping length increases with respect to that in the static caae and the waves become less damped. For backward propagating waves flow has the opposite effect. The damping length decreases and the damping is more efficient and causes fast damping of counterpropating waves. This phenomenon provides a natural explanation for the lack of observed backward propagating waves. Title: Non-linear damping of surface Alfvén waves due to Uniturbulence Authors: Ismayilli, Rajab; Van Doorsselaere, Tom; Goossens, Marcel; Magyar, Norbert Bibcode: 2022FrASS...8..241I Altcode: This investigation is concerned with uniturbulence associated with surface Alfvén waves that exist in a Cartesian equilibrium model with a constant magnetic field and a piece-wise constant density. The surface where the equilibrium density changes in a discontinuous manner are the source of surface Alfvén waves. These surface Alfvén waves create uniturbulence because of the variation of the density across the background magnetic field. The damping of the surface Alfvén waves due to uniturbulence is determined using the Elsässer formulation. Analytical expressions for the wave energy density, the energy cascade, and the damping time are derived. The study of uniturbulence due to surface Alfvén waves is inspired by the observation that (the fundamental radial mode of) kink waves behave similarly to surface Alfv\'en waves. The results for this relatively simple case of surface Alfv\'en waves can help us understand the more complicated case of kink waves in cylinders. We perform a series of 3D ideal MHD simulations for a numerical demonstration of the non-linearly self-cascading model of unidirectional surface Alfv\'en waves using the code \textrm{MPI-AMRVAC}. We show that surface Alfv\'en waves damping time in the numerical simulations follows well our analytical prediction for that quantity. Analytical theory and the simulations show that the damping time is inversely proportional to the amplitude of the surface Alfv\'en waves and the density contrast. This unidirectional cascade may play a role in heating the coronal plasma. Title: Acoustic Wave Properties in Footpoints of Coronal Loops in 3D MHD Simulations Authors: Riedl, Julia M.; Van Doorsselaere, Tom; Reale, Fabio; Goossens, Marcel; Petralia, Antonino; Pagano, Paolo Bibcode: 2021ApJ...922..225R Altcode: 2021arXiv210902971R Acoustic waves excited in the photosphere and below might play an integral part in the heating of the solar chromosphere and corona. However, it is yet not fully clear how much of the initially acoustic wave flux reaches the corona and in what form. We investigate the wave propagation, damping, transmission, and conversion in the lower layers of the solar atmosphere using 3D numerical MHD simulations. A model of a gravitationally stratified expanding straight coronal loop, stretching from photosphere to photosphere, is perturbed at one footpoint by an acoustic driver with a period of 370 s. For this period, acoustic cutoff regions are present below the transition region (TR). About 2% of the initial energy from the driver reaches the corona. The shape of the cutoff regions and the height of the TR show a highly dynamic behavior. Taking only the driven waves into account, the waves have a propagating nature below and above the cutoff region, but are standing and evanescent within the cutoff region. Studying the driven waves together with the background motions in the model reveals standing waves between the cutoff region and the TR. These standing waves cause an oscillation of the TR height. In addition, fast or leaky sausage body-like waves might have been excited close to the base of the loop. These waves then possibly convert to fast or leaky sausage surface-like waves at the top of the main cutoff region, followed by a conversion to slow sausage body-like waves around the TR. Title: Erratum: "Nonlinear Damping of Standing Kink Waves Computed With Elsässer Variables" (2021, ApJ, 910, 58) Authors: Van Doorsselaere, Tom; Goossens, Marcel; Magyar, Norbert; Ruderman, Michael S.; Ismayilli, Rajab Bibcode: 2021ApJ...920..162V Altcode: No abstract at ADS Title: Chromospheric Heating by Magnetohydrodynamic Waves and Instabilities Authors: Srivastava, A. K.; Ballester, J. L.; Cally, P. S.; Carlsson, M.; Goossens, M.; Jess, D. B.; Khomenko, E.; Mathioudakis, M.; Murawski, K.; Zaqarashvili, T. V. Bibcode: 2021JGRA..12629097S Altcode: 2021arXiv210402010S The importance of the chromosphere in the mass and energy transport within the solar atmosphere is now widely recognized. This review discusses the physics of magnetohydrodynamic waves and instabilities in large-scale chromospheric structures as well as in magnetic flux tubes. We highlight a number of key observational aspects that have helped our understanding of the role of the solar chromosphere in various dynamic processes and wave phenomena, and the heating scenario of the solar chromosphere is also discussed. The review focuses on the physics of waves and invokes the basics of plasma instabilities in the context of this important layer of the solar atmosphere. Potential implications, future trends and outstanding questions are also delineated. Title: Nonlinear Damping of Standing Kink Waves Computed With Elsässer Variables Authors: Van Doorsselaere, Tom; Goossens, Marcel; Magyar, Norbert; Ruderman, Michael S.; Ismayilli, Rajab Bibcode: 2021ApJ...910...58V Altcode: 2021arXiv210414331V In a previous paper, we computed the energy density and the nonlinear energy cascade rate for transverse kink waves using Elsässer variables. In this paper, we focus on the standing kink waves, which are impulsively excited in coronal loops by external perturbations. We present an analytical calculation to compute the damping time due to the nonlinear development of the Kelvin-Helmholtz instability. The main result is that the damping time is inversely proportional to the oscillation amplitude. We compare the damping times from our formula with the results of numerical simulations and observations. In both cases we find a reasonably good match. The comparison with the simulations shows that the nonlinear damping dominates in the high amplitude regime, while the low amplitude regime shows damping by resonant absorption. In the comparison with the observations, we find a power law inversely proportional to the amplitude η-1 as an outer envelope for our Monte Carlo data points. Title: Mixed properties of magnetohydrodynamic waves undergoing resonant absorption in the cusp continuum Authors: Goossens, M.; Chen, S. -X.; Geeraerts, M.; Li, B.; Van Doorsselaere, T. Bibcode: 2021A&A...646A..86G Altcode: 2020arXiv201206303G Context. Observations of magnetohydrodynamic (MHD) waves in the structured solar atmosphere have shown that these waves are damped and can thus contribute to atmospheric heating. In this paper, we focus on the damping mechanism of resonant absorption in the cusp continuum. This process takes places when waves travel through an inhomogeneous plasma.
Aims: Our aim is to determine the properties of MHD waves undergoing resonant absorption in the cusp continuum in the transition layer of a cylindrical solar atmospheric structure, such as a photospheric pore or a coronal loop. Depending on which quantities dominate, one can assess what type of classical MHD wave the modes in question resemble most.
Methods: In order to study the properties of these waves, we analytically determine the spatial profiles of compression, displacement, and vorticity for waves with frequencies in the cusp continuum, which undergo resonant absorption. We confirm these analytical derivations via numerical calculations of the profiles in the resistive MHD framework.
Results: We show that the dominant quantities for the modes in the cusp continuum are the displacement parallel to the background magnetic field and the vorticity component in the azimuthal direction (i.e. perpendicular to the background magnetic field and along the loop boundary). Title: Damping of Slow Surface Kink Modes in Solar Photospheric Waveguides Modeled by One-dimensional Inhomogeneities Authors: Chen, Shao-Xia; Li, Bo; Van Doorsselaere, Tom; Goossens, Marcel; Yu, Hui; Geeraerts, Michaël Bibcode: 2021ApJ...908..230C Altcode: 2020arXiv201215426C Given the recent interest in magnetohydrodynamic (MHD) waves in pores and sunspot umbrae, we examine the damping of slow surface kink modes (SSKMs) by modeling solar photospheric waveguides with a cylindrical inhomogeneity comprising a uniform interior, a uniform exterior, and a continuous transition layer (TL) in between. Performing an eigenmode analysis in linear, resistive, gravity-free MHD, our approach is idealized in that, among other things, our equilibrium is structured only in the radial direction. We can nonetheless address two damping mechanisms simultaneously, one being the ohmic resistivity and the other being the resonant absorption of SSKMs in the cusp and Alfvén continua. We find that the relative importance of the two mechanisms depends sensitively on the magnetic Reynolds number (Rm). Resonant absorption is the sole damping mechanism for realistically large values of Rm, and the cusp resonance in general dominates the Alfvén one unless the axial wavenumbers are at the lower end of the observationally relevant range. We also find that the thin-boundary approximation holds only when the TL-width-to-radius ratios are much smaller than nominally expected. The ohmic resistivity is far more important for realistically small Rm. Even in this case, SSKMs are only marginally damped, with damping-time-to-period ratios reaching ∼10 in the parameter range we examine. Title: Resonant absorption: Transformation of compressive motions into vortical motions Authors: Goossens, M.; Arregui, I.; Soler, R.; Van Doorsselaere, T. Bibcode: 2020A&A...641A.106G Altcode: 2020arXiv200908152G This paper investigates the changes in spatial properties when magnetohydrodynamic (MHD) waves undergo resonant damping in the Alfvén continuum. The analysis is carried out for a 1D cylindrical pressure-less plasma with a straight magnetic field. The effect of the damping on the spatial wave variables is determined by using complex frequencies that arise as a result of the resonant damping. Compression and vorticity are used to characterise the spatial evolution of the MHD wave. The most striking result is the huge spatial variation in the vorticity component parallel to the magnetic field. Parallel vorticity vanishes in the uniform part of the equilibrium. However, when the MHD wave moves into the non-uniform part, parallel vorticity explodes to values that are orders of magnitude higher than those attained by the transverse components in planes normal to the straight magnetic field. In the non-uniform part of the equilibrium plasma, the MHD wave is controlled by parallel vorticity and resembles an Alfvén wave, with the unfamiliar property that it has pressure variations even in the linear regime. Title: Wave Pressure and Energy Cascade Rate of Kink Waves Computed with Elsässer Variables Authors: Van Doorsselaere, Tom; Li, Bo; Goossens, Marcel; Hnat, Bogdan; Magyar, Norbert Bibcode: 2020ApJ...899..100V Altcode: 2020arXiv200715411V Numerical simulations have revealed a new type of turbulence of unidirectional waves in a plasma that is perpendicularly structured, named uniturbulence. For this new type of turbulence, the transverse structuring modifies the upward propagating wave to have both Elsässer variables, leading to the well-known perpendicular cascade. In this paper, we study an analytical description of the nonlinear evolution of kink waves in a cylindrical flux tube that are prone to uniturbulence. We show that they lead to a nonlinear cascade for both propagating and standing waves. We calculate explicit expressions for the wave pressure and energy cascade rate. The computed damping rate $\tau /P$ depends on the density contrast of the flux tube and the background plasma and is inversely proportional to the amplitude of the kink wave. The dependence on the density contrast shows that it plays a role especially in the lower solar corona. These expressions may be added in Alfvén wave driven models of the solar atmosphere (such as the Alfvén Wave Solar Model (AWSOM)), modifying it to UAWSOM (Uniturbulence and the Alfvén Wave Solar Model). Title: Ultra-long and quite thin coronal loop without significant expansion Authors: Li, Dong; Yuan, Ding; Goossens, Marcel; Van Doorsselaere, Tom; Su, Wei; Wang, Ya; Su, Yang; Ning, Zongjun Bibcode: 2020A&A...639A.114L Altcode: 2020arXiv200602629L Context. Coronal loops are the basic building blocks of the solar corona. They are related to the mass supply and heating of solar plasmas in the corona. However, their fundamental magnetic structures are still not well understood. Most coronal loops do not expand significantly, but the diverging magnetic field would have an expansion factor of about 5-10 over one pressure scale height.
Aims: We investigate a unique coronal loop with a roughly constant cross section. The loop is ultra long and quite thin. A coronal loop model with magnetic helicity is presented to explain the small expansion of the loop width.
Methods: This coronal loop was predominantly detectable in the 171 Å channel of the Atmospheric Imaging Assembly (AIA). Then, the local magnetic field line was extrapolated within a model of the potential field source-surface. Finally, the differential emission measure analysis made from six AIA bandpasses was applied to obtain the thermal properties of this loop.
Results: This coronal loop has a projected length of roughly 130 Mm, a width of about 1.5 ± 0.5 Mm, and a lifetime of about 90 min. It follows an open magnetic field line. The cross section expanded very little (i.e., 1.5-2.0) along the loop length during its whole lifetime. This loop has a nearly constant temperature at about 0.7 ± 0.2 MK, but its density exhibits the typical structure of a stratified atmosphere.
Conclusions: We use the theory of a thin twisted flux tube to construct a model for this nonexpanding loop and find that with sufficient twist, a coronal loop can indeed attain equilibrium. However, we cannot rule out other possibilities such as footpoint heating by small-scale reconnection or an elevated scale height by a steady flow along the loop.

Movie is available at https://www.aanda.org Title: Understanding Uniturbulence: Self-cascade of MHD Waves in the Presence of Inhomogeneities Authors: Magyar, N.; Van Doorsselaere, T.; Goossens, M. Bibcode: 2019ApJ...882...50M Altcode: 2019arXiv190710408M It is widely accepted in the MHD turbulence community that the nonlinear cascade of wave energy requires counterpropagating Alfvénic wave packets, along some mean magnetic field. This fact is an obvious outcome of the MHD equations under the assumptions of incompressibility and homogeneity. Despite attempts to relax these assumptions in the context of MHD turbulence, the central idea of turbulence generation persists. However, once the assumptions of incompressiblity and homogeneity break down, the generally accepted picture of turbulent cascade generation is not universal. In this paper, we show that perpendicular inhomogeneities (across the mean magnetic field) lead to propagating wave solutions that are necessarily described by co-propagating Elsässer fields, already in the incompressible case. One simple example of these wave solutions is the surface Alfvén wave on a planar discontinuity across the magnetic field. We show through numerical simulations how the nonlinear self-deformation of these unidirectionally propagating waves leads to a cascade of wave energy across the magnetic field. The existence of this type of unidirectional cascade might have an additional strong effect on the turbulent dissipation rate of dominantly outward-propagating Alfvénic waves in structured plasma, as in the solar corona and solar wind. Title: Resonant absorption of the slow sausage wave in the slow continuum (Corrigendum) Authors: Yu, D. J.; Van Doorsselaere, T.; Goossens, M. Bibcode: 2019A&A...626C...2Y Altcode: No abstract at ADS Title: Understanding uniturbulence: self-cascade of MHD waves in the presence of inhomogeneities Authors: Magyar, Norbert; Van Doorsselaere, Tom; Goossens, Marcel Bibcode: 2019AAS...23412506M Altcode: It is a generally accepted fact in the MHD turbulence community that the nonlinear cascade of wave energy requires the existence of counter-propagating Alfvénic wave-packets, along some mean magnetic field. This fact is an obvious outcome of the MHD equations when assuming an incompressible and homogenoeus plasma. There have been relatively few attempts to relax these assumptions in the context of MHD turbulence studies. However, it should be clear that once these assumptions brake down, the generally accepted picture of turbulent cascade generation is not universal. In the context of longitudinally stratified plasmas (i.e. gravitationally stratified coronal holes), it has been known since the 70's that inhomogeneities along the mean magnetic field lead to the linear coupling of sunward and anti-sunward propagating waves. This leads to co-propagating disturbances of Elsasser fields, which can interact coherently to initiate a nonlinear cascade. The alternative case of perpendicular inhomogeneity (across the mean magnetic field) was even less studied in the context of MHD turbulence. In this study we show that these type of inhomogeneities lead also to co-propagating Elsasser fields, already in the incompressible case. We show how the nonlinear self-deformation of these unidirectionally propagating waves leads to a cascade in k-space across the magnetic field. The existence of this type of unidirectional cascade might have an additional strong effect on the turbulent dissipation rate of dominantly outward propagating Alfvénic waves in structured plasma, as in solar coronal holes. Title: XMM-Newton and INTEGRALanalysis of the Supergiant Fast X-ray Transient IGR J17354-3255 Authors: Goossens, M. E.; Bird, A. J.; Hill, A. B.; Sguera, V.; Drave, S. P. Bibcode: 2019MNRAS.485..286G Altcode: 2018arXiv181111882G; 2018MNRAS.tmp.3090G We present the results of combined INTEGRALand XMM-Newton observations of the supergiant fast X-ray transient (SFXT) IGR J17354-3255. Three XMM-Newton observations of lengths 33.4, 32.5, and 21.9 ks were undertaken, the first an initial pointing to identify the correct source in the field of view and the latter two performed around periastron. Simultaneous INTEGRALobservations across {∼ }66 {{per cent}} of the orbital cycle were analysed but the source was neither detected by IBIS/ISGRI nor by JEM-X. The XMM-Newton light curves display a range of moderately bright X-ray activity but there are no particularly strong flares or outbursts in any of the three observations. We show that the spectral shape measured by XMM-Newton can be fitted by a consistent model throughout the observation, suggesting that the observed flux variations are driven by obscuration from a wind of varying density rather than changes in accretion mode. The simultaneous INTEGRALdata rule out simple extrapolation of the simple power-law model beyond the XMM-Newton energy range. Title: Mixed properties of MHD waves in non-uniform plasmas Authors: Goossens, Marcel L.; Arregui, Inigo; Van Doorsselaere, Tom Bibcode: 2019FrASS...6...20G Altcode: This paper investigates the mixed properties of MHD waves in a non-uniform plasma. It starts with a short revision of MHD waves in a uniform plasma of infinite extent. In that case the MHD waves do not have mixed properties. They can be separated in Alfvén waves and magneto-sonic waves. The Alfvén waves propagate parallel vorticity and are incompressible. In addition they have no parallel displacement component. The magneto-sonic waves are compressible and in general do have a parallel component of displacement but do not propagate parallel vorticity. This clear separation has been the reason why there has been a strong inclination in the literature to use this classification in the study of MHD waves in non-uniform plasmas. The main part of this paper is concerned with MHD waves in a non-uniform plasma. It is shown that the MHD waves in that situation in general propagate both vorticity and compression and hence have mixed properties. Finally, the close connection between resonant absorption and MHD waves with mixed properties is discussed. Title: The Nature of Elsässer Variables in Compressible MHD Authors: Magyar, N.; Van Doorsselaere, T.; Goossens, M. Bibcode: 2019ApJ...873...56M Altcode: 2019arXiv190201619M The Elsässer variables are often used in studies of plasma turbulence, in helping differentiate between MHD waves propagating parallel or antiparallel to the main magnetic field. While for pure Alfvén waves in a homogeneous plasma the method is strictly valid, we show that compressible, magnetoacoustic waves are in general described by both Elsässer variables. Furthermore, in a compressible and inhomogeneous plasma, the pure MHD waves (Alfvén, fast and slow) are no longer normal modes, but waves become linearly coupled or display mixed properties of Alfvén and magnetoacoustic nature. These waves are necessarily described by both Elsässer variables, and therefore the Elsässer formalism cannot be used to strictly separate parallel and antiparallel propagating waves. Nevertheless, even in an inhomogeneous plasma, for a highly Alfvénic wave the Elsässer variable corresponding to the propagation direction appears still dominating. We suggest that for Alfvénic waves, the relative amplitude of Elsässer variables depends on the local degree of inhomogeneity and other plasma and wave properties. This finding has implications for turbulence studies in inhomogeneous and compressible plasmas, such as the solar corona and solar wind. Title: No unique solution to the seismological problem of standing kink magnetohydrodynamic waves Authors: Arregui, I.; Goossens, M. Bibcode: 2019A&A...622A..44A Altcode: 2018arXiv181207266A The aim of this paper is to point out that the classic seismological problem using observations and theoretical expressions for the periods and damping times of transverse standing magnetohydrodynamic waves in coronal loops is better referred to as a reduced seismological problem. "Reduced" emphasises the fact that only a small number of characteristic quantities of the equilibrium profiles can be determined. Reduced also implies that there is no unique solution to the full seismological problem. Even the reduced seismological problem does not allow a unique solution. Bayesian inference results support our mathematical arguments and offer insight into the relationship between the algebraic and the probabilistic inversions. Title: First Evidence of the Frequency Filtering of Magnetoacoustic Waves in the Flaring Star EK Dra Authors: Srivastava, A. K.; Pandey, J. C.; Karmakar, Subhajeet; Chowdhury, Partha; Moon, Y. -J.; Goossens, Marcel; Jelínek, P.; Mathioudakis, M.; Doyle, J. G.; Dwivedi, B. N. Bibcode: 2018arXiv180408858S Altcode: Using the data obtained from XMM-Newton, we show the gradual evolution of two periodicities of ~4500 s and ~2200 s in the decay phase of the flare observed in a solar analog EK Dra. The longer period evolves firstly for first 14 ks, while the shorter period evolves for next 10 ks in the decay phase. We find that these two periodicities are associated with the magnetoacoustic waves triggered in the flaring region. The flaring loop system shows cooling and thus it is subjected to the change in the scale height and the acoustic cut-off period. This serves to filter the longer period magnetoacoustic waves and enables the propagation of the shorter period waves in the later phase of the flare. We provide the first clues of the dynamic behaviour of EK Dra's corona which affects the propagation of waves and causes their filtering. Title: Generalized Phase Mixing: Turbulence-like Behavior from Unidirectionally Propagating MHD Waves Authors: Van Doorsselaere, T.; Magyar, N.; Goossens, M. L. Bibcode: 2017AGUFMSH42B..04V Altcode: We introduce a new mechanism for the generation of turbulence in a perpendicularly structured plasma from unidirectional Alfvenic drivers. We present the results of three-dimensional (3D) ideal magnetohydrodynamics (MHD) simulations on the dynamics of a perpendicularly inhomogeneous plasma disturbed by propagating Alfvenic waves. Simpler versions of this scenario have been extensively studied as the phenomenon of phase mixing. We show that, by generalizing the textbook version of phase mixing, interesting phenomena are obtained, such as turbulence-like behavior and complex current-sheet structure, a novelty in longitudinally homogeneous plasma excited by unidirectionally propagating waves. This study is in the setting of a coronal hole. However, it constitutes an important finding for turbulence-related phenomena in astrophysics in general, relaxing the conditions that have to be fulfilled in order to generate turbulent behavior. Title: Driven Transverse Waves Lead to Turbulent Coronal Loops and Heating Authors: Van Doorsselaere, T.; Karampelas, K.; Magyar, N.; Antolin, P.; Goossens, M. L. Bibcode: 2017AGUFMSH41C..05V Altcode: In this talk, I will show our recent results on 3D simulations of coronal loops driven with transverse waves at the footpoints. We find that the transverse waves convert to turbulence via the Kelvin-Helmholtz instability (for standing waves) or uniturbulence (for propagating waves). The latter is turbulence generated from the interaction of the driven propagating waves with the counterpropagating waves which are generated in-situ because of the plasma structure. Both of these turbulence generation mechanisms lead to fully turbulent loops, which allow for efficient energy dissipation and heating. Title: Generalized phase mixing: Turbulence-like behaviour from unidirectionally propagating MHD waves Authors: Magyar, Norbert; Van Doorsselaere, Tom; Goossens, Marcel Bibcode: 2017NatSR...714820M Altcode: 2017arXiv170202346M We present the results of three-dimensional (3D) ideal magnetohydrodynamics (MHD) simulations on the dynamics of a perpendicularly inhomogeneous plasma disturbed by propagating Alfvénic waves. Simpler versions of this scenario have been extensively studied as the phenomenon of phase mixing. We show that, by generalizing the textbook version of phase mixing, interesting phenomena are obtained, such as turbulence-like behavior and complex current-sheet structure, a novelty in longitudinally homogeneous plasma excited by unidirectionally propagating waves. This study is in the setting of a coronal hole. However, it constitutes an important finding for turbulence-related phenomena in astrophysics in general, relaxing the conditions that have to be fulfilled in order to generate turbulent behavior. Title: Resonant Absorption of Surface Sausage and Surface Kink Modes under Photospheric Conditions Authors: Yu, Dae Jung; Van Doorsselaere, Tom; Goossens, Marcel Bibcode: 2017ApJ...850...44Y Altcode: 2017arXiv171003350Y We study the effect of resonant absorption of surface sausage and surface kink modes under photospheric conditions where the slow surface sausage modes undergo resonant damping in the slow continuum and the surface kink modes in the slow and Alfvén continua at the transitional layers. We use recently derived analytical formulas to obtain the damping rate (time). By considering linear density and linear pressure profiles for the transitional layers, we show that resonant absorption in the slow continuum could be an efficient mechanism for the wave damping of the slow surface sausage and slow surface kink modes while the damping rate of the slow surface kink mode in the Alfvén continuum is weak. It is also found that the resonant damping of the fast surface kink mode is much stronger than that of the slow surface kink mode, showing a similar efficiency as under coronal conditions. It is worth noting that the slow body sausage and kink modes can also resonantly damp in the slow continuum for those linear profiles. Title: Resonant absorption of the slow sausage wave in the slow continuum Authors: Yu, D. J.; Van Doorsselaere, T.; Goossens, M. Bibcode: 2017A&A...602A.108Y Altcode:
Aims: General analytical formulas for the damping rate by resonant absorption of slow sausage modes in the slow (cusp) continuum are derived and the resonant damping of the slow surface mode under photospheric conditions is investigated.
Methods: The connection formula across the resonant layer is used to derive the damping rate for the slow sausage mode in the slow continuum by assuming a thin boundary.
Results: It is shown that the effect of the resonant damping on the slow surface sausage mode in the slow continuum, which has been underestimated in previous interpretations, could be efficient under magnetic pore conditions. A simplified analytical formula for the damping rate of slow surface mode in the long wavelength limit is derived. This formula can be useful for a rough estimation of the damping rate due to resonant absorption for observational wave damping. Title: Resonant Absorption of Axisymmetric Modes in Twisted Magnetic Flux Tubes Authors: Giagkiozis, I.; Goossens, M.; Verth, G.; Fedun, V.; Van Doorsselaere, T. Bibcode: 2016ApJ...823...71G Altcode: 2017arXiv170609665G It has been shown recently that magnetic twist and axisymmetric MHD modes are ubiquitous in the solar atmosphere, and therefore the study of resonant absorption for these modes has become a pressing issue because it can have important consequences for heating magnetic flux tubes in the solar atmosphere and the observed damping. In this investigation, for the first time, we calculate the damping rate for axisymmetric MHD waves in weakly twisted magnetic flux tubes. Our aim is to investigate the impact of resonant damping of these modes for solar atmospheric conditions. This analytical study is based on an idealized configuration of a straight magnetic flux tube with a weak magnetic twist inside as well as outside the tube. By implementing the conservation laws derived by Sakurai et al. and the analytic solutions for weakly twisted flux tubes obtained recently by Giagkiozis et al. we derive a dispersion relation for resonantly damped axisymmetric modes in the spectrum of the Alfvén continuum. We also obtain an insightful analytical expression for the damping rate in the long wavelength limit. Furthermore, it is shown that both the longitudinal magnetic field and the density, which are allowed to vary continuously in the inhomogeneous layer, have a significant impact on the damping time. Given the conditions in the solar atmosphere, resonantly damped axisymmetric modes are highly likely to be ubiquitous and play an important role in energy dissipation. We also suggest that, given the character of these waves, it is likely that they have already been observed in the guise of Alfvén waves. Title: Spectral variation in the supergiant fast X-ray transient SAX J1818.6-1703 observed by XMM-Newton and INTEGRAL Authors: Boon, C. M.; Bird, A. J.; Hill, A. B.; Sidoli, L.; Sguera, V.; Goossens, M. E.; Fiocchi, M.; McBride, V. A.; Drave, S. P. Bibcode: 2016MNRAS.456.4111B Altcode: 2016arXiv160101591B We present the results of a 30 ks XMM-Newton observation of the supergiant fast X-ray transient (SFXT) SAX J1818.6-1703 - the first in-depth soft X-ray study of this source around periastron. INTEGRAL observations shortly before and after the XMM-Newton observation show the source to be in an atypically active state. Over the course of the XMM-Newton observation, the source shows a dynamic range of ∼100 with a luminosity greater than 1 × 1035 erg s-1 for the majority of the observation. After an ∼6 ks period of low-luminosity (∼1034 erg s-1) emission, SAX J1818.6-1703 enters a phase of fast flaring activity, with flares ∼250 s long, separated by ∼2 ks. The source then enters a larger flare event of higher luminosity and ∼8 ks duration. Spectral analysis revealed evidence for a significant change in spectral shape during the observation with a photon index varying from Γ ∼ 2.5 during the initial low-luminosity emission phase, to Γ ∼ 1.9 through the fast flaring activity, and a significant change to Γ ∼ 0.3 during the main flare. The intrinsic absorbing column density throughout the observation (nH ∼ 5 × 1023 cm-2) is among the highest measured from an SFXT, and together with the XMM-Newton and INTEGRAL luminosities, consistent with the neutron star encountering an unusually dense wind environment around periastron. Although other mechanisms cannot be ruled out, we note that the onset of the brighter flares occurs at 3 × 1035erg s-1, a luminosity consistent with the threshold for the switch from a radiative-dominated to Compton cooling regime in the quasi-spherical settling accretion model. Title: Dissipationless Damping of Compressive MHD Modes in Twisted Flux Tubes Authors: Giagkiozis, I.; Fedun, V.; Verth, G.; Goossens, M. L.; Van Doorsselaere, T. Bibcode: 2015AGUFMSH53B2488G Altcode: Axisymmetric modes in straight magentic flux tubes exhibit a cutoff in the long wavelength limit and no damping is predicted. However, as soon as weak magnetic twist is introduced inside as well as outside the magnetic flux tube the cutoff recedes. Furthermore, when density variations are also incomporated within the modelresonant absorption appears. In this work we explore analytically the expected damping times for waves within the Alfven continuum for different solar atmospheric conditions. Based on the results in this work we offer insight on recent observations of sausage wave damping in the chromosphere. Title: Apparent Cross-field Superslow Propagation of Magnetohydrodynamic Waves in Solar Plasmas Authors: Kaneko, T.; Goossens, M.; Soler, R.; Terradas, J.; Van Doorsselaere, T.; Yokoyama, T.; Wright, A. N. Bibcode: 2015ApJ...812..121K Altcode: 2015arXiv150903042K In this paper we show that the phase-mixing of continuum Alfvén waves and/or continuum slow waves in the magnetic structures of the solar atmosphere as, e.g., coronal arcades, can create the illusion of wave propagation across the magnetic field. This phenomenon could be erroneously interpreted as fast magnetosonic waves. The cross-field propagation due to the phase-mixing of continuum waves is apparent because there is no real propagation of energy across the magnetic surfaces. We investigate the continuous Alfvén and slow spectra in two-dimensional (2D) Cartesian equilibrium models with a purely poloidal magnetic field. We show that apparent superslow propagation across the magnetic surfaces in solar coronal structures is a consequence of the existence of continuum Alfvén waves and continuum slow waves that naturally live on those structures and phase-mix as time evolves. The apparent cross-field phase velocity is related to the spatial variation of the local Alfvén/slow frequency across the magnetic surfaces and is slower than the Alfvén/sound velocities for typical coronal conditions. Understanding the nature of the apparent cross-field propagation is important for the correct analysis of numerical simulations and the correct interpretation of observations. Title: MHD Seismology of a loop-like filament tube by observed kink waves Authors: Pant, Vaibhav; Srivastava, Abhishek K.; Banerjee, Dipankar; Goossens, Marcel; Chen, Peng-Fei; Joshi, Navin Chandra; Zhou, Yu-Hao Bibcode: 2015RAA....15.1713P Altcode: 2015arXiv150302281P We report and analyze observational evidence of global kink oscillations in a solar filament as observed in Hα by instruments administered by National Solar Observatory (NSO)/Global Oscillation Network Group (GONG). An M1.1-class flare in active region (AR) 11692 occurred on 2013 March 15 and induced a global kink mode in the filament lying towards the southwest of AR 11692. We find periods of about 61-67 minutes and damping times of 92-117 minutes at positions of three vertical slices chosen in and around the filament apex. We find that the waves are damped. From the observed period of the global kink mode and damping timescale using the theory of resonant absorption, we perform prominence seismology. We estimate a lower cut-off value for the inhomogeneity length scale to be around 0.34-0.44 times the radius of the filament cross-section. Title: Energy and energy flux in axisymmetric slow and fast waves Authors: Moreels, M. G.; Van Doorsselaere, T.; Grant, S. D. T.; Jess, D. B.; Goossens, M. Bibcode: 2015A&A...578A..60M Altcode:
Aims: We aim to calculate the kinetic, magnetic, thermal, and total energy densities and the flux of energy in axisymmetric sausage modes. The resulting equations should contain as few parameters as possible to facilitate applicability for different observations.
Methods: The background equilibrium is a one-dimensional cylindrical flux tube model with a piecewise constant radial density profile. This enables us to use linearised magnetohydrodynamic equations to calculate the energy densities and the flux of energy for axisymmetric sausage modes.
Results: The equations used to calculate the energy densities and the flux of energy in axisymmetric sausage modes depend on the radius of the flux tube, the equilibrium sound and Alfvén speeds, the density of the plasma, the period and phase speed of the wave, and the radial or longitudinal components of the Lagrangian displacement at the flux tube boundary. Approximate relations for limiting cases of propagating slow and fast sausage modes are also obtained. We also obtained the dispersive first-order correction term to the phase speed for both the fundamental slow body mode under coronal conditions and the slow surface mode under photospheric conditions.

Appendix A is available in electronic form at http://www.aanda.org Title: Prominence seismology using the period ratio of transverse thread oscillations Authors: Soler, R.; Goossens, M.; Ballester, J. L. Bibcode: 2015A&A...575A.123S Altcode: 2015arXiv150105238S The ratio of the period of the fundamental mode to that of the first overtone of kink oscillations (hereafter period ratio) is a seismology tool that can be used to infer information about the spatial variation of density along solar magnetic flux tubes. The period ratio is 2 in longitudinally homogeneous thin tubes, but it differs from 2 because of longitudinal inhomogeneity. In this paper we investigate the period ratio in longitudinally inhomogeneous prominence threads and explore its implications for prominence seismology. We numerically solve the two-dimensional eigenvalue problem of kink oscillations in a model of a prominence thread. We take into account three nonuniform density profiles along the thread. In agreement with previous works that used simple piecewise constant density profiles, we find that the period ratio is larger than 2 in prominence threads. When the ratio of the central density to that at the footpoints is fixed, the period ratio depends strongly on the form of the density profile along the thread. The more concentrated the dense prominence plasma near the center of the tube, the larger the period ratio. However, the period ratio is found to be independent of the specific density profile when the spatially averaged density in the thread is the same for all the profiles. An empirical fit of the dependence of the period ratio on the average density is given and its use for prominence seismology is discussed. Title: The Transverse and Rotational Motions of Magnetohydrodynamic Kink Waves in the Solar Atmosphere Authors: Goossens, M.; Soler, R.; Terradas, J.; Van Doorsselaere, T.; Verth, G. Bibcode: 2014ApJ...788....9G Altcode: Magnetohydrodynamic (MHD) kink waves have now been observed to be ubiquitous throughout the solar atmosphere. With modern instruments, they have now been detected in the chromosphere, interface region, and corona. The key purpose of this paper is to show that kink waves do not only involve purely transverse motions of solar magnetic flux tubes, but the velocity field is a spatially and temporally varying sum of both transverse and rotational motion. Taking this fact into account is particularly important for the accurate interpretation of varying Doppler velocity profiles across oscillating structures such as spicules. It has now been shown that, as well as bulk transverse motions, spicules have omnipresent rotational motions. Here we emphasize that caution should be used before interpreting the particular MHD wave mode/s responsible for these rotational motions. The rotational motions are not necessarily signatures of the classic axisymmetric torsional Alfvén wave alone, because kink motion itself can also contribute substantially to varying Doppler velocity profiles observed across these structures. In this paper, the displacement field of the kink wave is demonstrated to be a sum of its transverse and rotational components, both for a flux tube with a discontinuous density profile at its boundary, and one with a more realistic density continuum between the internal and external plasma. Furthermore, the Doppler velocity profile of the kink wave is forward modeled to demonstrate that, depending on the line of sight, it can either be quite distinct or very similar to that expected from a torsional Alfvén wave. Title: Nonlinear Kink Oscillations of Coronal Magnetic Loops Authors: Ruderman, M. S.; Goossens, M. Bibcode: 2014SoPh..289.1999R Altcode: We studied nonlinear kink oscillations of a thin magnetic tube using the cold-plasma approximation. We assumed that the plasma density varies along the tube but does not vary in the radial direction. Using the regular perturbation method, we show that the nonlinearity does not affect the oscillation amplitude. We also calculated the nonlinear correction to the oscillation frequency, which is proportional to the oscillation amplitude squared. As an example, we considered nonlinear oscillations of a coronal magnetic loop of half-circle shape in an isothermal atmosphere with equal plasma temperatures inside and outside the loop. Title: New insights on accretion in supergiant fast X-ray transients from XMM-Newton and INTEGRAL observations of IGR J17544-2619 Authors: Drave, S. P.; Bird, A. J.; Sidoli, L.; Sguera, V.; Bazzano, A.; Hill, A. B.; Goossens, M. E. Bibcode: 2014MNRAS.439.2175D Altcode: 2014MNRAS.tmp..299D; 2014arXiv1401.3570D XMM-Newton observations of the supergiant fast X-ray transient IGR J17544-2619 are reported and placed in the context of an analysis of archival INTEGRAL/IBIS data that provide a refined estimate of the orbital period at 4.9272 ± 0.0004 d. A complete outburst history across the INTEGRAL mission is reported. Although the new XMM-Newton observations (each lasting ∼15 ks) targeted the peak flux in the phase-folded hard X-ray light curve of IGR J17544-2619, no bright outbursts were observed, the source spending the majority of the exposure at intermediate luminosities of the order of several 1033 erg s-1 (0.5-10 keV) and displaying only low level flickering activity. For the final portion of the exposure, the luminosity of IGR J17544-2619 dropped to ∼4 × 1032 erg s-1 (0.5-10 keV), comparable with the lowest luminosities ever detected from this source, despite the observations being taken near to periastron. We consider the possible orbital geometry of IGR J17544-2619 and the implications for the nature of the mass transfer and accretion mechanisms for both IGR J17544-2619 and the supergiant fast X-ray transients (SFXTs) population. We conclude that accretion under the `quasi-spherical accretion' model provides a good description of the behaviour of IGR J17544-2619 and suggests an additional mechanism for generating outbursts based upon the mass accumulation rate in the hot shell (atmosphere) that forms around the neutron star under the quasi-spherical formulation. Hence, we hope to aid in explaining the varied outburst behaviours observed across the SFXT population with a consistent underlying physical model. Title: Frequency and Damping Rate of Fast Sausage Waves Authors: Vasheghani Farahani, S.; Hornsey, C.; Van Doorsselaere, T.; Goossens, M. Bibcode: 2014ApJ...781...92V Altcode: We investigate the frequency and damping rate of fast axisymmetric waves that are subject to wave leakage for a one-dimensional magnetic cylindrical structure in the solar corona. We consider the ideal magnetohydrodynamic (MHD) dispersion relation for axisymmetric MHD waves superimposed on a straight magnetic cylinder in the zero β limit, similar to a jet or loop in the solar corona. An analytic study accompanied by numerical calculations has been carried out to model the frequency, damping rate, and phase speed of the sausage wave around the cut-off frequency and in the long wavelength limit. Analytic expressions have been obtained based on equations around the points of interest. They are linear approximations of the dependence of the sausage frequency on the wave number around the cut-off wavelength for both leaky and non-leaky regimes and in the long wavelength limit. Moreover, an expression for the damping rate of the leaky sausage wave has been obtained both around the cut-off frequency and in the long wavelength limit. These analytic results are compared with numerical computations. The expressions show that the complex frequencies are mainly dominated by the density ratio. In addition, it is shown that the damping eventually becomes independent of the wave number in the long wavelength limit. We conclude that the sausage mode damping directly depends on the density ratios of the internal and external media where the damping declines in higher density contrasts. Even in the long wavelength limit, the sausage mode is weakly damped for high-density contrasts. As such, sausage modes could be observed for a significant number of periods in high-density contrast loops or jets. Title: The Behavior of Transverse Waves in Nonuniform Solar Flux Tubes. II. Implications for Coronal Loop Seismology Authors: Soler, Roberto; Goossens, Marcel; Terradas, Jaume; Oliver, Ramón Bibcode: 2014ApJ...781..111S Altcode: 2013arXiv1312.5079S The seismology of coronal loops using observations of damped transverse oscillations in combination with results from theoretical models is a tool to indirectly infer physical parameters in the solar atmospheric plasma. Existing seismology schemes based on approximations of the period and damping time of kink oscillations are often used beyond their theoretical range of applicability. These approximations assume that the variation of density across the loop is confined to a nonuniform layer much thinner than the radius of the loop, but the results of the inversion problem often do not satisfy this preliminary hypothesis. Here, we determine the accuracy of the analytic approximations of the period and damping time, and the impact on seismology estimates when largely nonuniform loops are considered. We find that the accuracy of the approximations when used beyond their range of applicability is strongly affected by the form of the density profile across the loop, that is observationally unknown and so must be arbitrarily imposed as part of the theoretical model. The error associated with the analytic approximations can be larger than 50% even for relatively thin nonuniform layers. This error directly affects the accuracy of approximate seismology estimates compared to actual numerical inversions. In addition, assuming different density profiles can produce noncoincident intervals of the seismic variables in inversions of the same event. The ignorance about the true shape of density variation across the loop is an important source of error that may dispute the reliability of parameters seismically inferred assuming an ad hoc density profile. Title: Wave Energy Deposition in the Solar Corona Authors: Van Doorsselaere, Tom; Goossens, Marcel; Verth, Gary; Soler, Roberto; Gijsen, Stief; Andries, Jesse Bibcode: 2014cosp...40E3464V Altcode: Recently, a significant amount of transverse wave energy has been estimated propagating along solar atmospheric magnetic fields. However, these estimates have been made with the classic bulk Alfven wave model which assumes a homogeneous plasma. In this talk, the kinetic, magnetic, and total energy densities and the flux of energy are first computed for transverse MHD waves in one-dimensional cylindrical flux tube models with a piecewise constant density profile. There are fundamental deviations from the properties for classic bulk Alfven waves. (1) There is no local equipartition between kinetic and magnetic energy. (2) The flux of energy and the velocity of energy transfer have, in addition to a component parallel to the magnetic field, components in the planes normal to the magnetic field. (3) The energy densities and the flux of energy vary spatially, contrary to the case of classic bulk Alfven waves. This last property is then used to connect the energy flux in such a simple model to the energy flux in multiple flux tube systems. We use the plasma filling factor f to derive an ad-hoc formula for estimating the energy that is propagated in bundles of loops. We find that the energy flux in kink waves is lower than the energy computed from a bulk Alfven wave interpretation, by a factor that is (approximately) between f and 2f. We consider some geometric models to quantify this correction factor. Title: Sausage wave oscillations and dampings in the corona Authors: Vasheghani Farahani, Soheil; Van Doorsselaere, Tom; Goossens, Marcel; Hornsey, Christopher Bibcode: 2014cosp...40E3475V Altcode: The frequency and damping rate of fast axisymmetric (Sausage)waves that experience leakage from a coronal structure e.g. jet or loop is studied. In this line we consider a 1-D magnetic cylindrical structure which resembles a jet or loop in the solar corona. We consider the ideal magnetohydrodynamic (MHD) dispersion relation for axisymmetric MHD waves superimposed on a straight magnetic cylinder in the zero β limit. An analytic study accompanied by numerical calculations has been carried out to model the frequency, damping rate, and phase speed of the sausage wave around the cut-off frequency and in the long wavelength limit. Analytic expressions have been obtained for the damping and frequency of the sausage wave around the cut-off and in the long wave-length limit. These analytic results are compared with numerical computations. The expressions show that the complex frequencies are mainly dominated by the density ratio. In addition, it is shown that the damping eventually becomes independent of the wave number in the long wavelength limit. Hence, interestingly when a high density jet or loop ejects from the solar atmosphere, long wave-length sausage waves guided by the Jet or loop would be observable for a significant number of periods. Title: Doppler displacements in kink MHD waves in solar flux tubes Authors: Goossens, Marcel; Van Doorsselaere, Tom; Terradas, Jaume; Verth, Gary; Soler, Roberto Bibcode: 2014cosp...40E1045G Altcode: Doppler displacements in kink MHD waves in solar flux tubes Presenting author: M. Goossens Co-authors: R. Soler, J. Terradas, T. Van Doorsselaere, G. Verth The standard interpretation of the transverse MHD waves observed in the solar atmosphere is that they are non-axisymmetric kink m=1) waves on magnetic flux tubes. This interpretation is based on the fact that axisymmetric and non-axisymmetric fluting waves do not displace the axis of the loop and the loop as a whole while kink waves indeed do so. A uniform transverse motion produces a Doppler displacement that is constant across the magnetic flux tube. A recent development is the observation of Doppler displacements that vary across the loop. The aim of the present contribution is to show that spatial variations of the Doppler displacements across the loop can be caused by kink waves. The motion associated with a kink wave is purely transverse only when the flux tube is uniform and sufficiently thin. Only in that case do the radial and azimuthal components of displacement have the same amplitude and is the azimuthal component a quarter of a period ahead of the radial component. This results in a unidirectional or transverse displacement. When the flux tube is non-uniform and has a non-zero radius the conditions for the generation of a purely transverse motion are not any longer met. In that case the motion in a kink wave is the sum of a transverse motion and a non-axisymmetric rotational motion that depends on the azimuthal angle. It can produce complicated variations of the Doppler displacement across the loop. I shall discuss the various cases of possible Doppler displacenents that can occur depending on the relative sizes of the amplitudes of the radial and azimuthal components of the displacement in the kink wave and on the orientation of the line of sight. Title: X6.9-class Flare-induced Vertical Kink Oscillations in a Large-scale Plasma Curtain as Observed by the Solar Dynamics Observatory/Atmospheric Imaging Assembly Authors: Srivastava, A. K.; Goossens, M. Bibcode: 2013ApJ...777...17S Altcode: We present rare observational evidence of vertical kink oscillations in a laminar and diffused large-scale plasma curtain as observed by the Atmospheric Imaging Assembly on board the Solar Dynamics Observatory. The X6.9-class flare in active region 11263 on 2011 August 9 induces a global large-scale disturbance that propagates in a narrow lane above the plasma curtain and creates a low density region that appears as a dimming in the observational image data. This large-scale propagating disturbance acts as a non-periodic driver that interacts asymmetrically and obliquely with the top of the plasma curtain and triggers the observed oscillations. In the deeper layers of the curtain, we find evidence of vertical kink oscillations with two periods (795 s and 530 s). On the magnetic surface of the curtain where the density is inhomogeneous due to coronal dimming, non-decaying vertical oscillations are also observed (period ≈ 763-896 s). We infer that the global large-scale disturbance triggers vertical kink oscillations in the deeper layers as well as on the surface of the large-scale plasma curtain. The properties of the excited waves strongly depend on the local plasma and magnetic field conditions. Title: The Behavior of Transverse Waves in Nonuniform Solar Flux Tubes. I. Comparison of Ideal and Resistive Results Authors: Soler, Roberto; Goossens, Marcel; Terradas, Jaume; Oliver, Ramón Bibcode: 2013ApJ...777..158S Altcode: 2013arXiv1309.3423S Magnetohydrodynamic (MHD) waves are ubiquitously observed in the solar atmosphere. Kink waves are a type of transverse MHD waves in magnetic flux tubes that are damped due to resonant absorption. The theoretical study of kink MHD waves in solar flux tubes is usually based on the simplification that the transverse variation of density is confined to a nonuniform layer much thinner than the radius of the tube, i.e., the so-called thin boundary approximation. Here, we develop a general analytic method to compute the dispersion relation and the eigenfunctions of ideal MHD waves in pressureless flux tubes with transversely nonuniform layers of arbitrary thickness. Results for kink waves are produced and compared with fully numerical resistive MHD eigenvalue computations in the limit of small resistivity. We find that the frequency and resonant damping rate are the same in both ideal and resistive cases. The actual results for thick nonuniform layers deviate from the behavior predicted in the thin boundary approximation and strongly depend on the shape of the nonuniform layer. The eigenfunctions in ideal MHD are very different from those in resistive MHD. The ideal eigenfunctions display a global character regardless of the thickness of the nonuniform layer, while the resistive eigenfunctions are localized around the resonance and are indistinguishable from those of ordinary resistive Alfvén modes. Consequently, the spatial distribution of wave energy in the ideal and resistive cases is dramatically different. This poses a fundamental theoretical problem with clear observational consequences. Title: Discovering a 5.72-d period in the supergiant fast X-ray transient AX J1845.0-0433 Authors: Goossens, M. E.; Bird, A. J.; Drave, S. P.; Bazzano, A.; Hill, A. B.; McBride, V. A.; Sguera, V.; Sidoli, L. Bibcode: 2013MNRAS.434.2182G Altcode: 2013MNRAS.tmp.1807G; 2013arXiv1307.0709G Temporal analysis of INTEGRAL/IBIS data has revealed a 5.7195 ± 0.0007 d periodicity in the supergiant fast X-ray transient source AX J1845.0-0433, which we interpret as the orbital period of the system. The new-found knowledge of the orbital period is utilized to investigate the geometry of the system by means of estimating an upper limit for the size of the supergiant (<27 R⊙) as well as the eccentricity of the orbit (ɛ < 0.37). Title: X6.9-class Flare Induced Vertical Kink Oscillations in a Large-Scale Plasma Curtain as Observed by SDO/AIA Authors: Srivastava, A. K.; Goossens, M. Bibcode: 2013arXiv1308.5758S Altcode: We present rare observational evidence of vertical kink oscillations in a laminar and diffused large-scale plasma curtain as observed by the Atmospheric Imaging Assembly (AIA) on board the Solar Dynamics Observatory (SDO). The X6.9 class flare in the Active Region 11263 on 09 August 2011, induces a global large-scale disturbance that propagates in a narrow lane above the plasma curtain and creates a low density region that appears as a dimming in the observational image data. This large-scale propagating disturbance acts as a non-periodic driver that interacts asymmetrically and obliquely with the top of the plasma curtain, and triggers the observed oscillations. In the deeper layers of the curtain, we find evidence of vertical kink oscillations with two periods (795 s and 530 s). On the magnetic surface of the curtain where the density is inhomogeneous due to the coronal dimming, non-decaying vertical oscillations are also observed (period $\approx$ 763-896 s). We infer that the global large-scale disturbance triggers vertical kink oscillations in the deeper layers as well as on the surface of the large-scale plasma curtain. The properties of the excited waves strongly depend on the local plasma and magnetic field conditions. Title: INTEGRAL and XMM-Newton observations of IGR J16418-4532: evidence of accretion regime transitions in a supergiant fast X-ray transient Authors: Drave, S. P.; Bird, A. J.; Sidoli, L.; Sguera, V.; McBride, V. A.; Hill, A. B.; Bazzano, A.; Goossens, M. E. Bibcode: 2013MNRAS.433..528D Altcode: 2013MNRAS.tmp.1439D; 2013arXiv1305.0430D We report on combined INTEGRAL and XMM-Newton observations of the supergiant fast X-ray transient (SFXT) IGR J16418-4532. The observations targeted the X-ray eclipse region of IGR J16418-4532's orbit with continuous INTEGRAL observations across ∼25 per cent of orbital phase and two quasi-simultaneous XMM-Newton observations of length 20 and 14 ks, occurring during and just after the eclipse, respectively. An enhanced INTEGRAL emission history is provided with 19 previously unreported outbursts identified in the archival 18-60 keV data set. The XMM-Newton eclipse observation showed prominent Fe emission and a flux of 2.8 × 10-13 erg cm-2 s-1 (0.5-10 keV). Through the comparison of the detected eclipse and post-eclipse flux, the supergiant mass-loss rate through the stellar wind was determined as Ṁw = 2.3-3.8 × 10-7 M⊙ yr-1. The post-eclipse XMM-Newton observation showed a dynamic flux evolution with signatures of the X-ray pulsation, a period of flaring activity, structured nH variations and the first ever detection of an X-ray intensity dip, or `off-state', in a pulsating SFXT. Consideration is given to the origin of the X-ray dip, and we conclude that the most applicable of the current theories of X-ray dip generation is that of a transition between Compton-cooling-dominated and radiative-cooling-dominated subsonic accretion regimes within the `quasi-spherical' model of wind accretion. Under this interpretation, which requires additional confirmation, the neutron star in IGR J16418-4532 possesses a magnetic field of ∼1014 G, providing tentative observational evidence of a highly magnetized neutron star in a SFXT for the first time. The implications of these results on the nature of IGR J16418-4532 itself and the wider SFXT class are discussed. Title: Cross-sectional area and intensity variations of sausage modes Authors: Moreels, M. G.; Goossens, M.; Van Doorsselaere, T. Bibcode: 2013A&A...555A..75M Altcode: Context. The observations obtained using the Rapid Oscillations in the Solar Atmosphere instrument (ROSA) show variations in both cross-sectional area and intensity for magnetic pores in the photosphere.
Aims: We study the phase behaviour between cross-sectional area and intensity variations for sausage modes in a photospheric context. We aim to determine the wave mode by looking at the phase difference between the cross-sectional area and intensity variations.
Methods: We used a straight cylinder as a model for the flux tube. The plasma is uniform both inside and outside the flux tube with a possible jump in the equilibrium values at the boundary, the magnetic field is directed along the flux tube. We derived analytic expressions for the cross-sectional area variation and the total intensity variation. Using these analytic expressions, we calculated the phase differences between the cross-sectional area and the intensity variations. These phase differences were then used to identify the wave mode.
Results: We found that for slow sausage modes the cross-sectional area and intensity variations are always in phase, while for fast sausage modes the variations are in antiphase.

Appendix A is available in electronic form at http://www.aanda.org Title: Erratum: "Energy Content and Propagation in Transverse Solar Atmospheric Waves" (2013, ApJ, 768, 191) Authors: Goossens, M.; Van Doorsselaere, T.; Soler, R.; Verth, G. Bibcode: 2013ApJ...771...74G Altcode: No abstract at ADS Title: Confirmation of the superorbital modulation of the high mass X-ray binaries 4U 1909+07, IGR J16479-4514 and IGR J16418-4532 with INTEGRAL/IBIS Authors: Drave, S. P.; Bird, A. J.; Goossens, M. E.; Sidoli, L.; Sguera, V.; Fiocchi, M.; Bazzano, A. Bibcode: 2013ATel.5131....1D Altcode: Following the recent announcement of the detection of superorbital periods in the wind-fed supergiant X-ray binaries 4U 1909+07, IGR J16418-4532 and IGR J16479-4514 by Corbet and Krimm 2013 (Atels #5119 and #5126) we investigated archival INTEGRAL data to search for additional signatures of these periods. Title: Kelvin-Helmholtz and Rayleigh-Taylor instabilities in partially ionised prominences Authors: Díaz, A. J.; Soler, R.; Ballester, J. L.; Goossens, M. Bibcode: 2013hsa7.conf..776D Altcode: We study the modification of the classical criterion for the linear onset and growing rate of the Kelvin-Helmholtz Instability (KHI) and the Rayleigh-Taylor instability (RTI) in a partially ionised plasma in the two-fluid description. The plasma is composed of a neutral fluid and an electron-ion fluid, coupled by means of particle collisions. The governing linear equations and appropriate boundary conditions, including gravitational terms, are derived and applied to the case a single interface between two partially ionised plasmas. For high collision frequencies and low density contrasts the KHI is present for super-Alfvénic velocity shear only. For high density contrasts the threshold velocity shear can be reduced to sub-Alfvénic values. For the particular case of turbulent plumes in prominences, we conclude that sub-Alfvénic flow velocities can trigger the KHI thanks to the ion-neutral coupling, but with long time scales. Ion-neutral collisions have a strong impact on the RTI growth rate, which can be decreased by an order of magnitude compared to the value in the collisionless case. The time scale for the development of the instability is much longer than in the classical incompressible fully ionised case. This result may explain the existence of prominence fine structures with life times of the order of 30 minutes. Title: Energy Content and Propagation in Transverse Solar Atmospheric Waves Authors: Goossens, M.; Van Doorsselaere, T.; Soler, R.; Verth, G. Bibcode: 2013ApJ...768..191G Altcode: Recently, a significant amount of transverse wave energy has been estimated propagating along solar atmospheric magnetic fields. However, these estimates have been made with the classic bulk Alfvén wave model which assumes a homogeneous plasma. In this paper, the kinetic, magnetic, and total energy densities and the flux of energy are computed for transverse MHD waves in one-dimensional cylindrical flux tube models with a piecewise constant or continuous radial density profile. There are fundamental deviations from the properties for classic bulk Alfvén waves. (1) There is no local equipartition between kinetic and magnetic energy. (2) The flux of energy and the velocity of energy transfer have, in addition to a component parallel to the magnetic field, components in the planes normal to the magnetic field. (3) The energy densities and the flux of energy vary spatially, contrary to the case of classic bulk Alfvén waves. This last property has the important consequence that the energy flux computed with the well known expression for bulk Alfvén waves could overestimate the real flux by a factor in the range 10-50, depending on the flux tube equilibrium properties. Title: Effect of partial ionization on wave propagation in solar magnetic flux tubes Authors: Soler, R.; Díaz, A. J.; Ballester, J. L.; Goossens, M. Bibcode: 2013A&A...551A..86S Altcode: 2013arXiv1301.5214S Observations show that waves are ubiquitous in the solar atmosphere and may play an important role for plasma heating. The study of waves in the solar corona is usually based on linear ideal magnetohydrodynamics (MHD) for a fully ionized plasma. However, the plasma in the photosphere and the chromosphere is only partially ionized. Here we theoretically investigate the impact of partial ionization on MHD wave propagation in cylindrical flux tubes in a two-fluid model. We derive the general dispersion relation that takes into account the effects of neutral-ion collisions and the neutral gas pressure. We assumed the neutral-ion collision frequency to be an arbitrary parameter. Specific results for transverse kink modes and slow magnetoacoustic modes are shown. We find that the wave frequencies only depend on the properties of the ionized fluid when the neutral-ion collision frequency is much lower that the wave frequency. For high collision frequencies that realistically represent the solar atmosphere, ions and neutrals behave as a single fluid with an effective density corresponding to the sum of densities of fluids plus an effective sound velocity computed as the average of the sound velocities of ions and neutrals. The MHD wave frequencies are modified accordingly. The neutral gas pressure can be neglected when studying transverse kink waves but it has to be included for a consistent description of slow magnetoacoustic waves. The MHD waves are damped by neutral-ion collisions. The damping is most efficient when the wave frequency and the collision frequency are on the same order of magnitude. For high collision frequencies slow magnetoacoustic waves are more efficiently damped than transverse kink waves. In addition, we find the presence of cut-offs for certain combinations of parameters that cause the waves to become non-propagating. Title: Analytic Approximate Seismology of Propagating Magnetohydrodynamic Waves in the Solar Corona Authors: Goossens, M.; Soler, R.; Arregui, I.; Terradas, J. Bibcode: 2012ApJ...760...98G Altcode: 2012arXiv1210.2689G Observations show that propagating magnetohydrodynamic (MHD) waves are ubiquitous in the solar atmosphere. The technique of MHD seismology uses the wave observations combined with MHD wave theory to indirectly infer physical parameters of the solar atmospheric plasma and magnetic field. Here, we present an analytical seismological inversion scheme for propagating MHD waves. This scheme uses the observational information on wavelengths and damping lengths in a consistent manner, along with observed values of periods or phase velocities, and is based on approximate asymptotic expressions for the theoretical values of wavelengths and damping lengths. The applicability of the inversion scheme is discussed and an example is given. Title: Transverse kink oscillations in the presence of twist Authors: Terradas, J.; Goossens, M. Bibcode: 2012A&A...548A.112T Altcode: 2012arXiv1210.8093T Context. Magnetic twist is thought to play an important role in coronal loops. The effects of magnetic twist on stable magnetohydrodynamic (MHD) waves is poorly understood because they are seldom studied for relevant cases.
Aims: The goal of this work is to study the fingerprints of magnetic twist on stable transverse kink oscillations.
Methods: We numerically calculated the eigenmodes of propagating and standing MHD waves for a model of a loop with magnetic twist. The azimuthal component of the magnetic field was assumed to be small in comparison to the longitudinal component. We did not consider resonantly damped modes or kink instabilities in our analysis.
Results: For a nonconstant twist the frequencies of the MHD wave modes are split, which has important consequences for standing waves. This is different from the degenerated situation for equilibrium models with constant twist, which are characterised by an azimuthal component of the magnetic field that linearly increases with the radial coordinate.
Conclusions: In the presence of twist standing kink solutions are characterised by a change in polarisation of the transverse displacement along the tube. For weak twist, and in the thin tube approximation, the frequency of standing modes is unaltered and the tube oscillates at the kink speed of the corresponding straight tube. The change in polarisation is linearly proportional to the degree of twist. This has implications with regard to observations of kink modes, since the detection of this variation in polarisation can be used as an indirect method to estimate the twist in oscillating loops. Title: Damped kink oscillations of flowing prominence threads Authors: Soler, R.; Ruderman, M. S.; Goossens, M. Bibcode: 2012A&A...546A..82S Altcode: 2012arXiv1209.3382S Transverse oscillations of thin threads in solar prominences are frequently reported in high-resolution observations. Two typical features of the observations are that the oscillations are damped in time and that simultaneous mass flows along the threads are detected. Flows cause the dense threads to move along the prominence magnetic structure while the threads are oscillating. The oscillations have been interpreted in terms of standing magnetohydrodynamic (MHD) kink waves of the magnetic flux tubes, which support the threads. The damping is most likely due to resonant absorption caused by plasma inhomogeneity. The technique of seismology uses the observations combined with MHD wave theory to estimate prominence physical parameters. This paper presents a theoretical study of the joint effect of flow and resonant absorption on the amplitude of standing kink waves in prominence threads. We find that flow and resonant absorption can either be competing effects on the amplitude or both can contribute to damp the oscillations depending on the instantaneous position of the thread within the prominence magnetic structure. The amplitude profile deviates from the classic exponential profile of resonantly damped kink waves in static flux tubes. Flow also introduces a progressive shift of the oscillation period compared to the static case, although this effect is in general of minor importance. We test the robustness of seismological estimates by using synthetic data aiming to mimic real observations. The effect of the thread flow can significantly affect the estimation of the transverse inhomogeneity length scale. The presence of random background noise adds uncertainty to this estimation. Caution needs to be paid to the seismological estimates that do not take the influence of flow into account. Title: Standing and propagating MHD waves in coronal loops Authors: Goossens, Marcel Bibcode: 2012cosp...39..648G Altcode: 2012cosp.meet..648G I shall review recent theoretical results on standing and propagating MHD waves in solar coronal loops. First, I shall focus on periods, damping times and damping lengths and show how they can be used to do seismology. Second I shall address the nature of non-axisymmetric MHD waves. I shall show that the fundamental radial modes of all non-axisymmetric MHD waves with phase velocities in between the internal and the external Alfven velocities are essentially surface waves. Consequences for the transport of energy will be discussed. Title: Surface Alfvén Waves in Solar Flux Tubes Authors: Goossens, M.; Andries, J.; Soler, R.; Van Doorsselaere, T.; Arregui, I.; Terradas, J. Bibcode: 2012ApJ...753..111G Altcode: 2012arXiv1205.0935G Magnetohydrodynamic (MHD) waves are ubiquitous in the solar atmosphere. Alfvén waves and magneto-sonic waves are particular classes of MHD waves. These wave modes are clearly different and have pure properties in uniform plasmas of infinite extent only. Due to plasma non-uniformity, MHD waves have mixed properties and cannot be classified as pure Alfvén or magneto-sonic waves. However, vorticity is a quantity unequivocally related to Alfvén waves as compression is for magneto-sonic waves. Here, we investigate MHD waves superimposed on a one-dimensional non-uniform straight cylinder with constant magnetic field. For a piecewise constant density profile, we find that the fundamental radial modes of the non-axisymmetric waves have the same properties as surface Alfvén waves at a true discontinuity in density. Contrary to the classic Alfvén waves in a uniform plasma of infinite extent, vorticity is zero everywhere except at the cylinder boundary. If the discontinuity in density is replaced with a continuous variation of density, vorticity is spread out over the whole interval with non-uniform density. The fundamental radial modes of the non-axisymmetric waves do not need compression to exist unlike the radial overtones. In thin magnetic cylinders, the fundamental radial modes of the non-axisymmetric waves with phase velocities between the internal and the external Alfvén velocities can be considered as surface Alfvén waves. On the contrary, the radial overtones can be related to fast-like magneto-sonic modes. Title: Search for counterparts of newly discovered INTEGRAL/IBIS sources Authors: Landi, R.; Bassani, L.; Masetti, N.; Bazzano, A.; Ubertini, P.; Bird, A. J.; Goossens, M. Bibcode: 2012ATel.4166....1L Altcode: With respect to the recent INTEGRAL/IBIS 9-year Galactic Hard X-ray Survey (Krivonos et al. 2012, arXiv:1205.3941), we used archival Swift/XRT data to find likely counterparts for two hard X-ray sources newly detected by INTEGRAL: SWIFT J0958.0-4208 and IGR J22534+6243.

SWIFT J0958.0-4208 This source is also reported in the Swift/BAT 58-month catalogue (http://heasarc.nasa.gov/docs/swift/results/bs58mon/). Title: On the nature of the SWIFT/INTEGRAL source SWIFT J1508.6-4953 (also PMN J1508-4953) Authors: Landi, R.; Bassani, L.; Masetti, N.; Bazzano, A.; Parisi, P.; Drave, S.; Goossens, M. Bibcode: 2012ATel.4167....1L Altcode: This source is listed in the recent INTEGRAL/IBIS 9-year Galactic Hard X-ray Survey (Krivonos et al. 2012, arXiv:1205.3941) and also appears in the BAT 58-month catalogue (http://heasarc.nasa.gov/docs/swift/results/bs58mon/).

It has been associated with the radio source PMN J1508-4953, also reported as a GeV emitter in the 2nd Fermi catalogue (Nolan et al. 2012, ApJS, 199, 31). We use archival Swift/XRT data to investigate its nature. Title: INTEGRAL detects the BeXRB GS 0834-43 returning to an active state Authors: Drave, S. P.; Sguera, V.; Bird, A. J.; Goossens, M.; Sidoli, L.; Bazzano, A.; Fiocchi, M. Bibcode: 2012ATel.4218....1D Altcode: During INTEGRAL Galactic Plane Scan (GPS) observations between 2012-06-26 06:44:07 and 2012-06-26 15:27:19 (UTC) the BeXRB GS 0834-43 was detected at a high level of significance of 47 sigma by IBIS/ISGRI (net exposure time of 15.8 ks). The source had a count rate of 20.1 ± 0.4 in the 18-60 keV energy band, corresponding to a flux of 109 ± 2 mCrab. GS 0834-43 was also in the field of view of the JEM-X soft X-ray instrument for an exposure time of 1.7 ks during these observations where it was detected at a significance of 19 sigma. Title: INTEGRAL detection of renewed activity from SAX J2103.5+4545 Authors: Sguera, V.; Drave, S.; Goossens, M.; Bird, A. J.; Sidoli, L.; Fiocchi, M.; Bazzano, A.; Tarana, A. Bibcode: 2012ATel.4168....1S Altcode: During recent INTEGRAL Galactic Plane Scanning observation (PI: A. Bazzano), starting on 2012 June 12 at 01:00 UTC, IBIS/ISGRI detected renewed activity from the Be HMXB SAX J2103.5+4545. The source was detected at 29 sigma level (18-60 keV) with a flux of 61 +- 2 mCrab (15 ks exposure time). This detection confirms the X-ray activity predicted by Konstantinova et al. (ATel #4068). A preliminary IBIS/ISGRI spectral analysis reveals a 18-60 keV spectrum which can be described by a power law with photon index 2.6 +- 0.2, the 18-60 keV flux is 7.6 x 10-10 erg cm-2 s-1. Title: Inversion of Physical Parameters in Solar Coronal Magnetic Structures Authors: Arregui, I. .; Ballester, J.; Goossens, M.; Oliver, R.; Ramos, A. Bibcode: 2012ASPC..456..121A Altcode: Magnetohydrodynamic seismology aims to determine difficult to measure physical parameters in the solar corona by a combination of observed and theoretical properties of waves and oscillations. We describe relevant examples of the application of seismology techniques to transversely oscillating coronal loops and prominence fine structures. We also show how the use of statistical techniques, based on Bayesian inference, can be of high value in the determination of physical parameters in these structures, by consistently taking into account the information from observations. Title: Kelvin-Helmholtz Instability in Partially Ionized Compressible Plasmas Authors: Soler, R.; Díaz, A. J.; Ballester, J. L.; Goossens, M. Bibcode: 2012ApJ...749..163S Altcode: 2012arXiv1202.4274S The Kelvin-Helmholtz instability (KHI) has been observed in the solar atmosphere. Ion-neutral collisions may play a relevant role for the growth rate and evolution of the KHI in solar partially ionized plasmas such as in, e.g., solar prominences. Here, we investigate the linear phase of the KHI at an interface between two partially ionized magnetized plasmas in the presence of a shear flow. The effects of ion-neutral collisions and compressibility are included in the analysis. We obtain the dispersion relation of the linear modes and perform parametric studies of the unstable solutions. We find that, in the incompressible case, the KHI is present for any velocity shear regardless of the value of the collision frequency. In the compressible case, the domain of instability depends strongly on the plasma parameters, especially the collision frequency and the density contrast. For high collision frequencies and low density contrasts the KHI is present for super-Alfvénic velocity shear only. For high density contrasts the threshold velocity shear can be reduced to sub-Alfvénic values. For the particular case of turbulent plumes in prominences, we conclude that sub-Alfvénic flow velocities can trigger the KHI thanks to the ion-neutral coupling. Title: Transverse coronal loop oscillations seen in unprecedented detail by AIA/SDO Authors: White, Rebecca.; Verwichte, Erwin.; Soler, Roberto.; Goossens, Marcel; Van Doorsselaere, Tom.; Arregui, Inigo. Bibcode: 2012decs.confE..18W Altcode: We present an observational study of transverse oscillations of eleven coronal loops observed in three separate events using data from the Solar Dynamics Observatory (SDO) which provides unprecedented temporal and spatial resolution of the solar corona. We study oscillatory events using the Atmospheric Imaging Assembly (AIA) instrument on board SDO, primarily in the 171 Angstrom bandpass to obtain information on loop lengths, periods and damping times. Where possible, data from SDO/AIA has been complimented with data from STEREO in order to obtain an estimation of the 3D loop geometry. Local coronal plasma properties are often difficult to measure using direct methods, however they can be probed using the diagnostic power of MHD waves. In particular, coronal loop oscillations interpreted as the fast MHD kink mode provide an excellent tool for investigating such properties using the technique of coronal seismology. By probing the local coronal plasma, important information on the physical conditions in the vicinity of events such as solar flares and CMEs can be determined. Further to the observational study, analytic and Bayesian seismology inversion techniques are applied to the transverse loop oscillations under the thin tube, thin boundary approximations and under the assumption that they are damped via the mechanism of resonant absorption. This technique allows a 3D parameter space to be constructed that relates the density contrast, the loop inhomogeneity length scale and the Alfven travel time. Title: Resonant Alfvén waves in partially ionized plasmas of the solar atmosphere Authors: Soler, R.; Andries, J.; Goossens, M. Bibcode: 2012A&A...537A..84S Altcode: 2011arXiv1111.4134S Context. Magnetohydrodynamic (MHD) waves are ubiquitous in the solar atmosphere. In magnetic waveguides resonant absorption due to plasma inhomogeneity naturally transfers wave energy from large-scale motions to small-scale motions. In the cooler parts of the solar atmosphere as, e.g., the chromosphere, effects due to partial ionization may be relevant for wave dynamics and heating.
Aims: We study resonant Alfvén waves in partially ionized plasmas.
Methods: We use the multifluid equations in the cold plasma approximation. We investigate propagating resonant MHD waves in partially ionized flux tubes. We use approximate analytical theory based on normal modes in the thin tube and thin boundary approximations along with numerical eigenvalue computations.
Results: We find that the jumps of the wave perturbations across the resonant layer are the same as in fully ionized plasmas. The damping length due to resonant absorption is inversely proportional to the frequency, while that due to ion-neutral collisions is inversely proportional to the square of the frequency. For observed frequencies in the solar atmosphere, the amplitude of MHD kink waves is more efficiently damped by resonant absorption than by ion-neutral collisions.
Conclusions: Most of the energy carried by chromospheric kink waves is converted into localized azimuthal Alfvén waves that can deposit energy in the coronal medium. The dissipation of wave energy in the chromosphere due to ion-neutral collisions is only effective for high-frequency waves. The chromosphere acts as a filter for kink waves with periods shorter than 10 s. Title: Spectral Analysis of New X-ray Outbursts from the SFXT AX J1845.0-0433 Authors: Goossens, M.; Bazzano, A.; Bird, T.; Drave, S.; Hill, A.; Sguera, V.; Sidoli, L. Bibcode: 2012int..workE..28G Altcode: 2012PoS...176E..28G No abstract at ADS Title: LYRA Observations of Two Oscillation Modes in a Single Flare Authors: Van Doorsselaere, T.; De Groof, A.; Zender, J.; Berghmans, D.; Goossens, M. Bibcode: 2011ApJ...740...90V Altcode: We analyze light curves from the LYRA irradiance experiment on board PROBA2 during the flare of 2010 February 8. We see both long- and short-period oscillations during the flare. The long-period oscillation is interpreted in terms of standing slow sausage modes; the short-period oscillation is thought to be a standing fast sausage mode. The simultaneous presence of two oscillation modes in the same flaring structure allows for new coronal seismological applications. The periods are used to find seismological estimates of the plasma-β and the density contrast of the flaring loop. Also the wave mode number is estimated from the observed periods. Title: Resonantly Damped Propagating Kink Waves in Longitudinally Stratified Solar Waveguides Authors: Soler, R.; Terradas, J.; Verth, G.; Goossens, M. Bibcode: 2011ApJ...736...10S Altcode: 2011arXiv1105.0067S It has been shown that resonant absorption is a robust physical mechanism for explaining the observed damping of magnetohydrodynamic kink waves in the solar atmosphere due to naturally occurring plasma inhomogeneity in the direction transverse to the direction of the magnetic field. Theoretical studies of this damping mechanism were greatly inspired by the first observations of post-flare standing kink modes in coronal loops using the Transition Region and Coronal Explorer. More recently, these studies have been extended to explain the attenuation of propagating coronal kink waves observed by the Coronal Multi-Channel Polarimeter. In the present study, for the first time we investigate the properties of propagating kink waves in solar waveguides including the effects of both longitudinal and transverse plasma inhomogeneity. Importantly, it is found that the wavelength is only dependent on the longitudinal stratification and the amplitude is simply a product of the two effects. In light of these results the advancement of solar atmospheric magnetoseismology by exploiting high spatial/temporal resolution observations of propagating kink waves in magnetic waveguides to determine the length scales of the plasma inhomogeneity along and transverse to the direction of the magnetic field is discussed. Title: Alfvénic waves with sufficient energy to power the quiet solar corona and fast solar wind Authors: McIntosh, Scott W.; de Pontieu, Bart; Carlsson, Mats; Hansteen, Viggo; Boerner, Paul; Goossens, Marcel Bibcode: 2011Natur.475..477M Altcode: Energy is required to heat the outer solar atmosphere to millions of degrees (refs 1, 2) and to accelerate the solar wind to hundreds of kilometres per second (refs 2-6). Alfvén waves (travelling oscillations of ions and magnetic field) have been invoked as a possible mechanism to transport magneto-convective energy upwards along the Sun's magnetic field lines into the corona. Previous observations of Alfvénic waves in the corona revealed amplitudes far too small (0.5kms-1) to supply the energy flux (100-200Wm-2) required to drive the fast solar wind or balance the radiative losses of the quiet corona. Here we report observations of the transition region (between the chromosphere and the corona) and of the corona that reveal how Alfvénic motions permeate the dynamic and finely structured outer solar atmosphere. The ubiquitous outward-propagating Alfvénic motions observed have amplitudes of the order of 20kms-1 and periods of the order of 100-500s throughout the quiescent atmosphere (compatible with recent investigations), and are energetic enough to accelerate the fast solar wind and heat the quiet corona. Title: Resonant MHD Waves in the Solar Atmosphere Authors: Goossens, Marcel; Erdélyi, Robert; Ruderman, Michael S. Bibcode: 2011SSRv..158..289G Altcode: 2010SSRv..tmp..182G The linear theory of MHD resonant waves in inhomogeneous plasmas is reviewed. The review starts from discussing the properties of driven resonant MHD waves. The dissipative solutions in Alfvén and slow dissipative layers are presented. The important concept of connection formulae is introduced. Next, we proceed on to non-stationary resonant MHD waves. The relation between quasi-modes of ideal MHD and eigenmodes of dissipative MHD are discussed. The solution describing the wave motion in non-stationary dissipative layers is given. It is shown that the connection formulae remain valid for non-stationary resonant MHD waves. The initial-value problem for resonant MHD waves is considered. The application of theory of resonant MHD waves to solar physics is discussed. Title: Magnetohydrodynamic Waves and Seismology of the Solar Atmosphere Authors: Erdélyi, Robertus; Goossens, Marcel Bibcode: 2011SSRv..158..167E Altcode: 2011SSRv..tmp..229E; 2011SSRv..tmp...84E; 2011SSRv..tmp..153E No abstract at ADS Title: Kink oscillations of flowing threads in solar prominences Authors: Soler, R.; Goossens, M. Bibcode: 2011A&A...531A.167S Altcode: 2011arXiv1106.3937S Context. Recent observations by Hinode/SOT show that MHD waves and mass flows are simultaneously present in the fine structure of solar prominences.
Aims: We investigate standing kink magnetohydrodynamic (MHD) waves in flowing prominence threads from a theoretical point of view. We model a prominence fine structure as a cylindrical magnetic tube embedded in the solar corona with its ends line-tied in the photosphere. The magnetic cylinder is composed of a region with dense prominence plasma, which is flowing along the magnetic tube, whereas the rest of the flux tube is occupied by coronal plasma.
Methods: We use the WKB approximation to obtain analytical expressions for the period and the amplitude of the fundamental mode as functions of the flow velocity. In addition, we solve the full problem numerically by means of time-dependent simulations.
Results: We find that both the period and the amplitude of the standing MHD waves vary in time as the prominence thread flows along the magnetic structure. The fundamental kink mode is a good description for the time-dependent evolution of the oscillations, and the analytical expressions in the WKB approximation are in agreement with the full numerical results.
Conclusions: The presence of flow modifies the period of the oscillations with respect to the static case. However, for realistic flow velocities this effect might fall within the error bars of the observations. The variation of the amplitude due to the flow leads to apparent damping or amplification of the oscillations, which could modify the real rate of attenuation caused by an additional damping mechanism. Title: Spatial Damping of Propagating Kink Waves Due to Resonant Absorption: Effect of Background Flow Authors: Soler, R.; Terradas, J.; Goossens, M. Bibcode: 2011ApJ...734...80S Altcode: 2011arXiv1104.1791S Observations show the ubiquitous presence of propagating magnetohydrodynamic (MHD) kink waves in the solar atmosphere. Waves and flows are often observed simultaneously. Due to plasma inhomogeneity in the direction perpendicular to the magnetic field, kink waves are spatially damped by resonant absorption. The presence of flow may affect the wave spatial damping. Here, we investigate the effect of longitudinal background flow on the propagation and spatial damping of resonant kink waves in transversely nonuniform magnetic flux tubes. We combine approximate analytical theory with numerical investigation. The analytical theory uses the thin tube (TT) and thin boundary (TB) approximations to obtain expressions for the wavelength and the damping length. Numerically, we verify the previously obtained analytical expressions by means of the full solution of the resistive MHD eigenvalue problem beyond the TT and TB approximations. We find that the backward and forward propagating waves have different wavelengths and are damped on length scales that are inversely proportional to the frequency as in the static case. However, the factor of proportionality depends on the characteristics of the flow, so that the damping length differs from its static analog. For slow, sub-Alfvénic flows the backward propagating wave gets damped on a shorter length scale than in the absence of flow, while for the forward propagating wave the damping length is longer. The different properties of the waves depending on their direction of propagation with respect to the background flow may be detected by the observations and may be relevant for seismological applications. Title: Magnetoseismological Determination of Magnetic Field and Plasma Density Height Variation in a Solar Spicule Authors: Verth, G.; Goossens, M.; He, J. -S. Bibcode: 2011ApJ...733L..15V Altcode: The variation of magnetic field strength and plasma density along a solar spicule is determined by the use of magnetoseismology. From Solar Optical Telescope observations of a kink wave propagating along a spicule, by estimating the spatial change in phase speed and velocity amplitude, a novel approach is demonstrated to determine the chromospheric height variation of both magnetic field and plasma density. Furthermore, the magnetoseismological estimate of the plasma density gradient is combined with electron density estimates from spectroscopy to determine the changing degree of ionization of hydrogen along a spicule. Title: Propagating Kink Waves in Stratified Magnetic Waveguides of the Solar Corona Authors: Soler, Roberto; Terradas, J.; Verth, G.; Goossens, M. Bibcode: 2011SPD....42.1805S Altcode: 2011BAAS..43S.1805S Recent observations using the Coronal Multi-Channel Polarimeter (CoMP) show ubiquitous propagating waves of low amplitude in magnetic loops of the solar corona. These observations have been interpreted as magnetohydrodynamic (MHD) resonant kink waves. It has been shown that resonant absorption is a robust physical mechanism to explain the observed damping of MHD kink waves in the solar atmosphere due to naturally occurring plasma inhomogeneity in the direction transverse to the magnetic field. In the present study, for the first time we investigate the properties of propagating kink waves in solar magnetic waveguides including the effects of both longitudinal and transverse plasma inhomogeneity. Importantly, it is found that the wavelength is only dependent on the longitudinal stratification and the amplitude is simply a product of the two effects. In light of these results the advancement of solar atmospheric magnetoseismology by exploiting high spatial/temporal resolution observations of propagating kink waves in magnetic waveguides to determine the length scales of the plasma inhomogeneity along and transverse to the direction of the magnetic field is discussed. Title: The Thermal Instability of Solar Prominence Threads Authors: Soler, R.; Ballester, J. L.; Goossens, M. Bibcode: 2011ApJ...731...39S Altcode: 2011arXiv1102.2317S The fine structure of solar prominences and filaments appears as thin and long threads in high-resolution images. In Hα observations of filaments, some threads can be observed for only 5-20 minutes before they seem to fade and eventually disappear, suggesting that these threads may have very short lifetimes. The presence of an instability might be the cause of this quick disappearance. Here, we study the thermal instability of prominence threads as an explanation of their sudden disappearance from Hα observations. We model a prominence thread as a magnetic tube with prominence conditions embedded in a coronal environment. We assume a variation of the physical properties in the transverse direction so that the temperature and density continuously change from internal to external values in an inhomogeneous transitional layer representing the particular prominence-corona transition region (PCTR) of the thread. We use the nonadiabatic and resistive magnetohydrodynamic equations, which include terms due to thermal conduction parallel and perpendicular to the magnetic field, radiative losses, heating, and magnetic diffusion. We combine both analytical and numerical methods to study linear perturbations from the equilibrium state, focusing on unstable thermal solutions. We find that thermal modes are unstable in the PCTR for temperatures higher than 80,000 K, approximately. These modes are related to temperature disturbances that can lead to changes in the equilibrium due to rapid plasma heating or cooling. For typical prominence parameters, the instability timescale is of the order of a few minutes and is independent of the form of the temperature profile within the PCTR of the thread. This result indicates that thermal instability may play an important role for the short lifetimes of threads in the observations. Title: Seismology of Transversely Oscillating Coronal Loops with Siphon Flows Authors: Terradas, J.; Arregui, I.; Verth, G.; Goossens, M. Bibcode: 2011ApJ...729L..22T Altcode: 2011arXiv1101.5238T There are ubiquitous flows observed in the solar atmosphere of sub-Alfvénic speeds; however, after flaring and coronal mass ejection events flows can become Alfvénic. In this Letter, we derive an expression for the standing kink mode frequency due to siphon flow in coronal loops, valid for both low and high speed regimes. It is found that siphon flow introduces a linear, spatially dependent phase shift along coronal loops and asymmetric eigenfunctions. We demonstrate how this theory can be used to determine the kink and flow speed of oscillating coronal loops with reference to an observational case study. It is shown that the presence of siphon flow can cause the underestimation of magnetic field strength in coronal loops using the traditional seismological methods. Title: Selective spatial damping of propagating kink waves due to resonant absorption Authors: Terradas, J.; Goossens, M.; Verth, G. Bibcode: 2010A&A...524A..23T Altcode: 2010arXiv1004.4468T Context. There is observational evidence of propagating kink waves driven by photospheric motions. These disturbances, interpreted as kink magnetohydrodynamic (MHD) waves are attenuated as they propagate upwards in the solar corona.
Aims: We show that resonant absorption provides a simple explanation to the spatial damping of these waves.
Methods: Kink MHD waves are studied using a cylindrical model of solar magnetic flux tubes, which includes a non-uniform layer at the tube boundary. Assuming that the frequency is real and the longitudinal wavenumber complex, the damping length and damping per wavelength produced by resonant absorption are analytically calculated in the thin tube (TT) approximation, valid for coronal waves. This assumption is relaxed in the case of chromospheric tube waves and filament thread waves.
Results: The damping length of propagating kink waves due to resonant absorption is a monotonically decreasing function of frequency. For kink waves with low frequencies, the damping length is exactly inversely proportional to frequency, and we denote this as the TGV relation. When moving to high frequencies, the TGV relation continues to be an exceptionally good approximation of the actual dependency of the damping length on frequency. This dependency means that resonant absorption is selective as it favours low-frequency waves and can efficiently remove high-frequency waves from a broad band spectrum of kink waves. The efficiency of the damping due to resonant absorption depends on the properties of the equilibrium model, in particular on the width of the non-uniform layer and the steepness of the variation in the local Alfvén speed.
Conclusions: Resonant absorption is an effective mechanism for the spatial damping of propagating kink waves. It is selective because the damping length is inversely proportional to frequency so that the damping becomes more severe with increasing frequency. This means that radial inhomogeneity can cause solar waveguides to be a natural low-pass filter for broadband disturbances. Kink wave trains travelling along, e.g., coronal loops, will therefore have a greater proportion of the high-frequency components dissipated lower down in the atmosphere. This could have important consequences for the spatial distribution of wave heating in the solar atmosphere. Title: Observational Evidence of Resonantly Damped Propagating Kink Waves in the Solar Corona Authors: Verth, G.; Terradas, J.; Goossens, M. Bibcode: 2010ApJ...718L.102V Altcode: 2010arXiv1007.1080V In this Letter, we establish clear evidence for the resonant absorption damping mechanism by analyzing observational data from the novel Coronal Multi-Channel Polarimeter. This instrument has established that in the solar corona there are ubiquitous propagating low-amplitude (≈1 km s-1) Alfvénic waves with a wide range of frequencies. Realistically interpreting these waves as the kink mode from magnetohydrodynamic wave theory, they should exhibit a frequency-dependent damping length due to resonant absorption, governed by the Terradas-Goossens-Verth relation showing that transverse plasma inhomogeneity in coronal magnetic flux tubes causes them to act as natural low-pass filters. It is found that the observed frequency dependence on damping length (up to about 8 mHz) can be explained by the kink wave interpretation; and furthermore, the spatially averaged equilibrium parameter describing the length scale of transverse plasma density inhomogeneity over a system of coronal loops is consistent with the range of values estimated from Transition Region and Coronal Explorer observations of standing kink modes. Title: The effect of longitudinal flow on resonantly damped kink oscillations Authors: Terradas, J.; Goossens, M.; Ballai, I. Bibcode: 2010A&A...515A..46T Altcode: 2009arXiv0912.4136T Context. The most promising mechanism acting towards damping the kink oscillations of coronal loops is resonant absorption. In this context most of previous studies neglected the effect of the obvious equilibrium flow along magnetic field lines. The flows are in general sub-Alfvénic and hence comparatively slow.
Aims: Here we investigate the effect of an equilibrium flow on the resonant absorption of linear kink MHD waves in a cylindrical magnetic flux tube with the aim of determining the changes in the frequency of the forward and backward propagating waves and in the modification of the damping times due to the flow.
Methods: A loop model with both the density and the longitudinal flow changing in the radial direction is considered. We use the thin tube thin boundary (TTTB) approximation in order to calculate the damping rates. The full resistive eigenvalue problem is also solved without assuming the TTTB approximation.
Results: Using the low ratio of flow and Alfvén speeds we derive simple analytical expressions to the damping rate. The analytical expressions are in good agreement with the resistive eigenmode calculations.
Conclusions: Under typical coronal conditions the effect of the flow on the damped kink oscillations is weak when the characteristic scale of the density layer is similar or lower than the characteristic width of the velocity layer. However, in the opposite situation the damping rates can be significantly altered, specially for the backward propagating wave which is undamped while the forward wave is overdamped. Title: Magnetoseismology: Eigenmodes of Torsional Alfvén Waves in Stratified Solar Waveguides Authors: Verth, G.; Erdélyi, R.; Goossens, M. Bibcode: 2010ApJ...714.1637V Altcode: There have recently been significant claims of Alfvén wave observation in the solar chromosphere and corona. We investigate how the radial and longitudinal plasma structuring affects the observational properties of torsional Alfvén waves in magnetic flux tubes for the purposes of solar magnetoseismology. The governing magnetohydrodynamic equations of these waves in axisymmetric flux tubes of arbitrary radial and axial plasma structuring are derived and we study their observable properties for various equilibria in both thin and finite-width magnetic flux tubes. For thin flux tubes, it is demonstrated that observation of the eigenmodes of torsional Alfvén waves can provide temperature diagnostics of both the internal and surrounding plasma. In the finite-width flux tube regime, it is shown that these waves are the ideal magnetoseismological tool for probing radial plasma inhomogeneity in solar waveguides. Title: Kelvin-Helmholtz Instability in Coronal Magnetic Flux Tubes due to Azimuthal Shear Flows Authors: Soler, R.; Terradas, J.; Oliver, R.; Ballester, J. L.; Goossens, M. Bibcode: 2010ApJ...712..875S Altcode: 2009arXiv0912.3649S Transverse oscillations of coronal loops are often observed and have been theoretically interpreted as kink magnetohydrodynamic (MHD) modes. Numerical simulations by Terradas et al. suggest that shear flows generated at the loop boundary during kink oscillations could give rise to a Kelvin-Helmholtz instability (KHI). Here, we investigate the linear stage of the KHI in a cylindrical magnetic flux tube in the presence of azimuthal shear motions. We consider the basic, linearized MHD equations in the β = 0 approximation and apply them to a straight and homogeneous cylindrical flux tube model embedded in a coronal environment. Azimuthal shear flows with a sharp jump of the velocity at the cylinder boundary are included in the model. We obtain an analytical expression for the dispersion relation of the unstable MHD modes supported by the configuration, and compute analytical approximations of the critical velocity shear and the KHI growth rate in the thin tube limit. A parametric study of the KHI growth rates is performed by numerically solving the full dispersion relation. We find that fluting-like modes can develop a KHI in timescales comparable to the period of kink oscillations of the flux tube. The KHI growth rates increase with the value of the azimuthal wavenumber and decrease with the longitudinal wavenumber. However, the presence of a small azimuthal component of the magnetic field can suppress the KHI. Azimuthal motions related to kink oscillations of untwisted coronal loops may trigger a KHI, but this phenomenon has not been observed to date. We propose that the azimuthal component of the magnetic field is responsible for suppressing the KHI in a stable coronal loop. The required twist is small enough to prevent the development of the pinch instability. Title: Torsional Alfvén waves in small scale current threads of the solar corona Authors: Copil, P.; Voitenko, Y.; Goossens, M. Bibcode: 2010A&A...510A..17C Altcode: Context. The magnetic field structuring in the solar corona occurs on large scales (loops and funnels), but also on small scales. For instance, coronal loops are made up of thin strands with different densities and magnetic fields across the loop.
Aims: We consider a thin current thread and model it as a magnetic flux tube with twisted magnetic field inside the tube and straight field outside. We prove the existence of trapped Alfvén modes in twisted magnetic flux tubes (current threads) and we calculate the wave profile in the radial direction for two different magnetic twist models.
Methods: We used the Hall MHD equations that we linearized in order to derive and solve the eigenmode equation for the torsional Alfvén waves.
Results: We show that the trapped Alfv én eigenmodes do exist and are localized in thin current threads where the magnetic field is twisted. The wave spectrum is discrete in phase velocity, and the number of modes is finite and depends on the amount of the magnetic field twist. The phase speeds of the modes are between the minimum of the Alfvén speed in the interior and the exterior Alfén speed.
Conclusions: Torsional Alfvén waves can be guided by thin twisted magnetic flux-tubes (current threads) in the solar corona. We suggest that the current threads guiding torsional Alfvén waves, are subject to enhanced plasma heating due to wave dissipation. Title: Farley-Buneman Instability in the Solar Chromosphere Authors: Gogoberidze, G.; Voitenko, Y.; Poedts, S.; Goossens, M. Bibcode: 2009ApJ...706L..12G Altcode: 2009arXiv0902.4426G The Farley-Buneman instability (FBI) is studied in the partially ionized plasma of the solar chromosphere taking into account the finite magnetization of the ions and Coulomb collisions. We obtain the threshold value for the relative velocity between ions and electrons necessary for the instability to develop. It is shown that Coulomb collisions play a destabilizing role in the sense that they enable the instability even in the regions where the ion magnetization is larger than unity. By applying these results to chromospheric conditions, we show that the FBI cannot be responsible for the quasi-steady heating of the solar chromosphere. However, we do not exclude the instability development locally in the presence of strong cross-field currents and/or strong small-scale magnetic fields. In such cases, FBI should produce locally small-scale, ~0.1-3 m, density irregularities in the solar chromosphere. These irregularities can cause scintillations of radio waves with similar wave lengths and provide a tool for remote chromospheric sensing. Title: On the nature of kink MHD waves in magnetic flux tubes Authors: Goossens, M.; Terradas, J.; Andries, J.; Arregui, I.; Ballester, J. L. Bibcode: 2009A&A...503..213G Altcode: 2009arXiv0905.0425G Context: Magnetohydrodynamic (MHD) waves are often reported in the solar atmosphere and usually classified as slow, fast, or Alfvén. The possibility that these waves have mixed properties is often ignored.
Aims: The goal of this work is to study and determine the nature of MHD kink waves.
Methods: This is done by calculating the frequency, the damping rate and the eigenfunctions of MHD kink waves for three widely different MHD waves cases: a compressible pressure-less plasma, an incompressible plasma and a compressible plasma which allows for MHD radiation.
Results: In all three cases the frequency and the damping rate are for practical purposes the same as they differ at most by terms proportional to (kz R)^2. In the magnetic flux tube the kink waves are in all three cases, to a high degree of accuracy incompressible waves with negligible pressure perturbations and with mainly horizontal motions. The main restoring force of kink waves in the magnetised flux tube is the magnetic tension force. The total pressure gradient force cannot be neglected except when the frequency of the kink wave is equal or slightly differs from the local Alfvén frequency, i.e. in the resonant layer.
Conclusions: Kink waves are very robust and do not care about the details of the MHD wave environment. The adjective fast is not the correct adjective to characterise kink waves. If an adjective is to be used it should be Alfvénic. However, it is better to realize that kink waves have mixed properties and cannot be put in one single box. Title: The Nature of Kink MHD Waves in Magnetic Flux Tubes Authors: Goossens, Marcel; Terradas, J.; Andries, J.; Arregui, I.; Ballester, J. Bibcode: 2009SPD....40.1306G Altcode: We examine the nature of MHD kink waves. This is done by determining the frequency, the damping rate and the eigenfunctions of MHD kink waves for three widely different MHD waves cases: a compressible pressure-less plasma, an incompressible plasma and a compressible plasma with non-zero plasma pressure which allows for MHD radiation. The overall conclusion is that kink waves are very robust and do not care about the details of the MHD wave environment. In all three cases the frequency and the damping rate are for most practical purposes the same. In the magnetic flux tube the kink waves are in all three cases, to a high degree of accuracy incompressible waves with negligible pressure perturbations and with mainly horizontal motions. The main restoring force of kink waves in the magnetized flux tube is the magnetic tension force. The gradient pressure force cannot be neglected except when the frequency of the kink wave is equal or slightly differs from the local Alfvén frequency, i.e. in the resonant layer. In a non-magnetic external plasma the wave is of course acoustic. The adjective fast is not the correct adjective to characterize kink waves. If an adjective is to be used it should be Alfvénic. However, it is better to realize that kink waves have mixed properties and cannot be put in one single box. Title: The influence of longitudinal density variation in coronal loops on the eigenfunctions of kink-oscillation overtones Authors: Andries, J.; Arregui, I.; Goossens, M. Bibcode: 2009A&A...497..265A Altcode: Context: As coronal loops are spatially at least partially resolved in the longitudinal direction, attempts have been made to use the longitudinal profiles of the oscillation amplitudes as a seismological tool.
Aims: We aim to derive simple formulae to assess which oscillation modes and which quantities of the oscillation (displacement or compression) are most prone to modifications induced by stratification of the equilibrium density along the loop. We furthermore clarify and quantify that the potential of such a method could be enhanced if observational profiles of the compression in the oscillations could be determined.
Methods: By means of a linear expansion in the longitudinal stratification along with the “thin tube” approximation, the modifications to the eigenfunctions are calculated analytically. The results are validated by direct numerical computations.
Results: Higher axial overtones are found to be more affected by equilibrium stratification and hence would provide a much better tool if observed. For the k-1th overtone the compression is found to be around (k + 2)^2/k2 times more sensitive to longitudinal density variation than the displacement. While the linear formulae do give a good indication of the strength of the effects of longitudinal density stratification, the numerical computations indicate that the corrections to the approximate analytical results are significant and cannot be neglected under the expected coronal conditions. Title: Damping of Filament Thread Oscillations: Effect of the Slow Continuum Authors: Soler, R.; Oliver, R.; Ballester, J. L.; Goossens, M. Bibcode: 2009ApJ...695L.166S Altcode: 2009arXiv0902.0572S Transverse oscillations of small amplitude are commonly seen in high-resolution observations of filament threads, i.e., the fine structures of solar filaments/prominences, and are typically damped in a few periods. Kink wave modes supported by the thread body offer a consistent explanation of these observed oscillations. Among the proposed mechanisms to explain the kink mode damping, resonant absorption in the Alfvén continuum seems to be the most efficient as it produces damping times of about three periods. However, for a nonzero-β plasma and typical prominence conditions, the kink mode is also resonantly coupled to slow (or cusp) continuum modes, which could further reduce the damping time. In this Letter, we explore for the first time both analytically and numerically the effect of the slow continuum on the damping of transverse thread oscillations. The thread model is composed of a homogeneous and straight cylindrical plasma, an inhomogeneous transitional layer, and the homogeneous coronal plasma. We find that the damping of the kink mode due to the slow resonance is much less efficient than that due to the Alfvén resonance. Title: Nonlinear Instability of Kink Oscillations due to Shear Motions Authors: Terradas, J.; Andries, J.; Goossens, M.; Arregui, I.; Oliver, R.; Ballester, J. L. Bibcode: 2008ApJ...687L.115T Altcode: 2008arXiv0809.3664T First results from a high-resolution three-dimensional nonlinear numerical study of the kink oscillation are presented. We show in detail the development of a shear instability in an untwisted line-tied magnetic flux tube. The instability produces significant deformations of the tube boundary. An extended transition layer may naturally evolve as a result of the shear instability at a sharp transition between the flux tube and the external medium. We also discuss the possible effects of the instability on the process of resonant absorption when an inhomogeneous layer is included in the model. One of the implications of these results is that the azimuthal component of the magnetic field of a stable flux tube in the solar corona, needed to prevent the shear instability, is probably constrained to be in a very specific range. Title: Three-Dimensional MHD Wave Propagation and Conversion to Alfvén Waves near the Solar Surface. I. Direct Numerical Solution Authors: Cally, P. S.; Goossens, M. Bibcode: 2008SoPh..251..251C Altcode: 2007arXiv0711.0498C The efficacy of fast - slow MHD mode conversion in the surface layers of sunspots has been demonstrated over recent years using a number of modelling techniques, including ray theory, perturbation theory, differential eigensystem analysis, and direct numerical simulation. These show that significant energy may be transferred between the fast and slow modes in the neighbourhood of the equipartition layer where the Alfvén and sound speeds coincide. However, most of the models so far have been two dimensional. In three dimensions the Alfvén wave may couple to the magnetoacoustic waves with important implications for energy loss from helioseismic modes and for oscillations in the atmosphere above the spot. In this paper, we carry out a numerical "scattering experiment," placing an acoustic driver 4 Mm below the solar surface and monitoring the acoustic and Alfvénic wave energy flux high in an isothermal atmosphere placed above it. These calculations indeed show that energy conversion to upward travelling Alfvén waves can be substantial, in many cases exceeding loss to slow (acoustic) waves. Typically, at penumbral magnetic field strengths, the strongest Alfvén fluxes are produced when the field is inclined 30° - 40° from the vertical, with the vertical plane of wave propagation offset from the vertical plane containing field lines by some 60° - 80°. Title: Resonant Absorption in Complicated Plasma Configurations: Applications to Multistranded Coronal Loop Oscillations Authors: Terradas, J.; Arregui, I.; Oliver, R.; Ballester, J. L.; Andries, J.; Goossens, M. Bibcode: 2008ApJ...679.1611T Altcode: 2008arXiv0802.0591T We study the excitation and damping of transverse oscillations in a multistranded model of a straight line-tied coronal loop. The transverse geometry of our equilibrium configuration is quite irregular and more realistic than the usual cylindrical loop model. By numerically solving the time-dependent ideal magnetohydrodynamic equations in two dimensions, we show how the global motion of the whole bundle of strands, excited by an external disturbance, is converted into localized Alfvénic motions due to the process of resonant absorption. This process produces the attenuation of the transverse oscillations. At any location in the structure, two dominant frequencies are found: the frequency of the global mode or quasi-mode, and the local Alfvén frequency. We find that the mechanism of mode conversion, due to the coupling between fast and Alfvén waves, is not compromised by the complicated geometry of the model. We also show that it is possible to have energy conversion not only at the external edge of the composite loop, but also inside the structure. The implications of these results and their relationship with the observations are discussed. Title: Analytic approximate seismology of transversely oscillating coronal loops Authors: Goossens, M.; Arregui, I.; Ballester, J. L.; Wang, T. J. Bibcode: 2008A&A...484..851G Altcode: 2008arXiv0804.3877G Aims: We present an analytic approximate seismic inversion scheme for damped transverse coronal loop oscillations based on the thin tube and thin boundary approximation for computing the period and the damping time.
Methods: Asymptotic expressions for the period and damping rate are used to illustrate the process of seismological inversion in a simple and easy to follow manner. The inversion procedure is formulated in terms of two simple functions, which are given by simple closed expressions.
Results: The analytic seismic inversion shows that an infinite amount of 1-dimensional equilibrium models can reproduce the observed periods and damping times. It predicts a specific range of allowable values for the Alfvén travel time and lower bounds for the density contrast and the inhomogeneity length scale. When the results of the present analytic seismic inversion are compared with those of a previous numerical inversion, excellent agreement is found up to the point that the analytic seismic inversion emerges as a tool for validating results of numerical inversions. Actually it helped us to identify and correct inaccuracies in a previous numerical investigation. Title: Seismology of kink oscillations in coronal loops: Two decades of resonant damping Authors: Goossens, Marcel Bibcode: 2008IAUS..247..228G Altcode: 2007IAUS..247..228G The detection of rapidly damped transverse oscillations in coronal loops by Aschwanden et al. (1999) and Nakariakov et al. (1999) gave a strong impetus to the study of MHD waves and their damping. The common interpretation of the observations of these oscillations is based on kink modes. This paper reviews how the observed period and damping time can be reproduced by MHD wave theory when non-uniform equilibrium models are considered that have a transversal variation of the local Alfven velocity. The key point here is that resonant absorption cannot be avoided and occurs as natural damping mechanism for kink waves in non-uniform equilibrium models. The present paper starts with work by Hollweg & Yang (1988) and discusses subsequent developments in theory and their applications to seismology of coronal loops. It addresses the consistent use of observations of periods and damping times as seismological tools within the framework of resonant absorption. It shows that within the framework of resonant absorption infinitely many equilibrium models can reproduce the observed values of periods and damping times. Title: On the Scaling of the Damping Time for Resonantly Damped Oscillations in Coronal Loops Authors: Arregui, Iñigo; Ballester, José Luis; Goossens, Marcel Bibcode: 2008ApJ...676L..77A Altcode: 2008arXiv0802.1143A There is not as yet full agreement on the mechanism that causes the rapid damping of the oscillations observed by TRACE in coronal loops. It has been suggested that the variation of the observed values of the damping time as function of the corresponding observed values of the period contains information on the possible damping mechanism. The aim of this Letter is to show that, for resonant absorption, this is definitely not the case unless detailed a priori information on the individual loops is available. Title: Torsional Alfvén waves in small scale density threads of the solar corona Authors: Copil, P.; Voitenko, Y.; Goossens, M. Bibcode: 2008A&A...478..921C Altcode: The density structuring of the solar corona is observed at large scales (loops and funnels), but also at small scales (sub-structures of loops and funnels). Coronal loops consist of thin density threads with sizes down to (and most probably below) the resolution limit. We study properties of torsional Alfvén waves propagating in inhomogeneous cylindrical density threads using the two-fluid magnetohydrodynamic equations. The eigenmode solutions supported by such a structure are obtained and analysed. It is shown that the dispersive and dissipative effects become important for the waves localised in thin threads. In this case, the Alfvén wave continuum is replaced with a discrete spectrum of Alfvén waves. This mathematical model is applied to the waves propagating in coronal structures. In particular, we consider ~1 Hz Alfvén waves propagating along density threads with a relatively smooth radial profile, where a density contrast of about 1.1 is attained at radial distances of about 0.1 km. We found that the dissipation distance of these waves is less than the typical length of hot coronal loops, 50 Mm. Torsional Alfvén waves are localised in thin density threads and produce localised heating. Therefore, these waves can be responsible for coronal heating and for maintenance of small-scale coronal structuring. Title: On the Excitation of Leaky Modes in Cylindrical Loops Authors: Terradas, J.; Andries, J.; Goossens, M. Bibcode: 2007SoPh..246..231T Altcode: The role of leaky waves in the coronal loop oscillations observed by TRACE is not yet clearly understood. In this work, the excitation of fast waves in solar coronal loops modelled as dense plasma cylindrical tubes in a uniform straight magnetic field is investigated. We study the trapped and especially leaky modes (whose energy escapes from the tube) that result from an initial disturbance by solving the time-dependent problem numerically. We find that the stationary state of the tube motion is given by the trapped normal modes. By contrast, the transient behaviour between the initial and the stationary phase is dominated by wave leakage. The so-called trig leaky modes are clearly identified since the transient behaviour shows periods and damping times that are in agreement with the values calculated from the normal-mode analysis. Consequently, these radiating modes have physical significance. However, we have not found any evidence for the excitation of other types of modes, such as the principal leaky kink mode. Title: Spatial magneto-seismology: effect of density stratification on the first harmonic amplitude profile of transversal coronal loop oscillations Authors: Verth, G.; Van Doorsselaere, T.; Erdélyi, R.; Goossens, M. Bibcode: 2007A&A...475..341V Altcode: Context: The new generation of extreme-ultraviolet (EUV) imagers onboard missions such as the Solar Dynamics Observatory (SDO) and Solar Orbiter (SO) will provide the most accurate spatial measurements of post-flare coronal loop oscillations yet. The amplitude profiles of these loop oscillations contain important information about plasma fine structure in the corona.
Aims: We show that the position of the anti-nodes of the amplitude profile of the first harmonic of the standing fast kink wave of a coronal loop relate to the plasma density stratification of that loop.
Methods: The MHD kink transversal waves of coronal loops are modelled both numerically and analytically. The numerical model implements the implicit finite element code pollux. Dispersion relations are derived and solved analytically. The results of the two methods are compared and verified.
Results: Density stratification causes the anti-nodes of the first harmonic to shift towards the loop footpoints. The greater the density stratification, the larger the shift. The anti-node shift of the first harmonic of a semi-circular coronal loop with a density scale height H=50 Mm and loop half length L=100 Mm is approximately 5.6 Mm. Shifts in the Mm range are measureable quantities providing valuable information about the subresolution structure of coronal loops.
Conclusions: The measurement of the anti-node shift of the first harmonic of the standing fast kink wave of coronal loops is potentially a new tool in the field of solar magneto-seismology, providing a novel complementary method of probing plasma fine structure in the corona. Title: Coronal loop oscillations: energy considerations and initial value problem Authors: Terradas, J.; Andries, J.; Goossens, M. Bibcode: 2007A&A...469.1135T Altcode: Context: Flares and eruptions in the solar corona generate oscillations of loops which have been interpreted as eigenmodes (mainly the fundamental kink mode, although other modes can also be excited). From the theoretical point of view the excitation of the tube eigenmodes due to an initial disturbance has not been studied in much detail.
Aims: The main aim of this work is to calculate for a given initial disturbance the amount of energy that is deposited in the trapped fast mode oscillation, how it depends on the initial perturbation and how it is distributed among the different eigenmodes (kink and fluting and also the longitudinal harmonics).
Methods: We calculate, using analytical expressions, the amplitude and the energy of the oscillation of the magnetic tube for different kinds of initial excitations.
Results: We find that external excitations deposit a small amount of energy in the tube. We show that fluting modes have quite small energies in comparison with the energy of the kink mode (around three orders of magnitude for the first fluting mode). On the contrary, the longitudinal fundamental mode and the longitudinal harmonics have energies of the same order of magnitude. In addition, we find that the loop length and density contrast can be important factors that determine the amount of energy that is trapped by the loop.
Conclusions: The energy deposited in loops is typically six orders of magnitude smaller than the energy of the initial disturbance (for external excitations). However, it strongly depends on the distance of the initial perturbation and also on the loop properties (length and density). Fluting modes in coronal loops are very difficult to excite. Longitudinal harmonics are in principle more easily excited. Title: Global oscillations in a magnetic solar model. II. Oblique propagation Authors: Pintér, B.; Erdélyi, R.; Goossens, M. Bibcode: 2007A&A...466..377P Altcode: The coupling of solar global acoustic oscillations to a magnetised solar atmosphere is studied here. The solar interior - atmosphere interface is modelled by a non-magnetic polytrope interior overlayed by a planar atmosphere embedded in non-uniform horizontal atmospheric magnetic field. Pintér & Goossens (1999, A&A, 347, 321) showed that parallel propagating acoustic waves can couple resonantly to local magnetohydrodynamic (MHD) slow continuum modes only. In general, global acoustic modes can, however, propagate in arbitrary directions with respect to local atmospheric fields giving rise to an additional efficient coupling mechanism that has consequences on mode damping and atmospheric energetics. In this paper we study obliquely propagating global modes that can couple also to local MHD Alfvén continuum modes. The atmospheric magnetic effects on global mode frequencies are still much of a debate. In particular, the resulting frequency shifts and damping rates of global modes caused by the resonant interaction with both local Alfvén and slow waves are investigated. We found the coupling of global f and p modes and the Lamb mode, that penetrate into the magnetic solar atmosphere, will strongly depend on the direction of propagation with respect to the solar atmospheric magnetic field. These frequency shifts, as a function of the propagation direction, give us a further elegant tool and refinement method of local helioseismology techniques. Finally we briefly discuss the importance of studying obliquely propagating waves and discuss the results in the context of possible helioseismic observations.

Appendix A is only available in electronic form at http://www.aanda.org Title: Damping of Torsional Modes in the Solar Corona Authors: Copil, Paula; Voitenko, Yuriy; Goossens, Marcel Bibcode: 2007AIPC..895..147C Altcode: The Alfvén wave is one of the classic waves in magnetoplasma. It is an electromagnetic-hydrodynamic wave, in which the restoring force comes from the magnetic tension, while the ions provide the inertia. We have studied the propagation and dissipation of torsional Alfvén waves in an inhomogeneous cylindrical plasma taking into account the effects due to finite Larmor gyroradius. Title: MHD seismology of coronal loops using the period and damping of quasi-mode kink oscillations Authors: Arregui, I.; Andries, J.; Van Doorsselaere, T.; Goossens, M.; Poedts, S. Bibcode: 2007A&A...463..333A Altcode: Aims:We combine the magnetohydrodynamic (MHD) theory of resonantly damped quasi-mode kink oscillations with observational estimates of the period and damping of transverse coronal loop oscillations to extract information on physical parameters in oscillating loops.
Methods: A numerical study of the quasi-mode period and damping, in one-dimensional fully non-uniform flux tubes, is used to obtain equilibrium models that reproduce the observed periods and damping rates. This scheme is applied to 11 loop oscillation events.
Results: When only the damping rate is used, the valid equilibrium models form a one-dimensional solution curve in the two-dimensional parameter space (density contrast, transverse inhomogeneity length-scale). Lower limits to the transverse inhomogeneity are obtained in the limit of high contrast loops. When both the period and the damping rate are used, the equilibrium Alfvén speed (or Alfvén travel time) comes into play. The valid equilibrium models then form a one-dimensional solution curve in the three-dimensional parameter space (density contrast, transverse inhomogeneity length-scale, Alfvén speed or Alfvén travel time). The projection of these solutions onto the Alfvén speed axis is found to be constrained to a rather limited interval. Upper limits to the internal Alfvén speed are derived for 9 of the 11 analysed events. Title: MHD Waves and Shocks Generated during Magnetic Field Reconnection Authors: Bárta, M.; Karlický, M.; Vršnak, B.; Goossens, M. Bibcode: 2007CEAB...31..165B Altcode: We use a 2D MHD model of magnetic field reconnection to investigate if and how bursts of reconnection activity, changes of the magnetic field and shock wave generation are related. We found that major bursts of power dissipated into Joule heat occur during topological transitions of the magnetic field structure. These bursts are followed by shocks and waves. Along the plasma outflow jet not only MHD waves, but also ion-sound shocks are formed. After the phase of more or less quiet reconnection (Petschek-type) the tearing mode produces plasmoids. The interactions of these plasmoids are associated with further bursts of the reconnection activity and a complex structure of shock waves. Finally, all these processes are discussed as possible sources of various radio bursts. Title: Seismology of Coronal Loops Using the Period and Damping of Quasi-Mode Kink Oscillations Authors: Arregui, I.; Andries, J.; Van Doorsselaere, T.; Goossens, M.; Poedts, S. Bibcode: 2006ESASP.617E..81A Altcode: 2006soho...17E..81A No abstract at ADS Title: Seismology of Transversely Oscillating Loops Using Periods and Damping Times Authors: Goossens, Marcel; Arregui, I.; Andries, J.; Van Doorsselaere, T. Bibcode: 2006SPD....37.1804G Altcode: 2006BAAS...38..247G Periods and damping times of quasi-mode fundamental kink oscillations have been computed for non-uniform cylindrical models of coronal loops. The radial inhomogeneity length-scale, the density contrast and the internal Alfvén velocity are three equilibrium quantities that determine the theoretical values of the period and damping times in 1-D equilibrium models. From a seismological point of view this means that observed values of period and damping time can be recovered by an infinite number of equilibrium models. In other words, observed values of period and damping time of the fundamental kink oscillation mode do not allow a unique identification of even a 1-D equilibrium model. Only if there is additional information on one of the three equilibrium quantities, can we use the observed values of period and damping time to determine the two remaining equilibrium quantities. However, it is not all bad news. It turns out that, even without additional information, we can determine upper limits to the internal Alfvén velocity. We apply this scheme to the set of 11 loop oscillation events studied in Goossens et al. 2002 and find constraints on the equilibrium parameters for these 11 events. Title: Damping of magnetohydrodynamic waves by resonant absorption in the solar atmosphere Authors: Goossens, M.; Andries, J.; Arregui, I. Bibcode: 2006RSPTA.364..433G Altcode: No abstract at ADS Title: Quasi-mode damping in two-dimensional fully non-uniform coronal loops Authors: Arregui, I.; Van Doorsselaere, T.; Andries, J.; Goossens, M.; Poedts, S. Bibcode: 2006RSPTA.364..529A Altcode: No abstract at ADS Title: Energization of Plasma Species by Intermittent Kinetic Alfvén Waves Authors: Voitenko, Yuriy; Goossens, Marcel Bibcode: 2006SSRv..122..255V Altcode: We propose a new phase-mixing sweep model of coronal heating and solar wind acceleration based on dissipative properties of kinetic Alfvén waves (KAWs). The energy reservoir is provided by the intermittent ∼1 Hz MHD Alfvén waves excited at the coronal base by magnetic restructuring. These waves propagate upward along open magnetic field lines, phase-mix, and gradually develop short wavelengths across the magnetic field. Eventually, at 1.5-4 solar radii they are transformed into KAWs. We analyze several basic mechanisms for anisotropic energization of plasma species by KAWs and find them compatible with observations. In particular, UVCS (onboard SOHO) observations of intense cross-field ion energization at 1.5-4 solar radii can be naturally explained by non-adiabatic ion acceleration in the vicinity of demagnetizing KAW phases. The ion cyclotron motion is destroyed there by electric and magnetic fields of KAWs. Title: Oblique aperiodic instability driven by cross-field current in space plasmas Authors: Siversky, T.; Voitenko, Yu.; Goossens, M. Bibcode: 2006AdSpR..37..625S Altcode: Electric currents across the magnetic field can occur in the solar atmosphere because of quasi-stationary magnetic shear, plasma non-uniformity, or MHD waves. We propose a new physical mechanism that can cause the anomalous dissipation of these currents and initiate energy release in solar plasmas. In the framework of linear kinetic theory, we show that the cross-field currents are unstable with respect to low-frequency perturbations. The instability growth rate is quite high, about 2% of the ion-cyclotron frequency when the differential electron/ion velocity is 0.2 of the ion thermal speed. We identify the unstable perturbations as degenerated ion-acoustic modes coupled with backward kinetic Alfvén modes. Title: Magnetic interfaces in the solar atmosphere: waves, instabilities and energy release Authors: Voitenko, Y.; Siversky, T.; Copil, P.; Goossens, M. Bibcode: 2006cosp...36.3364V Altcode: 2006cosp.meet.3364V Numerous Yohkoh and SOHO observations suggest that the events of impulsive plasma heating in the solar atmosphere flares nanoflares blinkers etc are due to the energy released during magnetic reconnection Magnetic reconnection occurs in magnetic interfaces between interacting magnetic fluxes Classical transport coefficients cannot explain the observed rates of energy release As a consequence several current-driven plasma micro-instabilities have been suggested as mechanisms causing anomalous resistivity and faster energy release The common difficulty of models based on the current-driven instabilities is that the threshold currents for these instabilities are rather high and require very thin interfaces which are subject to quick disruption In this situation the fast Petschek regime of magnetic reconnection can hardly be obtained In our study we take into account that inhomogeneous shear plasma flows and currents as well as considerable guide magnetic field components are typical for coronal magnetic interfaces We find that the shear plasma flows and current inhomogeneity drastically decrease the threshold currents for kinetic Alfven and ion-acoustic instabilities As a result these instabilities can develop anomalous resistivity much earlier in relatively smooth and stable interfaces which make the standard Petschek model more realistic for the solar corona Moreover inhomogeneous currents that are typical for the quasi-steady solar corona can also drive these instabilities which can therefore contribute to the quasi-steady heating of the corona Title: Non-adiabatic acceleration of ions by kinetic Alfven waves Authors: Voitenko, Y.; Goossens, M. Bibcode: 2006cosp...36.3372V Altcode: 2006cosp.meet.3372V Strong energization of ions across the background magnetic field is one of most interesting observations in the solar corona at 1 5-4 solar radii and in the auroral zones of the terrestrial magnetosphere at 1 5-4 Earth radii The commonly accepted interpretation of this phenomenon is based on the ion-cyclotron resonant heating by high-frequency waves in the solar corona or stochastic heating by small-scale waves in the auroral zones We propose another mechanism where the cross-field ion energization is due to non-adiabatic acceleration by low-frequency kinetic Alfven waves KAWs In the vicinity of even demagnetizing wave phases all ions undergo a simultaneous increase of their cross-field velocities similar to particle acceleration in quasi-perpendicular shocks It is therefore intuitively understandable why the particles that move against the waves enter the regime of acceleration easier In-situ measurements of electro-magnetic fields in the auroral zones and remote spectroscopic coronal observations are compatible with low-frequency KAW turbulence We demonstrate that the sporadic appearance of super-critical gradients in KAW turbulence is sufficient for the cross-field energization of ions observed in these regions Title: Voitenko and Goossens Reply: Authors: Voitenko, Y.; Goossens, M. Bibcode: 2005PhRvL..95z9502V Altcode: A Reply to the Comment by P. K. Shukla and L. Stenflo. Title: Seismology of Coronal Loops Using Resonant Absorption Authors: Arregui, I.; van Doorsselaere, T.; Andries, J.; Goossens, M.; Poedts, S. Bibcode: 2005ESASP.600E..21A Altcode: 2005dysu.confE..21A; 2005ESPM...11...21A No abstract at ADS Title: Anomalous Viscous Dissipation of Slow Magneto-Acoustic Waves Authors: Siversky, T.; Voitenko, Y.; Goossens, M. Bibcode: 2005ESASP.600E..99S Altcode: 2005ESPM...11...99S; 2005dysu.confE..99S No abstract at ADS Title: Phase Mixing of MHD ALFVÉN Waves and Origin of Solar Wind Authors: Voitenko, Y.; Goossens, M. Bibcode: 2005ESASP.600E.103V Altcode: 2005ESPM...11..103V; 2005dysu.confE.103V No abstract at ADS Title: Linear Sources of Acousticwaves in the Shear Flows of Solar Convection Authors: Tevzadze, A. G.; Chagelishvili, G. D.; Goossens, M. Bibcode: 2005ESASP.600E..53T Altcode: 2005ESPM...11...53T; 2005dysu.confE..53T No abstract at ADS Title: Dynamics of Coronal Loop Oscillations Recent Improvements and Computational Aspects Authors: van Doorsselaere, T.; Arregui, I.; Andries, J.; Goossens, M.; Poedts, S. Bibcode: 2005SSRv..121...79V Altcode: We will discuss the observed, heavily damped transversal oscillations of coronal loops. These oscillations are often modeled as transversal kink oscillations in a cylinder. Several features are added to the classical cylindrical model. In our models we include loop curvature, longitudinal density stratification, and highly inhomogeneous radial density profiles. In this paper, we will first give an overview of recently obtained results, both analytically and numerically. After that, we shed a light on the computational aspects of the modeling process. In particular, we will focus on the parallellization of the numerical codes. Title: Foreword: Computing in Space and Astrophysical Plasmas Authors: Goossens, Marcel; Poedts, Stefaan; Voitenko, Yuriy; Chian, Abraham C. -L. Bibcode: 2005SSRv..121....1G Altcode: No abstract at ADS Title: Shear Flow Instabilities in Low-Beta Space Plasmas Authors: Siversky, Taras; Voitenko, Yuriy; Goossens, Marcel Bibcode: 2005SSRv..121..343S Altcode: We study instabilities driven by a sheared plasma flow in the low-frequency domain. Two unstable branches are found: the ion-sound mode and the kinetic Alfvén mode. Both instabilities are aperiodic. The ion-sound instability does not depend on the plasma β (gas/magnetic pressure ratio) and has a maximum growth rate of about 0.1 of the velocity gradient dV 0/dx. On the other hand, the kinetic Alfvén instability is stronger for larger β and dominates the ion-sound instability for β > 0.05. Possible applications for space plasmas are shortly discussed. Title: Dynamics of Coronal Loop Oscillations Authors: van Doorsselaere, T.; Arregui, I.; Andries, J.; Goossens, M.; Poedts, S. Bibcode: 2005ESASP.596E..44V Altcode: 2005ccmf.confE..44V No abstract at ADS Title: Resonantly damped fast MHD kink modes in longitudinally stratified tubes with thick non-uniform transitional layers Authors: Arregui, I.; Van Doorsselaere, T.; Andries, J.; Goossens, M.; Kimpe, D. Bibcode: 2005A&A...441..361A Altcode: Resonantly damped fast kink quasi-modes are computed in fully

resistive magnetohydrodynamics (MHD) for two-dimensional equilibrium

models. The equilibrium model is a straight cylindrically symmetric flux

tube with a plasma density that is non-uniform both across and along the

loop. The non-uniform layer across the loop is not

restricted to be thin, but its thickness can reach values up to the

loop diameter.

Our results indicate that

the period and damping of coronal loop oscillations mainly depend on the density contrast

and the inhomogeneity length-scale and are independent of the details of

longitudinal stratification, depending on the weighted mean density,

weighted with the wave energy. For fully non-uniform loops, quasi-modes can

interact with resistive Alfvén eigenmodes leading to avoided crossings

and gaps in the complex frequency plane. The present study extends previous

studies on coronal loop oscillations in one-dimensional equilibrium models

with thick boundary layers and in equilibria with longitudinally stratified loops under the

thin boundary approximation, and allow for a better comparison between

observations and theory raising the prospect of coronal seismology using

the time damping of coronal loop oscillations. Title: Nonlinear coupling of Alfvén waves with widely different cross-field wavelengths in space plasmas Authors: Voitenko, Yuriy M.; Goossens, Marcel Bibcode: 2005JGRA..11010S01V Altcode: Multiscale activity and dissipation of Alfvén waves play an important role in a number of space and astrophysical plasmas. A popular approach to study the evolution and damping of MHD Alfvén waves assumes a gradual evolution of the wave energy to small dissipative length scales. This can be done by local nonlinear interactions among MHD waves with comparable wavelengths resulting in turbulent cascades or by phase mixing and resonant absorption. We investigate an alternative nonlocal transport of wave energy from large MHD length scales directly into the dissipation range formed by the kinetic Alfvén waves (KAWs). KAWs have very short wavelengths across the magnetic field irrespectively of their frequency. We focus on the nonlinear mechanism for the excitation of KAWs by MHD Alfvén waves via resonant decay AW → KAW1 + KAW2. The resonant decay conditions can be satisfied in a rarified plasmas, where the gas/magnetic pressure ratio is less than the electron/ion mass ratio. The decay is efficient at low amplitudes of the magnetic field in the MHD waves, B/B0 ∼ 10-2. In turn, the nonlinearly driven KAWs have sufficiently short wavelengths for the dissipative effects to become significant. Therefore the cross-scale nonlinear coupling of Alfvén waves can provide a mechanism for the replenishment of the dissipation range and the consequent energization in space plasmas. Two relevant examples of this scenario in the solar corona and auroral zones are discussed. Title: Solar coronal loop oscillations: theory of resonantly damped oscillations and comparison with observations Authors: Goossens, M.; Andries, J.; Arregui, I.; Doorsselaere, T. V.; Poedts, S. Bibcode: 2005AIPC..784..114G Altcode: One of the proposed damping mechanisms of coronal transverse loop oscillations in the kink mode is resonant absorption as a result of the spatial variation of the Alfvén velocity in the equilibrium configuration. Analytical expressions for the period and the damping time exist for 1-D cylindrical equilibrium models with thin non-uniform transitional layers. Comparison with observations indicates that the assumption of thin non-uniform transitional layers is not a very accurate approximation of reality. This contributions starts with a short review of observations on transverse oscillations in solar coronal loops. Then it presents results on periods and damping times of resonantly damped kink mode oscillations for (i) fully non-uniform 1-D cylindrical equilibrium models in which the equilibrium quantities vary in the radial direction across the magnetic field from the centre of the loop up to its boundary and (ii) non-uniform 2-D cylindrical equilibrium models in which the equilibrium quantities vary both in the radial direction across the magnetic field and in the axial direction along the magnetic field. An important point is that the periods and damping times obtained for these fully non-uniform models can differ substantially from those obtained for thin non-uniform transitional layers. This contribution then reports on a consistency test between theory and observations showing that there is a very good agreement within the observational inaccuracies. Title: Damping of phase-mixed slow magneto-acoustic waves: Real or apparent? Authors: Voitenko, Y.; Andries, J.; Copil, P. D.; Goossens, M. Bibcode: 2005A&A...437L..47V Altcode: The propagation of slow magnetoacoustic waves along a multithreaded coronal loop is modelled analytically by means of a ray tracing method. It is shown how cross field gradients build up due to phase mixing. The cross field gradients can enhance shear viscosity so that it dominates over compressive viscosity. Nevertheless the short dissipation distances (~107 m) observed for slow waves in coronal loops require very small cross field length scales which imply a filamentary structure on scales at least three orders of magnitude below the current detection limit of TRACE and close to the limit where magnetohydrodynamic (MHD) theory breaks down. The observed dissipation distances can alternatively be explained by phase mixing in its ideal regime, where the apparent damping is due to the spatial integration of the phase mixed amplitudes by the observation. Title: Determination of the Coronal Density Stratification from the Observation of Harmonic Coronal Loop Oscillations Authors: Andries, Jesse; Arregui, Inigo; Goossens, Marcel Bibcode: 2005ApJ...624L..57A Altcode: The recent detection of multiple harmonic standing transverse oscillations in coronal loops by Verwichte et al. is of special importance, as it allows one to obtain information on the longitudinal density variation in loops. Verwichte et al. detected the simultaneous presence of both the fundamental and the first-overtone mode in two coronal loops. Here we point out that the ratio of the period of the fundamental mode to the period of the overtone mode differs from 2 in loops with longitudinal density stratification. Conversely, the difference between this ratio and 2 can be used as a seismological tool to obtain information about the density scale height in loops. Title: Cross-Scale Nonlinear Coupling and Plasma Energization by Alfvén Waves Authors: Voitenko, Y.; Goossens, M. Bibcode: 2005PhRvL..94m5003V Altcode: We present a new channel for the nonlocal transport of wave energy from the large (MHD) scales to the small (kinetic) scales generated by the resonant decay of MHD Alfvén waves into kinetic Alfvén waves. This process does not impose any restriction on the wave numbers or frequencies of initial MHD waves, which makes it superior compared to the mechanisms of spectral transport studied before. Because of dissipative properties of the nonlinearly driven kinetic Alfvén waves, the decay leads to plasma heating and particle acceleration, which is observed in a variety of space and astrophysical plasmas. Two examples in the solar corona and the terrestrial magnetosphere are briefly discussed. Title: Coronal loop oscillations. Calculation of resonantly damped MHD quasi-mode kink oscillations of longitudinally stratified loops Authors: Andries, J.; Goossens, M.; Hollweg, J. V.; Arregui, I.; Van Doorsselaere, T. Bibcode: 2005A&A...430.1109A Altcode: The observed coronal loop oscillations and their damping are often theoretically described by the use of a very simple coronal loop model, viz. a straight, longitudinally invariant, axi-symmetric, and pressureless flux tube with a different density inside and outside of the loop. In this paper we generalize the model by including longitudinal density stratification and we examine how the longitudinal density stratification alters the linear eigenmodes of the system, their oscillation frequencies, and the damping rates by resonant absorption.

Appendix A is only available in electronic form at http://www.edpsciences.org Title: Proton versus electron heating in solar flares Authors: Gordovskyy, M.; Zharkova, V. V.; Voitenko, Yu. M.; Goossens, M. Bibcode: 2005AdSpR..35.1743G Altcode: Proton and electron heating of a flaring atmosphere is compared in a kinetic approach for the particles ejected from a non-neutral reconnecting current sheet (RCS) located above the top of reconnected flaring loops in a two-ribbon flare. Two kinds of high-energy particles are considered: particles accelerated by a super-Dreicer electric field and those ejected from the reconnection region as neutral outflows, or separatrix jets. The beam electrons are assumed to deposit their energy in Coulomb collisions and Ohmic heating of the ambient plasma particles by the electric field induced by the precipitating beams. The protons are assumed to deposit their energy in generation of kinetic Alfvén waves (KAWs), which, in turn, dissipate due to Cherenkov resonant scattering on the ambient plasma electrons. The beam electrons are found to provide a fast (within a few tenth of a second) heating of the atmosphere that is well spread in depth from the corona to the lower chromosphere. The protons are shown to precipitate to the lower atmosphere much slower (up to few seconds for beam and up to 10-20 s for slow jets). Slow jet protons provide heating of the two compact regions: the first located at the top of a flaring loop just below the RCS, and the second one appearing at the transition region (TR) and upper chromosphere; fast beam protons deposit their energy in the TR and chromosphere only. Title: Numerical Solutions for Resonantly Damped MHD Quasi-Modes in Two-Dimensional Coronal Loops Authors: Arregui, I.; van Doorsselaere, T.; Andries, J.; Goossens, M. Bibcode: 2004ESASP.575...85A Altcode: 2004soho...15...85A No abstract at ADS Title: Damping of Coronal Loop Oscillations: Calculation of Resonantly Damped Kink Oscillations of One-dimensional Nonuniform Loops Authors: Van Doorsselaere, T.; Andries, J.; Poedts, S.; Goossens, M. Bibcode: 2004ApJ...606.1223V Altcode: The analytic study of coronal loop oscillations in equilibrium states with thin nonuniform boundary layers is extended by a numerical investigation for one-dimensional nonuniform equilibrium states. The frequency and the damping time of the ideal kink quasi mode are calculated in fully resistive MHD. In this numerical investigation there is no need to adopt the assumption of a thin nonuniform boundary layer, which is essential for analytic theory. An important realization is that analytical expressions for the damping rate that are equivalent for thin nonuniform layers give results differing by a factor of 2 when they are used for thick nonuniform layers. Analytical theory for thin nonuniform layers does not allow us to discriminate between these analytical expressions. The dependence of the complex frequency of the kink mode on the width of the nonuniform layer, on the length of the loop, and on the density contrast between the internal and the external region is studied and is compared with analytical theory, which is valid only for thin boundaries. Our numerical results enable us to show that there exists an analytical expression for thin nonuniform layers that might be used as a qualitative tool for extrapolation into the regime of thick nonuniform layers. However, when the width of the nonuniform layer is varied, the differences between our numerical results and the results obtained with the version of the analytical approximation that can be extended into the regime of thick nonuniform layers are still as large as 25%. Title: Cross-Field Heating of Coronal Ions by Low-Frequency Kinetic Alfvén Waves Authors: Voitenko, Yuriy; Goossens, Marcel Bibcode: 2004ApJ...605L.149V Altcode: Low-frequency kinetic Alfvén waves (KAWs) are studied as a possible source for the strong heating of ions across the magnetic field in the solar corona. It is shown that test ions moving in the electromagnetic fields of KAWs undergo an increase in their cross-field energy because of the superadiabatic acceleration in the vicinity of the demagnetizing wave phases. In particular, it is found that KAW wave trains, with a transversal wavelength of the order of 40 proton gyroradii and with a peak wave/background magnetic field ratio >~0.1, increase the cross-field energy of O5+ oxygen ions by 1-2 orders. The required short perpendicular wavelengths can be produced by the phase mixing of MHD Alfvén waves, propagating upward from the coronal base. The superadiabatic acceleration provides an alternative to the ion-cyclotron explanation for the intense transverse heating of O+5 and Mg9+ ions observed by the Solar and Heliospheric Observatory at 1.5-3 solar radii. Title: Radio signatures of Langmuir-Alfvén turbulence in the solar atmosphere Authors: Chian, A. C. -L.; Goossens, M.; Miranda, R. A.; Rempel, E. L.; Sirenko, O.; Voitenko, Y. Bibcode: 2004IAUS..223...95C Altcode: 2005IAUS..223...95C Radio emissions from the solar active regions can be generated by nonlinear coupling of Langmuir waves with Alfvén waves. Multi-wavelength observations can be used to provide evidence for Langmuir-Alfvén turbulence in the solar atmosphere. Title: Damping of Coronal Loop Oscillations Authors: van Doorsselaere, T.; Andries, J.; Poedt, S.; Goossens, M. Bibcode: 2004ESASP.547..453V Altcode: 2004soho...13..453V The analytic study of coronal loop oscillations in equilibrium states with thin nonuniform boundary layers is extended by a numerical investigation for 1D nonuniform equilibrium states. The frequency and the damping time of the ideal kink quasi-mode are calculated in fully resistive MHD. In this numerical investigation there is no need to adopt the assumption of a thin nonuniform boundary layer which is essential for analytic theory. The dependence of the complex frequency of the kink mode on the width of the nonuniform layer, the length of the loop and the density contrast between the internal and the external region is studied and is compared with analytical theory which is only valid for thin boundaries. When the width of the nonuniformlayer is varied, the differences between our numerical results and the results obtained with analytical formula, still amount up to 25%. Title: Cross-field ion acceleration by intermittent kinetic Alfven waves in space plasmas Authors: Voitenko, Yu.; Goossens, M. Bibcode: 2004cosp...35.4011V Altcode: 2004cosp.meet.4011V Intense cross-field energization of the ions is often observed in the solar corona, solar wind and terrestrial magnetosphere. This energization has been mainly attributed to the ion-cyclotron damping or stochastic acceleration by high-frequency waves. We investigate the possibility that this energization is due to low-frequency Alfven waves that are short-wavelength across the magnetic field - kinetic Alfven waves (KAWs). The energy reservoir for KAWs is provided by the large-scale MHD waves that are widespread in space. Phase mixing, parametric decay instabilities and turbulent cascade work in the same direction: they reduce the perpendicular length scales of MHD waves and convert them into KAWs. Short transversal wavelengths of the order of several proton gyroradii make KAWs accessible for the super-adiabatic acceleration of the ions in the vicinity of demagnetizing wave phases. The resulting ion energization is primarily across the background magnetic field. The main properties of this process are: (i) it is non-resonant, hence it does not need any wave coherence; (ii) it has a well-defined threshold character ; (iii) it can be efficient with rare super-critical waves; (iv) it can be reduced or enforced by the bulk field-aligned ion motion. Title: Ion Heating across the Magnetic Field in the Solar Corona by Kinetic Alfvén Waves Authors: Voitenko, Y.; Goossens, M. Bibcode: 2004ESASP.547..381V Altcode: 2004soho...13..381V The perpendicular heating of the ions observed by SOHO in the solar corona at 2-4 solar radii has been mainly attributed to the ion-cyclotron damping of high-frequency Alfvén waves. We investigate an alternative mechanism of heating by low-frequency Alfvén waves that have short wavelengths across the magnetic field - kinetic Alfvén waves (KAWs). The energy reservoir for these kinetic waves is provided by low-frequency large-scale MHD waves that are launched in the corona by the photospheric motions or excited at the coronal base by magnetic restructuring. The short perpendicular wavelengths, developed by phase mixing, convert MHD Alfvén waves into KAWs. KAWs can be also excited in situ by various linear and nonlinear mechanisms. We show that above a threshold value of the wave amplitude, KAWs can stochastically accelerate ions across the background magnetic field. In particular, KAWs with transversal wavelengths of the order of the ion inertial length and with a wave/background magnetic field ratio of the order 0.1, can contribute to the stochastic heating of oxygen ions O5+ . We discuss advantages of this mechanism over the ion-cyclotron heating scheme for the intense transverse heating of ions observed by SOHO at 2-4 solar radii. Title: Nonlinear damping of MHD waves and origin of solar wind Authors: Voitenko, Yu.; Goossens, M. Bibcode: 2004cosp...35.3973V Altcode: 2004cosp.meet.3973V We propose a new wave model for the fast solar wind heating and acceleration. The principal point of our model is that the energy is deposited in the plasma by the kinetic Alfven waves (KAWs), which have a sufficiently short wavelength across the magnetic field for the dissipative effects to become significant. The energy reservoir is provided by the low-frequency large-scale MHD waves that are far from the dissipative range. Such waves, polarized in the sense of Alfven wave (AW) and/or fast wave (FW), are supposed to be launched in the corona by the photospheric motions or excited at the coronal base by magnetic restructuring. We show that the presence of finite-amplitude MHD waves gives rise to the nonlinear excitation of KAWs via parametric decay, which results in a jump-like transport of MHD wave energy directly in the dissipation range. The part of wave flux polarized in the sense of FW decay very fast, as soon as resonant propagation angle is developed due to wave refraction. The FW-driven KAWs provide heating at low heights, at the coronal base. A flux of MHD AWs propagates farther upward up to the height where plasma beta becomes equal to the electron/ion mass ratio Me/Mi. As soon as plasma beta drops below Me/Mi, MHD AWs undergo a strong parametric decay into KAWs. Due to their short perpendicular wavelengths, the nonlinearly excited KAWs dissipate via collisionless and collisional wave-particle interaction, which, in turn, gives rise to the plasma heating and particles acceleration. Thus, the flux of KAWs, that propagates further upward, can easily increase plasma beta again well above Me/Mi in the high corona and provide the energy source for the solar wind acceleration. Title: Current driven kinetic Alfven instabilities in the solar atmosphere Authors: Voitenko, Yu.; Siverskyy, T.; Goossens, M. Bibcode: 2004cosp...35.4032V Altcode: 2004cosp.meet.4032V We study two physical mechanisms that can cause anomalous dissipation of currents in the solar atmosphere. The first one is a resonant kinetic instability of ion-cyclotron kinetic Alfvén waves (ICKAWs) driven by currents flowing parallel or perpendicular to the background magnetic field [1]. These currents can be generated by coronal magnetic shears or plasma non-uniformity, or by MHD wave phase mixing. Since the frequencies of the excited ICKAWs are close to the proton cyclotron frequency, the inverse turbulent cascade transports the wave energy to lower frequencies where the waves can induce transversal heating of heavier ion species by the ion-cyclotron resonant interaction. Another, non-resonant instability of low-frequency KAWs, can be excited by electrons due to their acceleration in the electric field which is parallel to the magnetic field. Strong, super-Dreicer electric fields, which are required for this instability, can be generated during magnetic reconnection events in the solar atmosphere (flares, micro- and nanoflares). This non-resonant KAW instability can produce low-frequency pulsations of plasma emission, as is observed during solar flares. Both resonant and non-resonant instabilities excite waves with very short transversal wavelengths of the order of the ion gyroradius. This makes these waves accessible for the plasma heating and stochastic ion acceleration across the magnetic field. Both mechanisms transform the energy of currents into the perpendicular energy of ions. The scattering of current electrons by waves results in anomalous transport coefficients and fast energy release. The large transversal temperatures of ions in the places where the energy is released could serve as a signature for these processes. Title: Observational Tests of Damping by Resonant Absorption in Coronal Loop Oscillations Authors: Aschwanden, Markus J.; Nightingale, Richard W.; Andries, Jesse; Goossens, Marcel; Van Doorsselaere, Tom Bibcode: 2003ApJ...598.1375A Altcode: 2003astro.ph..9470A One of the proposed damping mechanisms of coronal (transverse) loop oscillations in the kink mode is resonant absorption as a result of the Alfvén speed variation at the outer boundary of coronal loops. Analytical expressions for the period and damping time exist for loop models with thin nonuniform boundaries. They predict a linear dependency of the ratio of the damping time to the period on the thickness of the nonuniform boundary layer. Ruderman and Roberts used a sinusoidal variation of the density in the nonuniform boundary layer and obtained the corresponding analytical expression for the damping time. Here we measure the thickness of the nonuniform layer in oscillating loops for 11 events, by forward-fitting of the cross-sectional density profile ne(r) and line-of-sight integration to the cross-sectional fluxes F(r) observed with TRACE 171 Å. This way we model the internal (ni) and external electron density (ne) of the coronal plasma in oscillating loops. This allows us to test the theoretically predicted damping rates for thin boundaries as a function of the density ratio χ=ne/ni. Since the observations show that the loops have nonuniform density profiles, we also use numerical results for damping rates to determine the value of χ for the loops. We find that the density ratio predicted by the damping time, χLEDA=0.53+/-0.12, is a factor of ~1.2-3.5 higher than the density ratio estimated from the background fluxes, χ=0.30+/-0.16. The lower densities modeled from the background fluxes are likely to be a consequence of the neglected hotter plasma that is not detected with the TRACE 171 Å filter. Taking these corrections into account, resonant absorption predicts damping times of kink-mode oscillations that are commensurable with the observed ones and provides a new diagnostic of the density contrast of oscillating loops. Title: Nonlinear excitation of kinetic Alfvén waves and whistler waves by electron beam-driven Langmuir waves in the solar corona Authors: Voitenko, Yu.; Goossens, M.; Sirenko, O.; Chian, A. C. -L. Bibcode: 2003A&A...409..331V Altcode: We study a new nonlinear excitation mechanism of kinetic Alfvén waves (KAWs) and whistler waves (Ws) by electron beam-driven Langmuir waves (Ls). The generation conditions for the parametric decay instability L rightleftarrows W + KAW are determined and the growth rate is calculated. We show that the resonant pairs of KAWs and whistler waves are nonlinearly coupled to the pump Langmuir waves and their amplitudes undergo exponential growth from the thermal level. The perpendicular dispersion of KAWs strongly increases the coupling due to the nonlinear current parallel to the ambient magnetic field. Our study suggests that the nonlinear coupling of Langmuir wave energy into KAWs and whistlers can provide an efficient sink for weakly dispersive Langmuir waves excited by fast electron beams in the solar corona when the electron plasma frequency is lower than the electron gyrofrequency. This condition can be satisfied in the low-density magnetic filaments that are rooted in the depleted patches at the coronal base and extend to the high corona. At the same time, the Langmuir-driven KAWs and whistlers give rise to scattering and/or thin structures of radio emission penetrating through, or generated in these regions. Since the decay into sunward propagating KAWs is strongest, the nonlinearly driven KAWs can be easily distinguished from the waves generated at the coronal base and propagating away from the Sun. Our results may be used in the analysis of solar radio data and for remote probing of the coronal plasma, magnetic fields, and waves. Title: An introduction to plasma astrophysics and magnetohydrodynamics Authors: Goossens, Marcel Bibcode: 2003ASSL..294.....G Altcode: 2003ipam.book.....G No abstract at ADS Title: Kinetic Excitation Mechanisms for ION-Cyclotron Kinetic Alfvén Waves in Sun-Earth ConnectionI Authors: Voitenko, Yuriy; Goossens, Marcel Bibcode: 2003SSRv..107..387V Altcode: We study kinetic excitation mechanisms for high-frequency dispersive Alfvén waves in the solar corona, solar wind, and Earth's magnetosphere. The ion-cyclotron and Cherenkov kinetic effects are important for these waves which we call the ion-cyclotron kinetic Alfvén waves (ICKAWs). Ion beams, anisotropic particles distributions and currents provide free energy for the excitation of ICKAWs in space plasmas. As particular examples we consider ICKAW instabilities in the coronal magnetic reconnection events, in the fast solar wind, and in the Earth's magnetopause. Energy conversion and transport initiated by ICKAW instabilities is significant for the whole dynamics of Sun-Earth connection chain, and observations of ICKAW activity could provide a diagnostic/predictive tool in the space environment research. Title: Nonlinear wave dynamics in the dissipation range Authors: Voitenko, Y.; Goossens, M. Bibcode: 2003PADEU..13..153V Altcode: There is abundant observational evidence that the ions in the solar corona (in particular, O(+5) ) are heated anisotropicaly, predominantly across the background magnetic field. This heating is usually attributed to the dissipation of ion-cyclotron waves. We study an alternative possibility with the dissipation range in the solar corona formed by the kinetic Alfvén waves (KAWs) which are very short- wavelengths across the magnetic field. Instead of transport of MHD wave energy towards to the range of ion-cyclotron waves, we study transport into the dissipation range of KAWs. We show that the nonlinear excitation of short-wavelength (of the order 10 m) KAWs in the extended solar corona and solar wind can be provided by upward-propagating fast and Alfvén MHD waves launched from the coronal base by the convection or magnetic reconnection. KAWs are very efficient in the energy exchange with plasma particles, providing plasma heating and particles acceleration. In particular, these transversal wavelengths make KAWs accessible for the stochastic perpendicular heating of oxygen ions when the wave/background magnetic field ratio exceeds 0.005. Both the quasi-steady coronal heating and the transient heating events observed by Yohkoh and SOHO may be due to KAWs that are nonlinearly excited by MHD waves. Title: On the quasi-current-free electrodynamics of current-carrying hot space plasma Authors: Gubchenko, V. M.; Biernat, H. K.; Goossens, M. Bibcode: 2003AdSpR..31.1277G Altcode: A reduced self-consistent kinetic approach is developed for the study of nonlinear plasma electrodynamics near weakly magnetized regions in a current carrying collisionless plasma. In these regions in addition to quasineutral we have quasi-current-free dynamics. Quasi-current free nonlinear plasma dynamics is realized when the diamagnetic spatial dispersion parameter originating from the diamagnetic current is small compared to the plasma and field dynamic scales. In this case, the eddy currents consisting of diamagnetic and resistive parts are mutually compensated. We illustrate this effect in a liner approach to plasma electrodynamics. A quasi MHD beam-like approach to the accelerated electrons forming resistivity and a kinetic approach to the diamagnetic plasma particles allows us to develop an analytical self-similar solution to the one dimensional magnetic annihilation problem. Title: Influence of a uniform coronal magnetic field on solar p-modes Authors: Vanlommel, P.; Debosscher, A.; Andries, J.; Goossens, M. Bibcode: 2002ESASP.506..893V Altcode: 2002svco.conf..893V; 2002ESPM...10..893V The influence of a constant coronal magnetic field on solar global oscillations is investigated for a simple planar equilibrium model. The model consists of an atmosphere with a constant horizontal magnetic field on top of an unmagnetized solar interior. The focus is on the possible resonant coupling of global solar oscillation modes to local slow continuum modes of the atmosphere and the consequent damping of the global oscillations. The physical process of resonant absorption of the acoustic modes with frequency in the cusp continuum is mathematically completely described by the ideal MHD differential equations which for this particular equilibrium model reduce to the hypergeometric differential equation. Title: On the nature of umbral oscillations: theory and observation by CDS/SoHO Authors: Banerjee, D.; O'Shea, E.; Goossens, M.; Poedts, S.; Doyle, J. G. Bibcode: 2002ESASP.506..427B Altcode: 2002ESPM...10..427B; 2002svco.conf..427B We will present solutions for magneto-acoustic-gravity (or MAG) waves. The possible wave modes in the 3-5 min range will be discussed. We will then present observations of sunspots performed in the EUV wavelength range with the Coronal Diagnostic Spectrometer (CDS) on SoHO. We examine the time series for the line intensities and relative velocities and calculate their power spectrum using wavelet transforms. We find oscillations in the chromosphere and transition region above the sunspots in the temperature range logT = 4.6 -5.4. Most of the spectral power above the umbra is contained in the 5-7 mHz frequency range. When the CDS slit crosses the sunspot plume a clear 3 min oscillation is observed. The observations are interpreted in terms of slow magnetoacoustic waves propagating upwards. Title: Damping of coronal loop oscillations by resonant absorption of quasi-mode kink oscillations Authors: Goossens, M.; Andries, J.; Aschwanden, M. J. Bibcode: 2002ESASP.506..629G Altcode: 2002svco.conf..629G; 2002ESPM...10..629G Damped quasi-mode kink oscillations in cylindrical flux tubes are capable of explaining the observed rapid damping of the coronal loop oscillations when the ratio of the inhomogneity length scale to the radius of the loop is allowed to vary from loop to loop. They do not need to invoke anomalously low Reynolds numbers. The theoretical expressions for the decay time by Hollweg & Yang (1988) and Ruderman & Roberts (2002) are used to estimate the ratio of the length scale of inhomogneity compared to the loop radius for a collection of loop oscillations. Title: Coronal loop oscillations. An interpretation in terms of resonant absorption of quasi-mode kink oscillations Authors: Goossens, M.; Andries, J.; Aschwanden, M. J. Bibcode: 2002A&A...394L..39G Altcode: Damped quasi-mode kink oscillations in cylindrical flux tubes are capable of explaining the observed rapid damping of the coronal loop oscillations when the ratio of the inhomogeneity length scale to the radius of the loop is allowed to vary from loop to loop, without the need to invoke anomalously low Reynolds numbers. The theoretical expressions for the decay time by Hollweg & Yang (\cite{hollweg1988}) and Ruderman & Roberts (\cite{ruderman2002}) are used to estimate the ratio of the length scale of inhomogeneity compared to the loop radius for a collection of loop oscillations. Title: On the theory of MAG waves and a comparison with sunspot observations from CDS/SoHO Authors: Banerjee, D.; O'Shea, E.; Goossens, M.; Doyle, J. G.; Poedts, S. Bibcode: 2002A&A...395..263B Altcode: We examine the influence of non-adiabatic effects on the modes of an isothermal stratified magnetic atmosphere. We present new solutions for magneto-acoustic-gravity (or MAG) waves in the presence of a radiative heat exchange based on Newton's law of cooling. An analytic expression for the dispersion relation is derived, which allows the effect of a weak magnetic field on the modes to be studied. The insight so gained proves useful in extending the computations to the moderate-high field case. In the second part we present observations of two sunspots obtained in the EUV wavelength range with the Coronal Diagnostic Spectrometer (CDS) on SoHO. We examine the time series for the line intensities and relative velocities and calculate their power spectra using wavelet transforms. We find oscillations in the chromosphere and transition region above the sunspots in the temperature range log T = 4.6-5.4 K. Most of the spectral power above the umbra is contained in the 5-7 mHz frequency range. When the CDS slit crosses the sunspot umbra a clear 3 min oscillation is observed. The observed oscillation frequencies are compared with the computed frequencies and the observations are interpreted in terms of the slow magneto-acoustic waves. Title: Waves and oscillations in magnetic fields Authors: Goossens, Marcel; de Groof, Anik; Andries, Jesse Bibcode: 2002ESASP.505..137G Altcode: 2002solm.conf..137G; 2002IAUCo.188..137G This paper gives an overview of the theory of MHD waves in magnetic plasma configurations in the solar atmosphere. The emphasis is on basic properties that are independent of specific equilibrium models but are rather related to the intrinsic structuring and non-uniformity of the plasma. The discussion is confined to MHD waves in uniform and 1-d cylindrical equilibrium models of magnetic flux tubes with a straight magnetic field. These models contain sufficient physics for understanding basic properties of MHD waves and still allow for a relatively straightforward and transparent mathematical analysis. Title: Slow MAG waves in the sunspot umbra as observed by CDS/SOHO Authors: Banerjee, D.; O'Shea, E.; Doyle, J. G.; Goossens, M.; Poedts, S. Bibcode: 2002ESASP.505..187B Altcode: 2002solm.conf..187B; 2002IAUCo.188..187B We present observations, in the EUV wavelength range, of two sunspots, carried out by the Coronal Diagostic Spectrometer (CDS) on SoHO. We examine the time series for the line intensities and relative velocities and calculate their power spectrum using wavelet transforms. We find oscillations in the chromosphere and transition region above the sunspots in the temperature range logT = 4.6 - 5.4. Most of the spectral power above the umbra are contained in the 5 - 7 mHz frequency range. When the CDS slit croses the sunspot plume a clear 3 in oscillation is observed. We also present new solutions for magnetic-acoustic-gravity (or MAG) waves in the presence of radiative heat exchange based on Newton's law of cooling. The observed oscillation frequencies are compared with the computed frequencies. The observations are interpreted in terms of slow magnetoacoustic waves propagating upwards. Title: Frame dependence of the negative energy wave formula!? Authors: Andries, Jesse; Goossens, Marcel Bibcode: 2002ESASP.505..341A Altcode: 2002solm.conf..341A; 2002IAUCo.188..341A In this paper we show that the classical negative energy wave (N.E.W.) formula is frame dependent. By analogy with a simple mechanical problem, we show that the negligible second order perturbations become energetically important and function as an energy source for the linear waves. Title: Fast and Alfvén waves driven by azimuthal footpoint motions Authors: de Groof, Anik; Goossens, Marcel Bibcode: 2002ESASP.505..389D Altcode: 2002solm.conf..389D; 2002IAUCo.188..389D The excitation of Alfvén and fast magnetosonic waves in footpoint driven coronal loops is studied in the framework of resonant absorption. Previous studies revealed that in case of radial footpoint motions, quasi-modes are essential for effective wave dissipation in the loops. We now investigate the role they play in azimuthally driven loops. For a periodic driver, the efficiency of resonant absorption strongly depends on the driving frequency ωd: only for quasi-mode frequencies coupling has a positive effect on the growth of the (single) Alfvén resonance. The problem of single-shell heating can be solved by considering a more realistic, random driver: a variety of resonant Alfvén waves are excited and multiple resonant peaks appear, with length scales which are short enough for effective dissipation. When more realistic loop lengths are considered, the resonant surfaces are even more numerous resulting in globally heated loops. Title: Nonlinear excitation of small-scale Alfvén waves by fast waves and plasma heating in the solar atmosphere Authors: Voitenko, Yuriy; Goossens, Marcel Bibcode: 2002SoPh..209...37V Altcode: We study a nonlinear mechanism for the excitation of kinetic Alfvén waves (KAWs) by fast magneto-acoustic waves (FWs) in the solar atmosphere. Our focus is on the excitation of KAWs that have very small wavelengths in the direction perpendicular to the background magnetic field. Because of their small perpendicular length scales, these waves are very efficient in the energy exchange with plasmas and other waves. We show that the nonlinear coupling of the energy of the finite-amplitude FWs to the small-scale KAWs can be much faster than other dissipation mechanisms for fast wave, such as electron viscous damping, Landau damping, and modulational instability. The nonlinear damping of the FWs due to decay FW = KAW + KAW places a limit on the amplitude of the magnetic field in the fast waves in the solar corona and solar-wind at the level B/B0∼10−2. In turn, the nonlinearly excited small-scale KAWs undergo strong dissipation due to resistive or Landau damping and can provide coronal and solar-wind heating. The transient coronal heating observed by Yohkoh and SOHO may be produced by the kinetic Alfvén waves that are excited by parametric decay of fast waves propagating from the reconnection sites. Title: Nonlinear interaction of kinetic Alfvén waves and radio waves in the solar corona Authors: Sirenko, O.; Voitenko, Yu.; Goossens, M. Bibcode: 2002A&A...390..725S Altcode: This paper investigates the nonlinear interaction of short wavelength kinetic Alfvén waves (KAWs) with extraordinary (x-) and ordinary (o-) mode radio waves using two fluid magnetohydrodynamics. The focus is on the interaction of a preexistent KAW with an ordinary electromagnetic wave, giving rise to an extraordinary electromagnetic wave. The equation governing the time evolution of the amplitude of the excited x-mode is derived. The growth time of the x-mode wave is determined and the corresponding interaction distance is computed for active regions in the low corona and for high corona. The nonlinear coupling appears to be quite efficient for reasonable amplitudes of KAWs in the corona, BA/B0=0.02-0.2. We suggest that this process provides a new possibility for the detection and remote sensing of coronal kinetic Alfvén waves by means of radio observations. Title: Fast and Alfvén waves driven by azimuthal footpoint motions. I. Periodic driver Authors: De Groof, A.; Paes, K.; Goossens, M. Bibcode: 2002A&A...386..681D Altcode: The excitation of Alfvén and fast magneto-acoustic waves in coronal loops driven by footpoint motions is studied in linear, ideal MHD. The analysis is restricted to azimuthally polarized footpoint motions so that only Alfvén waves are directly excited which couple to fast magneto-acoustic waves at later times. In the present study a periodic driver is applied at one end of the loop. The effects of a more realistic random driver are studied in the companion paper De Groof & Goossens (2002) (hereafter referred to as Paper II). The first part of the paper is devoted to the study of resonant absorption and phase-mixing in the absence of coupling (azimuthal wavenumber ky=0). Since the density varies across the loop, resonances occur at the magnetic surfaces where the driving frequency equals the local Alfvén frequency. In a second part where Alfvén waves with ky !=q 0 coupling to fast waves are taken into account, we find that the behaviour of the MHD waves is strongly dependent on the driving frequency omegad . Especially driving frequencies equal to a quasi-mode frequency seem to make the difference. The fast waves excited in these cases are global oscillations of the system and form quasi-modes as they are damped through the resonant coupling with Alfvén modes. Since these resonances occur at the same location where the original Alfvén wave peaks, the resonant peak is further amplified. While in most cases coupling has a negative effect on the growth of the directly excited Alfvén waves, driving with a quasi-mode frequency leads to a faster growth of the resonant peaks and a more efficient decrease in length scales than in the uncoupled case. Title: Fast and Alfvén waves driven by azimuthal footpoint motions. II. Random driver Authors: De Groof, A.; Goossens, M. Bibcode: 2002A&A...386..691D Altcode: The excitation of Alfvén and fast magneto-acoustic waves in coronal loops driven by footpoint motions is studied in linear, ideal MHD. The analysis is restricted to azimuthally polarized footpoint motions so that only Alfvén waves are directly excited to couple to fast magneto-acoustic waves at later times. In the companion paper De Groof et al. (\cite{Groof02a}) (hereafter referred to as Paper I), the behaviour of the MHD waves is studied in case of a monochromatic driver. In the present study, the effects of a more realistic random driver are investigated.\ First, we consider loops of equal length and width in order to limit the number of quasi-modes in the frequency range of the driver so that the influence of quasi-modes in the system can easily be detected. In contrast to the single resonant surface which was found in case of a periodic driver (see Paper I), a random pulse train excites a variety of resonant Alfvén waves and consequently the small length scales built up are spread over the whole width of the loop. The specific effects of the quasi-modes are not so easily recognized as for radial footpoint motions (De Groof & Goossens \cite{Groof00a}) since the resonances corresponding to directly and indirectly excited Alfvén waves are mixed together. In the second part of the paper, longer loops are considered. Since more quasi-modes are involved, the resonant surfaces are more numerous and widely spread throughout the whole loop volume. On the other hand, it takes more time for the MHD waves to cross the loop and to form standing waves. Nevertheless this negative effect does not have too much impact since the simulations show that after a small time interval, resonant surfaces are created all over the loop, with length scales which are short enough for effective dissipation. Title: Excitation of high-frequency Alfvén waves by plasma outflows from coronal reconnection events Authors: Voitenko, Yuriy; Goossens, Marcel Bibcode: 2002SoPh..206..285V Altcode: We study a kinetic excitation mechanism for high-frequency dispersive Alfvén waves in the solar corona by magnetic reconnection events. The ion-cyclotron and Cerenkov kinetic effects are important for these waves which we call the ion-cyclotron kinetic Alfvén waves (IC KAWs). The plasma outflowing from the reconnection site sets up a neutralized proton beam in the surrounding plasma, providing free energy for the excitation of waves. The dependence of the phase velocity of the IC KAW on the parallel wavenumber is different from that on the perpendicular wavenumber. The phase velocity is an increasing function of the perpendicular wavenumber and overtakes the Alfvén velocity for sufficiently large values of k⊥. However, the phase velocity is a decreasing function of k∥, and sufficiently large values of k∥ result in a phase velocity below the Alfvén velocity. As a result, the IC KAWs can undergo the Cerenkov resonance with both super- and sub-Alfvénic particles, and for the waves to be excited the outflow velocity does not need to be super-Alfvénic, as for KAWs, but the beam/Alfvén velocity ratio can span a wide range of values. High growth rates of the order of γ∼104 s−1 are found for the values of the plasma parameters typical for the low solar corona. The waves excited by (sub-)Alfvénic beams are damped mainly due to kinetic wave-particle interactions with ions at the cyclotron resonance (ion-cyclotron damping), and with ions and electrons at the Cerenkov resonance (Landau damping). Therefore, IC KAWs can heat the plasma species of the corona in both the parallel and perpendicular direction, giving rise to an anisotropic heating of the ions. The observational consequences of the processes under study are discussed. Title: Long-Period Oscillations in Polar Coronal Holes as Observed by CDS on SOHO Authors: Banerjee, D.; O'Shea, E.; Doyle, J. G.; Goossens, M. Bibcode: 2002mwoc.conf...19B Altcode: We examine spectral time series of the coronal line Mg ix 368Å, the transition region line O v 629Å, and the chromospheric line He i 584Å observed during several periods of 2000, with the Coronal Diagnostic Spectrometer (CDS) onboard the SoHO spacecraft. We study different parts of coronal holes, plumes and inter-plumes (off-limb) as a separate study. We report here on a time series analysis, using wavelet methods, of small individual regions in the polar coronal hole. The wavelet analysis allows us to derive the duration as well as the periods of the oscillations. The statistical significance of the oscillations was estimated by using a randomisation method. Our observations indicate the presence of compressional waves with periods of 20-30 minutes or longer. These slow magneto-acoustic waves may provide enough energy flux for the acceleration of the fast solar wind. Title: Influence of a uniform coronal magnetic field on solar p modes: coupling to slow resonant MHD waves Authors: Vanlommel, P.; Debosscher, A.; Andries, J.; Goossens, M. Bibcode: 2002SoPh..205....1V Altcode: The influence of a constant coronal magnetic field on solar global oscillations is investigated for a simple planar equilibrium model. The model consists of an atmosphere with a constant horizontal magnetic field and a constant sound speed, on top of an adiabatic interior having a linear temperature profile. The focus is on the possible resonant coupling of global solar oscillation modes to local slow continuum modes of the atmosphere and the consequent damping of the global oscillations. In order to avoid Alfvén resonances, the analysis is restricted to propagation parallel to the coronal magnetic field. Parallel propagating oscillation modes in this equilibrium model have already been studied by Evans and Roberts (1990). However, they avoided the resonant coupling to slow continuum modes by a special choice of the temperature profile. The physical process of resonant absorption of the acoustic modes with frequency in the cusp continuum is mathematically completely described by the ideal MHD differential equations which for this particular equilibrium model reduce to the hypergeometric differential equation. The resonant layer is correctly dealt with in ideal MHD by a proper treatment of the logarithmical branch cut of the hypergeometric function. The result of the resonant coupling with cusp waves is twofold. The eigenfrequencies become complex and the real part of the frequency is shifted. The shift of the real part of the frequency is not negligible and within the limit of observational accuracy. This indicates that resonant interactions should definitely be taken into account when calculating the frequencies of the global solar oscillations. Title: Influence of a Uniform Coronal Magnetic Field on Solar p Modes: Coupling to Slow Resonant MHD Waves Authors: Vanlommel, P.; Debosscher, A.; Andries, J.; Goossens, M. Bibcode: 2002ASPC..259..480V Altcode: 2002rnpp.conf..480V; 2002IAUCo.185..480V No abstract at ADS Title: Signatures of very long period waves in the polar coronal holes Authors: Banerjee, D.; O'Shea, E.; Doyle, J. G.; Goossens, M. Bibcode: 2001A&A...380L..39B Altcode: We examine long spectral time series of a coronal hole observed on the 7th March 2000 with the Coronal Diagnostic Spectrometer (CDS) on-board SoHO. The observations were obtained in the chromospheric He I, and a series of higher temperature oxygen lines. In this letter we report on the presence of long period oscillations in a polar coronal hole region on the disk. Our observations indicate the presence of compressional waves with periods of 20-30 min or longer. Title: Long period oscillations in the inter-plume regions of the Sun Authors: Banerjee, D.; O'Shea, E.; Doyle, J. G.; Goossens, M. Bibcode: 2001A&A...377..691B Altcode: We examine long spectral time series of inter-plume lanes observed on the 14th and 15th March 2000 with the Coronal Diagnostic Spectrometer (CDS) on-board SoHO. The observations were obtained in lines over a wide temperature range, from the chromosphere to the corona. The statistical significance of the oscillations was estimated by using a randomisation method. Our observations indicate the presence of compressional waves with periods of 20-50 min or longer, both off-limb and on-disk and up to 70 min further out to at least 25 arcsec off-limb. To our knowledge this is the first time that long period oscillations in the inter-plume regions close to the limb of the Sun have been detected. We interpret these oscillations as outward propagating slow magneto-acoustic waves which may contribute significantly to the heating of the lower corona by compressive dissipation and which may also provide some of the enough energy flux required for the acceleration of the fast solar wind. These slow waves may have been produced at the network boundaries in the coronal hole. Title: Hidden problems of thin-flux-tube approximation Authors: Zhugzhda, Y. D.; Goossens, M. Bibcode: 2001A&A...377..330Z Altcode: This paper scrutinizes the validity of the thin-flux-tube approximation for magnetic flux tubes embedded in a surrounding magnetic plasma. It is shown that the thin-flux-tube approximation gives an accurate description of surface waves for CT2> CAe2, body waves for C_Te2> CT2 and surface leaky waves for CTe2< CT2 < CAe2. The Leibovich-Roberts equation for nonlinear surface waves in a flux tube embedded in a field free plasma is generalized to a flux tube immersed in a magnetic plasma. The generalized Leibovich-Roberts (GLR) equation describes the propagation of nonlinear slow surface, body and surface leaky waves in tubes. The shortcomings of the GLR equation are discussed. The Korteweg-de Vries equation (KdV) is generalized for surface waves. The advantage of the second order thin-flux-tube approximation is shown. Two scenarios for the heating of coronal loops are discussed. It is emphasized, that the application of the thin-flux-tube approximation to thin tubes of non-zero diameter has to take into account possible wave emission by the tube and shock front formation for amplitudes in excess of some critical value. Title: The influence of resonant MHD wave coupling in the boundary layer on the reflection and transmission process Authors: Andries, J.; Goossens, M. Bibcode: 2001A&A...375.1100A Altcode: When a wave is incident on an inhomogeneous boundary layer separating two plasmas in relative motion, it is often argued that the resonant absorption rate can become negative when there is a sufficiently large velocity shear, thus giving energy back to the wave. However such treatment fails to distinguish the two energy exchange processes that are operative: extraction of wave energy by dissipative processes around the resonance point and energy exchange between the wave and the flow of the medium. By aid of the proper wave energy definitions recently discussed by Walker (\cite{walker}), rather than by the conventional concept of ``negative energy" waves we reveal the important dependence of the resonant amplification process on the precise structure of the boundary layer profiles. We conclude that stratification in boundary layers is very important not only because the resulting wave coupling can cause resonant instabilities for velocity shears below the Kelvin-Helmholtz threshold, but also because the coupling can stabilize the Kelvin-Helmholtz instability above this threshold. Title: On the role of ion-cyclotron kinetic Alfvén waves in the solar wind: results from HELIOS and expectations for Solar Orbiter Authors: Voitenko, Yu.; Goossens, M.; Marsch, E. Bibcode: 2001ESASP.493..411V Altcode: 2001sefs.work..411V No abstract at ADS Title: The nature of network oscillations Authors: Banerjee, D.; O'Shea, E.; Doyle, J. G.; Goossens, M. Bibcode: 2001A&A...371.1137B Altcode: We examine time-series of spectral data obtained from the Coronal Diagnostic Spectrometer (CDS) and the Solar Ultraviolet Measurements of Emitted Radiation instrument (SUMER) onboard the Solar Heliospheric Observatory (SOHO) spacecraft, in the period 30-31 July 1996. The observations were obtained in lines, ranging in temperature from 12 000 K to 106 K, covering the low chromosphere to the corona. We report here on a time series analysis, using wavelet methods, of small individual network regions in the quiet Sun. The wavelet analysis allows us to derive the duration as well as the periods of the oscillations. The statistical significance of the oscillations was estimated by using a randomisation method. The oscillations are considered to be due to waves, which are produced in short bursts with coherence times of about 10-20 min. The low chromospheric and transition region lines show intensity and velocity power in the 2-4 mHz range. The coronal line Mg x does not show any statistically significant power in this range. In general, it is thought likely that the chromosphere and possibly the transition region oscillates in response to forcing by the p-modes, but they are also influenced strongly by the presence of magnetic fields. The observed 2-4 mHz network oscillations can thus be interpreted in terms of kink and sausage waves propagating upwards along thin magnetic flux tubes. We perform a linear numerical computation comparing the results with our observations. Title: Nonlinear resonant absorption of fast magnetoacoustic waves due to coupling into slow continua in the solar atmosphere Authors: Erdélyi, R.; Ballai, I.; Goossens, M. Bibcode: 2001A&A...368..662E Altcode: Nonlinear resonant absorption of fast magnetoacoustic (FMA) waves in inhomogeneous weakly dissipative, isotropic and anisotropic plasmas in static and steady equilibria is studied. Both isotropic and anisotropic plasmas are considered and for the background equilibrium state 1D planar static and steady models are used. The equilibrium configuration consists of three layers, where an inhomogeneous magnetised plasma slab is surrounded by two homogeneous magnetised semi-infinite plasma regions. The propagating FMA waves are partly absorbed due to coupling to local nonlinear slow magnetohydrodynamic (MHD) waves in the inhomogeneous layer, and are partly reflected. The coefficient of wave energy resonant absorption is derived using two simplifying assumptions (i) weak nonlinearity and (ii) the thickness of the inhomogeneous layer is small compared to the wavelength of the waves, i.e. the so-called long-wavelength approximation is used. Title: Kelvin-Helmholtz instabilities and resonant flow instabilities for a coronal plume model with plasma pressure Authors: Andries, J.; Goossens, M. Bibcode: 2001A&A...368.1083A Altcode: In this paper we continue the study of the effect of the velocity shear between the coronal plume and the interplume region on the spectrum of MHD waves trapped in the plume. In Andries et al. (\cite{andries}) we have illustrated the concept of resonant flow instability of the trapped modes both in a 1-D slab model and a 1-D cylindrical model for a coronal plume in which plasma-pressure was neglected. The important result of that paper was that the threshold values of the velocity shear are significantly smaller for resonant instability than for Kelvin-Helmholtz instability to occur. The aim of this paper is to study the effect of plasma pressure on the eigenmodes of the plume. As expected we find slow waves in addition to the fast waves. Furthermore there are two different types of Kelvin-Helmholtz instability. Along with the fact that now not only Alfvén but also slow resonances can occur this all leads to a wide variety of ranges of the velocity shear for which instability can be present. Estimates of these ranges for different equilibrium quantities can be obtained without going through the elaborate numerical procedures of calculating the eigenmodes. We show that the instability that will most probably occur in coronal plumes is due to an Alfvén resonance of slow body modes. These instabilities could lead to disruption of the coronal plumes and to the mixing with interplume plasma. However we point out that there might be a strong dependence of the resonant flow instability upon the velocity profile that is to be investigated further. Title: On the nature of network oscillations Authors: Banerjee, D.; O'Shea, E.; Doyle, J. G.; Goossens, M.; Fleck, B. Bibcode: 2001ESASP.464..175B Altcode: 2001soho...10..175B We examine time-series of spectral data obtained from the Solar Ultraviolet Measurements of Emitted Radiation instrument (SUMER), on board SOHO in the period 10-31 July 1996. Observations were obtained in lines, ranging in temperature from 12,000 K to 106K, covering the low chromosphere to the corona. In this short contribution we report on the time series analysis on one of these dataset, using wavelet methods, of small individual network regions in the quiet Sun. The wavelet analysis allows us to derive the duration as well as the periods of the oscillations. The statistical significance of the oscillations was estimated by using a randomisation method. The oscillations are considered to be due to waves, which are produced in short bursts with coherence times of about 10-20 minutes. The low chromospheric and transition region lines show intensity and velocity power in the 2.4 mHz range. The observed 2-4 mHz network oscillations can be interpreted in terms of kink and sausage waves propagating upwards along thin magnetic flux tubes. The kink waves can be generated by random foot-point motions, e.g. by exploding granules, at the photospheric level. As they propagate within flux tubes, their amplitude grows exponentially with height and becomes non-linear. The waves can thereby undergo a mode transformation and become sausage type waves, which are more easily detected on the disk. Title: Nonlinear Damping of Fast Waves and Plasma Heating in the Solar Corona Authors: Voitenko, Y.; Goossens, M. Bibcode: 2001IAUS..203..517V Altcode: Fast waves can be excited in the corona by compressional perturbations of magnetic field lines which are anchored into the dense convective zone and displaced by the plasma motions there. The consequent linear dissipation of fast waves in the resonant layers can contribute to coronal heating. A difficulty of this dissipation mechanism is that the setup time of the linear resonance (the time required for the creation of sufficiently short length-scales) is long compared to the sub-minute variations in the coronal heating process. This suggests a more effective mechanism for the structurization of waves in the solar corona. We propose a new, nonlinear mechanism for the dissipation of fast waves in the corona. In the framework of two-fluid MHD we show that fast waves are nonlinearly coupled to the kinetic Alfvén waves - Alfvén waves with short wavelengths across B0, background magnetic field. The nonlinear coupling is effective for the amplitudes of the launched fast waves in the range 0.01 to 0.03 for B/B0 (B is wave magnetic field), implied by spectroscopic observations. As the excited AWs have very short wavelengths, they are damped almost immediatelly by the linear kinetic or collisional dissipation. Therefore, the resulting plasma heating has the overall timescale of the order of the characteristic time of nonlinear interaction, which can easily be in the sub-minute range. Title: Long Period Oscillations in Polar Plumes as observed by CDS on SoHO Authors: Banerjee, D.; O'Shea, E.; Doyle, J. G.; Goossens, M. Bibcode: 2001IAUS..203..244B Altcode: We examine spectral time series of coronal line Mg IX 368 Å and transition region line O V 629 Å, observed with the Coronal Diagnostic Spectrometer (CDS) onboard the SOHO spacecraft. Primarily we were looking for intensity and velocity oscillations in polar plumes, however by chance we detected a giant macro-spicule at the limb and were able to follow its dynamical structure. Blue and red-shifted emission in the O V line indicates that it is probably a rotating twisted magnetic jet. Emission is also detected in the Mg IX 368 Å line, at a temperature of 1 million K. Both Fourier and wavelet transforms have been applied independently to the analysis of the oscillations in order to find the most reliable periods. We report here on the existence of long period oscillations in the polar plumes as observed in the O V 629 Å line. Our observations indicate the presence of compressional waves with periods of 20-25 minutes. Title: Influence of equilibrium flows and the atmospheric magnetic field on solar oscillation modes Authors: Pintér, B.; Erdélyi, R.; New, R.; Goossens, M. Bibcode: 2001ESASP.464..227P Altcode: 2001soho...10..227P The competing effects of an atmospheric magnetic field and an equilibrium flow in the internal regions of the Sun are studied on the helioseismic f- and p-modes. The Sun is modeled as a multi-layered plasma, where the upper parts, representing the chromosphere and corona, are embedded in a unidirectional though inhomogeneous magnetic field, meanwhile the lower part, representing the sub-photospheric polytropic region, is in a steady equilibrium state. The steady state sub-surface region can be considered as a first approximation of dynamic motions (e.g., convective motion, differential rotation, sub-surface flows, meridional flows, etc.). The obtained frequency shifts of the different eigenmodes are associated with flow and magnetic effects. We also found damping of the eigenfrequencies which apparently can be associated with the universal mechanism of resonant absorption. Resonant absorption (already known as a viable heating mechanism in the solar corona) is present due to inhomogeneities in the atmosphere which give rise to Alfvén and slow continua. Damping of helioseismic modes occurs when the modes are coupled into these continua. When both atmospheric magnetic field and sub-surface flows are present, a complex picture of competition of these two effects is found. The theoretically predicted frequency shifts in a steady state are in excellent agreement with the observed values. For related works see also the papers by Erdélyi & Taroyan and Varga & Erdélyi in the present Volume. Title: Alfvén waves in space plasmas: dispersive and kinetic effects Authors: Voitenko, Yu.; Goossens, M.; Yukhimuk, A.; Voytsekhovskaia, A. Bibcode: 2001KosNT...7S..67V Altcode: New linear and nonlinear properties of Alfvén waves induced by finite-ion-Larmor radius effects in space plasmas are discussed. Title: Nonlinear coupling of O- and X-mode radio emission and Alfven waves in the solar corona Authors: Sirenko, O.; Voitenko, Yu.; Goossens, M.; Yukhimuk, A. Bibcode: 2000AIPC..537..287S Altcode: 2000wdss.conf..287S The nonlinear coupling of extraordinary and ordinary waves via kinetic Alfven waves (KAWs) is investigated on the basis of two fluid magnetohydrodynamics. The equation governing the time dependence of electric field of excited O-mode is found. We estimate the time of effective coupling between modes and corresponding interaction distance in solar corona. Our theoretical results show that the X- and O-mode couplings via Alfven waves can be efficient depolarization mechanism for the coronal radioemission. . Title: Resonant absorption in randomly driven coronal loops Authors: de Groof, Anik; Goossens, Marcel Bibcode: 2000AIPC..537..208D Altcode: 2000wdss.conf..208D De Groof et al. '98 [1] and '00 [2] studied the time evolution of fast magnetosonic and Alfvén waves in a coronal loop driven by radially polarized footpoint motions in linear ideal MHD. Footpoint driving seems to be an efficient way of generating resonant absorption since the input energy is mainly stored in body modes which keep the energy in the loop. The most important feature in this study is the stochastic driving of the loop. While in earlier models with a periodic driver or a single pulse, the loop is only heated at one single layer, we now find multiple resonance layers which results in a more globally heated loop. Moreover, these resonances (created on a realistic time scale) have length scales which are small enough to explain energy dissipation. An important aspect to take into account is the mass transfer between corona and chromosphere since the density becomes time dependent and consequently, the resonant surfaces shift throughout the loop [3]. Combined with the multiple resonances we found in the previous study, this result can lead to the globally heated coronal loops we observe. . Title: Linear dynamics of the solar convection zone: Excitation of waves in unstably stratified shear flows Authors: Chagelishvili, G. D.; Tevzadze, A. G.; Goossens, M. Bibcode: 2000AIPC..537..200C Altcode: 2000astro.ph..6132C; 2000wdss.conf..200C In this paper we report on the nonresonant conversion of convectively unstable linear gravity modes into acoustic oscillation modes in shear flows. The convectively unstable linear gravity modes can excite acoustic modes with similar wave-numbers. The frequencies of the excited oscillations may be qualitatively higher than the temporal variation scales of the source flow, while the frequency spectra of the generated oscillations should be intrinsically correlated to the velocity field of the source flow. We anticipate that this nonresonant phenomenon can significantly contribute to the production of sound waves in the solar convection zone. . Title: Long period oscillations in the polar plumes Authors: Banerjee, D.; O'Shea, E.; Doyle, J. G.; Goossens, M. Bibcode: 2000AIPC..537..160B Altcode: 2000wdss.conf..160B We examine spectral time series of the transition region line O v 629 Å, observed with the Coronal Diagnostic Spectrometer (CDS) on the SoHO spacecraft. Both Fourier and wavelet transforms have been applied independently to the analysis of plume oscillations in order to find the most reliable periods. The wavelet analysis enables us to derive the duration as well as the periods of the oscillations. Our observations indicate the presence of compressional waves with periods of 10-20 minutes. We have also detected a 10+/-2 minute periodicity in the network regions of the north polar coronal hole. The waves are produced in short bursts with coherence times of about 20-30 minutes. We interpret these oscillations as outward propagating slow magneto-acoustic waves, which may contribute significantly to the heating of the lower corona by compressive dissipation and which may also provide enough energy flux for the acceleration of the fast solar wind. The data support the idea that the same driver is responsible for the network and plume oscillations with the network providing the magnetic channel through which the waves propagate upwards from the lower atmosphere to the plumes. . Title: Note on dispersive Alfven waves in the solar corona Authors: Voitenko, Yu.; Goossens, M.; Shukla, P.; Stenflo, L. Bibcode: 2000AIPC..537..303V Altcode: 2000wdss.conf..303V The dispersive (kinetic) Alfvén waves in the ion-cyclotron frequency regime (ICKAWs), with frequencies close to the ion cyclotron frequency and with wavelengths close to the ion gyroradius, are studied in view of their ability to interact strongly with the plasma of solar corona. The combined action of finite ion cyclotron frequency and finite ion gyroradius effects has a profound influence on the Alfvén wave. The phase velocity of ICKAWs along the background magnetic field can be slower than the Alfvén velocity (due to finite ion cyclotron frequency effects), but also faster than the Alfvén velocity (due to finite ion gyroradius effects). The phase velocity depends on both the perpendicular and parallel wavenumbers, and spans a range of velocities from sub-Alfvénic to super-Alfvénic. Since these waves have a field-aligned component of electric field, they undergo Cherenkov resonant interaction and can be excited by the ion beam component set up in the low corona by the reconnection outflows from chromospheric reconnection events. . Title: Linear and nonlinear waves in dilute plasmas Authors: Ballai, István; Erdélyi, Róbert; Goossens, Marcel Bibcode: 2000AIPC..537..152B Altcode: 2000wdss.conf..152B Small-amplitude magnetohydrodynamic (MHD) waves are studied in a dilute collisionless plasma with an anisotropic pressure distribution. The parallel and perpendicular pressure are defined with the aid of two polytropic pressure laws. For specific values of the polytropic indices, previous results obtained with the usual Chew-Goldberger-Low (CGL) double-adiabatic (i) and double-isothermal (ii) models are recovered. The double-polytropic model can be considered as the counterpart of the single-polytropic model. Dispersion relations for the linear waves are derived and analyzed in the presence of pressure anisotropy. The weakly nonlinear dynamics is shown to be governed by the Benjamin-Ono equation. The results are discussed in the CGL and double-isothermal limits. . Title: Absorption of fast magnetosonic waves in the solar atmosphere in the limit of weak nonlinearity Authors: Ballai, István; Erdélyi, Róbert; Goossens, Marcel Bibcode: 2000AIPC..537..144B Altcode: 2000wdss.conf..144B We study the resonant absorption of fast magnetoacoustic (FMA) waves in inhomogeneous weakly dissipative, isotropic and anisotropic plasmas. The equilibrium states on which the waves are superimposed is static or stationary and are assumed to be in a 1-D planar geometry. The equilibrium model consists of three layers with an inhomogeneous magnetized plasma surrounded by two homogeneous magnetized semi-infinite plasmas. The propagating FMA waves are partly absorbed and partly reflected by coupling to local nonlinear slow magnetohydrodynamic (MHD) waves in the inhomogeneous layer. The dissipation acts only in a narrow layer called the dissipative layer which embraces the resonant magnetic surface. In linear theory it has been shown that in the vicinity of the resonant surface the energy density, the amplitudes of waves and the spatial gradients become large, suggesting that in this region nonlinearity might be important. The wave motions far from the dissipative layer are described by the linear, ideal MHD equations, while inside this layer the wave motions are governed by the full system of the dissipative, nonlinear MHD equations. The coefficient of wave energy resonant absorption is derived assuming weak nonlinearity and long-wavelength approximation. . Title: Alternating current generation in flux tubes by pressure fluctuations Authors: Zhugzhda, Yuzef; Goossens, Marcel Bibcode: 2000AIPC..537..317Z Altcode: 2000wdss.conf..317Z Alternating current in flux tubes is one of the possible contributors to the heating of the solar corona. The mechanism of the generation of alternating currents in flux tubes by turbulent pressure fluctuations in convective zone is proposed. The thin-flux-tube approximation shows, that the linear and weakly nonlinear torsional waves in twisted flux tube, are accompanied by tube cross section fluctuations. Consequently, external pressure fluctuations generate not only slow MHD waves but torsional waves as well. The torsional waves are nothing else than alternating current. . Title: Kelvin-Helmholtz instability and resonant flow instability in a 1-dimensional coronal plume model Authors: Andries, J.; Goossens, M. Bibcode: 2000AIPC..537..136A Altcode: 2000wdss.conf..136A In a previous paper we have illustrated the concept of resonant flow instability of the trapped modes both in a 1-D slab model and a 1-D cylindrical model for a coronal plume in a cold plasma. We found that much larger values of the velocity shear are needed for Kelvin-Helmholtz than for resonant instability to occur. The aim of this paper is to study the effect of a non-zero plasma pressure on the eigenmodes of the plume structure. We show that the instability most probably to occur in coronal plumes is due to the resonant coupling of slow body modes to local resonant Alfvén waves. These instabilities could lead to disruption of the coronal plumes and to the mixing with interplume plasma. . Title: Kinetic Alfvén turbulence and non-thermal broadening in solar flares Authors: Voitenko, Yu.; Goossens, M. Bibcode: 2000KFNTS...3..437V Altcode: Recent observations of soft X-ray nonthermal line broadening and hard X-ray emission in solar flares suggest that the nonthermal broadening is due to plasma turbulence created in the energy release. We develop a model of the impulsive excitation of Alfvén wave turbulence and propose the mechanism for the interruption of spectral energy fluxes in flaring loops. This interruption determines the nonthermal broadening in flares and is important for the selective heating of plasma species and for the acceleration of particles to high energies. Title: Frequency dependence of resonant absorption and over-reflection of magnetosonic waves in nonuniform structures with shear mass flow Authors: Csík, Á. T.; Čadež, V. M.; Goossens, M. Bibcode: 2000A&A...358.1090C Altcode: Processes of resonant absorption and over-reflection of magnetosonic modes may occur in nonuniform plasmas with a shear mass flow along the magnetic field. In this work, we study how these two phenomena depend on the frequency omega of waves propagating in a given direction prescribed by polar angles theta and phi of wave vector vec k. Plasma is assumed nonuniform within a transitional layer that separates two semi-infinite uniform regions. The considered wave propagates only in one of the two regions and is reflected from the nonuniform transitional layer either totally or partially depending on the efficiency of resonant processes. The resonant absorption and over-reflection are strongly dependent on wave frequency for both the slow and fast magnetosonic mode as shown in corresponding figures. Under conditions relevant to the solar atmosphere, we found that typical MHD waves with periods from few seconds up to much larger values of several minutes and more, can be resonantly absorbed and also over-reflected. This important fact has to be taken into account in making models of energy transports in the corona. Title: Competition of damping mechanisms for the phase-mixed Alfvén waves in the solar corona Authors: Voitenko, Y.; Goossens, M. Bibcode: 2000A&A...357.1086V Altcode: The competition of the linear and nonlinear damping mechanisms for phase-mixed Alfvén waves in the solar corona is studied. It is shown that the nonlinear damping of the phase-mixed Alfvén waves due to their parametric decay is stronger than both collisional and Landau damping for waves with frequencies below a critical frequency which depends on the wave amplitude. This critical frequency is close to the cyclotron frequency ( ~ 105 s-1 in holes) even for small wave amplitudes of the order of 1% of the background value for the magnetic field. This means that the dissipation of the Alfvén wave flux in the corona can be significantly affected by the nonlinear wave dynamics. Nonlinear decay of the low-frequency Alfvén waves transmits a part of the wave energy from the length-scales created by phase mixing to smaller scales, where the waves damp more strongly. However, the direction of the effect can be reversed in the high-frequency domain, 10 s-1<allowbreak omega <allowbreak 104 s-1, where the decay into counterstreaming waves is strongest, because the wave energy is quickly transferred to larger scales, where the actual dissipation is reduced. These effects are introduced by the vector nonlinearity which involves waves propagating in the different directions across magnetic field. The effects introduced by the scalar nonlinearity may also become important in phase mixing (Voitenko & Goossens, in preparation). Title: Nonlinear decay of phase-mixed Alfvén waves in the solar corona Authors: Voitenko, Yu.; Goossens, M. Bibcode: 2000A&A...357.1073V Altcode: This paper presents an analytical investigation of the nonlinear interaction of phase-mixed Alfvén waves in the framework of two-fluid magnetohydrodynamics. It focuses on the parametric decay of the phase-mixed pump Alfvén wave into two daughter Alfvén waves. This parametric decay is a nonlinear phenomenon which does not occur in ideal MHD since it is induced by the combined action of finite wave amplitude and the non-zero gyroradius of the ions. In contrast to intuitive expectation, the effects of the non-zero gyroradius of the ions are already important at length scales that are substantially longer than the ion gyroradius. The parametric decay occurs for relatively small wave amplitude and is more efficient than collisional damping. Title: Randomly driven fast waves in coronal loops. II. with coupling to Alfvén waves Authors: De Groof, A.; Goossens, M. Bibcode: 2000A&A...356..724D Altcode: We study the time evolution of fast magnetosonic and Alfvén waves in a coronal loop driven by random footpoint motions. The footpoint motions are assumed to be polarized normal to the magnetic flux surfaces in linear ideal MHD. De Groof et al. (1998) (Paper I) showed that the input energy is mainly stored in the body modes when the fast waves are decoupled from the Alfvén waves. Hence driving at the loop's feet forms a good basis for resonant absorption as heating mechanism. In order to determine the efficiency of resonant absorption, we therefore study the energy transfer from the body modes to the resonant Alfvén waves in the case of coupling. We find that the growth of Alfvén mode energy depends on several parameters. Subsequently we check whether the necessary small lengthscales are created on a realistic time scale for the coronal loop. We find that Alfvén resonances are built up at the magnetic surfaces, where local Alfvén frequencies equal the quasi-modes frequencies, on time scales comparable to the lifetime of the loop. Finally we conclude that a random footpoint driving can produce enough resonances to give rise to a globally heated coronal loop. Title: Modified Kelvin-Helmholtz Instabilities and Resonant Flow Instabilities in a One-dimensional Coronal Plume Model: Results for Plasma β=0 Authors: Andries, J.; Tirry, W. J.; Goossens, M. Bibcode: 2000ApJ...531..561A Altcode: In this manuscript we study the effect of the velocity shear in the mass flow between the coronal plume structure and the interplume region on the spectrum of magnetohydrodynamic (MHD) waves trapped in the plume structure. To illustrate the concept of resonant flow instability of the trapped modes, we consider both a one-dimensional slab model and a one-dimensional cylindrical model for a coronal plume. A nonuniform intermediate region between the plume and the interplume region is taken into account so that the waves can be subject to resonant absorption. We show how the resonance can lead to instability of the trapped modes and that this resonant instability, which is physically distinct from the nonresonant Kelvin-Helmholtz instability, occurs for velocity shears significantly below the Kelvin-Helmholtz threshold. These resonant flow instabilities could lead to disruption of the coronal plumes and mixing with interplume plasma. The dependence of the critical velocity shear for which the resonant instability occurs on the difference between plume and interplume density is investigated. Our results seem to suggest that resonant flow instability in a pressureless plasma will only appear for rather high density contrasts. However, it is clearly shown that the velocity shear needed for Kelvin-Helmholtz instability to occur is too high for all density contrasts. Hence, Kelvin-Helmholtz instability will not be operative in pressureless coronal plumes. Title: Slow surface wave damping in plasmas with anisotropic viscosity and thermal conductivity Authors: Ruderman, M. S.; Oliver, R.; Erdélyi, R.; Ballester, J. L.; Goossens, M. Bibcode: 2000A&A...354..261R Altcode: This paper studies the damping of slow surface MHD waves propagating along the equilibrium magnetic field on a finite-thickness magnetic interface. The plasma is assumed to be strongly magnetised, and the full Braginskii's expressions for viscosity and the heat flux are used. The primary focus of the paper is on the competition between resonant absorption in the thin dissipative layer embracing the ideal resonant position and the bulk wave damping due to viscosity and thermal conductivity as damping mechanisms for surface MHD waves. The dependence of the wave damping decrement on the wave length and the dissipative coefficients is studied. Application of the obtained results to the surface MHD wave damping in the solar chromosphere is discussed. Title: Waves in Dusty, Solar, and Space Plasmas Authors: Verheest, F.; Goossens, M.; Hellberg, M. A.; Bharuthram, R. Bibcode: 2000AIPC..537.....V Altcode: 2000wdss.conf.....V No abstract at ADS Title: Nonlinear Evolution and Interaction of Phase-Mixed Alfvén Waves in Solar Corona Authors: Voitenko, Yu. M.; Goossens, M. Bibcode: 1999ESASP.448..409V Altcode: 1999mfsp.conf..409V; 1999ESPM....9..409V No abstract at ADS Title: Randomly Driven Fast Waves in Coronal Loops Authors: de Groof, A.; Goossens, M. Bibcode: 1999ESASP.448..251D Altcode: 1999ESPM....9..251D; 1999mfsp.conf..251D No abstract at ADS Title: Influence of a Chromospheric Magnetic Field on Solar Acoustic Modes Authors: Vanlommel, P.; Goossens, M. Bibcode: 1999ESASP.448..399V Altcode: 1999ESPM....9..399V; 1999mfsp.conf..399V No abstract at ADS Title: Turbulent Dynamics of Kinetic Alfvén Waves in a Transient Flare Loop Authors: Voitenko, Yu. M.; Goossens, M. Bibcode: 1999ESASP.448..735V Altcode: 1999mfsp.conf..735V; 1999ESPM....9..735V No abstract at ADS Title: Generation of Oscillations in the Solar Convection Zone: Linear Mechanism of Mode Conversion in Shear Flows Authors: Chagelishvili, G. D.; Tevzadze, A. G.; Goossens, M. Bibcode: 1999ESASP.448...75C Altcode: 1999ESPM....9...75C; 1999mfsp.conf...75C No abstract at ADS Title: Oscillations in a magnetic solar model. I. Parallel propagation in a chromospheric and coronal magnetic field with constant Alfvén speed Authors: Pintér, Balázs; Goossens, Marcel Bibcode: 1999A&A...347..321P Altcode: Oscillation eigenmodes are studied for a planar solar model with a non-uniform horizontal magnetic field in the atmosphere. The three layer atmospheric model is the same as in \cite{t2}. The analysis in that paper is extended to a wide range of parameters. Different types of oscillation modes are determined for a wide range of the magnetic field strength and for different degrees of the spherical harmonic. The emphasis is on the possible coupling of global solar oscillation modes to localized continuum eigenmodes of the magnetic atmosphere. For propagation parallel to the magnetic field, the global oscillation modes can couple only to slow continuum modes and this is found to occur for a rather large range of parameters. In addition to the damping of global oscillation modes due to resonant absorption it was found that the interaction of global eigenmodes with slow continuum modes leads to unanticipated behaviour of global eigenmodes. The rather strange behaviour in the slow continuum involves the disappearance and appearance of global modes and splitting and merging of global modes. Additionally, frequency shifts of global modes due to the magnetic field have been examined. The shifts are compared to observations. Title: Influence of a chromospheric magnetic field on solar acoustic modes Authors: Vanlommel, P.; Goossens, M. Bibcode: 1999SoPh..187..357V Altcode: This paper studies the effect of a magnetic atmosphere on the global solar acoustic oscillations in a simple Cartesian model. First, the influence of the ratio of the coronal and the photospheric temperature τ and the strength of the magnetic field at the base of the corona Bc on the oscillation modes is studied for a convection zone-corona model with a true discontinuity. The ratio τ seems to be an important parameter. Subsequently, the discontinuity is replaced by an intermediate chromospheric layer of thickness L and the effect of the thickness on the frequencies of the acoustic waves is studied. In addition, nonuniformity in the magnetic field, plasma density and temperature in the transition layer gives rise to continuous Alfvén and slow spectra. Modes with characteristic frequencies lying within the range of the continuum may resonantly couple to Alfvén and/or slow waves. Title: Leaky and resonantly damped flux tube modes reconsidered Authors: Stenuit, H.; Tirry, W. J.; Keppens, R.; Goossens, M. Bibcode: 1999A&A...342..863S Altcode: In this research note the results for the eigenfrequencies of the uniform and non-uniform magnetic flux tubes of Stenuit et al. (1998) are reconsidered. In that paper it is shown that the eigenfrequencies may have a damping rate due to two mechanisms causing a loss of energy. In non-uniform flux tubes the eigenmodes can be damped by resonant absorption. The other mechanism is leakage of wave energy into the surroundings, which can occur for both uniform and non-uniform flux tubes. We point out that the dispersion relations obtained by Stenuit et al. are correct for leaky and undamped non-leaky modes, but are not correct for resonantly damped non-leaky modes. Title: Effects of mass flow on resonant absorption and on over-reflection of magnetosonic waves in low begin {equation}ta solar plasmas Authors: Csik, A. T.; Cadez, V. M.; Goossens, M. Bibcode: 1998A&A...339..215C Altcode: The influence of a stationary mass flow on driven resonant MHD waves is studied for incoming slow and fast magnetosonic waves with frequencies in the slow and the Alfven continua. In addition to the classic resonant absorption already present in a static plasma, driven resonant waves can also undergo over-reflection. Depending on the strength of the equilibrium flow a variety of resonant MHD wave phenomena comes into existence. The resonant absorption and over-reflection are found for both, slow and fast magnetosonic waves. The main result of this paper is that even relatively slow flows can have a drastic effect on the behaviour of MHD waves. This is in particular true under solar conditions. Title: Resonant Damping of Solar p-Modes by the Chromospheric Magnetic Field Authors: Tirry, W. J.; Goossens, M.; Pintér, B.; Čadež, V.; Vanlommel, P. Bibcode: 1998ApJ...503..422T Altcode: In this paper, we demonstrate how solar p-mode energy can be resonantly absorbed by coupling to localized Alfvén waves in the chromosphere. Nonuniformity in the magnetic field, plasma density, and temperature in the solar atmosphere give rise to a continuous spectrum of resonant frequencies. P-modes with characteristic frequencies within the range of the continuous spectrum may resonantly couple to localized Alfvén and slow magnetohydrodynamic (MHD) waves, and hence heat the chromospheric plasma. In dissipative MHD, these p-modes are recovered as eigenmodes with a damping rate that becomes independent of the dissipation mechanism in the limit of vanishing dissipation. An analytical solution of these p-modes is found in the dissipative layer embracing the resonant magnetic surface. Using the analytical solution to cross the quasi-singular dissipative layer, the required numerical effort is limited to the integration of the ideal MHD equations away from any singularity. This results in a powerful tool for investigating in a mathematically consistent way the damping by resonant absorption and the frequency shifts of the solar oscillations arising from the presence of an overlying magnetic atmosphere in combination with the resonant absorption process. The outcome is that the mechanism of resonant absorption might be responsible for the damping of solar oscillations and should be taken into account in producing a definite solar model reproducing the observed frequencies of the global solar oscillations to within the limit of observational uncertainties. Title: Random driven fast waves in coronal loops. I. Without coupling to Alfven waves Authors: de Groof, A.; Tirry, W. J.; Goossens, M. Bibcode: 1998A&A...335..329D Altcode: In this paper we study the time evolution of fast MHD waves in a coronal loop driven by footpoint motions in linear ideal MHD. We restrict the analysis to footpoint motions polarized normal to the magnetic flux surfaces such that the fast waves are driven directly. By supposing the azimuthal wave number k_y to be zero, the fast waves are decoupled from the Alfven waves. As a first step to real stochastic driving, we consider the loop to be driven by a train of identical pulses with random time intervals in between. The solution is written as a superposition of eigenmodes whose excitation is determined by the time dependence of the footpoint motion through a convolution and by the spatial dependence of the footpoint motion through a scalar product. An important result from the simulations is that the amount of kinetic energy associated with the body modes is much larger than the amount corresponding to the leaky modes. This means that most of the input energy is stored within the loop. For k_y!=q 0, body modes can resonantly couple to Alfven waves at certain magnetic surfaces and hence the energy of the body modes can then be dissipated around the resonant magnetic surfaces. Using a gamma distribution for the time intervals between the successive pulses, we analytically derive a relation between the mean value of the kinetic energy contribution of each eigenmode, the eigenfrequency, the number of pulses and the width of the pulses. The larger the variance of the distribution, the less the power spectrum reveals fine structure, peaks around certain preferred frequencies. The analytical results confirm the output from the numerical simulations. Title: MHD eigenmodes in a semi-infinite structured solar atmosphere Authors: Pinter, B.; Cadez, V. M.; Goossens, M. Bibcode: 1998A&A...332..775P Altcode: Linear eigenmodes are determined for the solar atmosphere in the presence of a gravitational field and a magnetic field. The atmosphere consists of a horizontal nonuniform chromosphere and a semi-infinite nonuniform corona. It is bounded from below by a heavy and immovable photosphere. Inhomogeneity is confined to the vertical direction. The gravitational acceleration is constant and the equilibrium magnetic field is horizontal. The equilibrium temperature increases linearly with height in the chromosphere and is constant in the corona. The equilibrium magnetic field is constant in the chromosphere and it decreases with height in the corona in such a way that the Alfven speed is constant there. The results show that there are two sets of eigenmodes which can be viewed as p- and g-modes modified by the immobile lower boundary of the atmosphere and by the magnetic field. The modes can become damped quasi-modes with complex frequencies arising from the resonant coupling of eigenmodes to the local MHD continua in the nonuniform chromospheric layer. Title: Resonant flow instability of MHD surface waves Authors: Tirry, W. J.; Cadez, V. M.; Erdelyi, R.; Goossens, M. Bibcode: 1998A&A...332..786T Altcode: We study the effect of velocity shear on the spectrum of MHD surface waves. A nonuniform intermediate region is taken into account, so that the surface wave can be subject to resonant absorption. In order to deal in a mathematically and also physically consistent manner with the resonant wave excitation, we analytically derive the dissipative solution around the resonant surface in resistive MHD. Using these analytical solutions in our eigenvalue code, the effect of the velocity shear on the damping rate of the surface wave can easily be investigated with limited numerical effort. The presence of the flow can both increase and decrease the efficiency of resonant absorption. We also show how the resonance can lead to instability of the global surface mode for a certain range of values for the velocity shear. The resonant flow instabilities, which are physically distinct from the nonresonant Kelvin-Helmholz instabilities can occur for velocity shears significantly below the Kelvin-Helmholz threshold. Although resonant absorption as dissipation mechanism is present, the amplitude of the surface mode grows in time. The resonant flow instability can be explained in terms of negative energy waves : to get an unstable negative energy wave, some dissipative process is required to ensure energy dissipation. Title: Eigenfrequencies and optimal driving frequencies of 1D non-uniform magnetic flux tubes Authors: Stenuit, H.; Keppens, R.; Goossens, M. Bibcode: 1998A&A...331..392S Altcode: The eigenfrequencies and the optimal driving frequencies for flux tubes embedded in uniform but wave-carrying surroundings are calculated, based on matching conditions formulated in terms of the normal acoustic impedances at the flux tube boundary. The requirement of the equality of the normal acoustic impedance of the transmitted wave field with the normal acoustic impedance of the outgoing wave field selects the eigenmodes, while the equality of the ingoing and the transmitted normal acoustic impedance selects the optimal driving frequencies (Keppens 1996). Even if the flux tube is uniform, the eigenfrequencies can be complex due to leakage of wave energy into the surroundings. The case of uniform flux tubes has been considered previously (e.g. Cally 1986), and serves as a testcase of our formalism. We extend Cally's results by taking a radial stratification of the flux tube into account. The non-uniformity of the flux tube can introduce another cause for energy loss, namely resonant absorption internal to the flux tube. When resonant absorption occurs, we must incorporate the appropriate jump conditions over the dissipative layer(s). This can be done using a simple numerical scheme as introduced by Stenuit et al. (1995). Title: Numerical simulation of twisted solar corona Authors: Parhi, S.; Goossens, M.; Lakhina, G. S. Bibcode: 1998IAUS..185..467P Altcode: The solar corona, modelled by a low beta, resistive plasma slab sustains MHD wave propagations due to footpoint motions in the photosphere. The profiles for density, magnetic field and driver are considered to be steep. The numerical simulation presents the evolution of MHD waves. The resonance layer is clearly observed at the slab edges. Dissipation takes place around the resonance layer where the perturbation develops large gradients. The width of the resonance layer is calculated. It is observed that the thickness of the Alfven resonance layer is more that that of the slow wave resonance layer. Effort is made to distinguish between slow and Alfven wave resonance layers. Fast waves develop kink instability. As plasma evolves the current sheets which provide the heating at the edges gets distorted and fragment into two current sheets at each edge which, in turn come closer when the twist is enhanced. Title: Resonant Alfven waves in coronal arcades driven by footpoint motions Authors: Ruderman, M. S.; Goossens, M.; Ballester, J. L.; Oliver, R. Bibcode: 1997A&A...328..361R Altcode: X-ray spectroscopy performed from different astronomical spacecrafts has shown that the solar corona is structured by magnetic fields having the shape of loops and arcades. These structures are formed by stretching and reconnection of magnetic fields, and remain stable from days to weeks. Also, sporadic or periodic brightenings of such structures have been detected in UV and soft X-ray observations, suggesting the existence of propagating waves and plasma heating within them. In this paper, a mechanism for the deposition of Alfven wave energy and heating of coronal arcades via resonant absorption is investigated. An analytical solution to the linear viscous, resistive MHD equations that describes the steady state of resonant shear Alfven oscillations in coronal arcades driven by toroidal footpoint motions is obtained. General expressions for the total amount of dissipated wave energy and for its spatial distribution within the resonant magnetic surface is derived. Title: Absorption of magnetosonic waves in presence of resonant slow waves in the solar atmosphere. Authors: Cadez, V. M.; Csik, A.; Erdelyi, R.; Goossens, M. Bibcode: 1997A&A...326.1241C Altcode: The resonant absorption of slow and fast magnetosonic waves in a nonuniform magnetic plasma is studied for a simple planar equilibrium model. Propagating slow and fast magnetosonic waves are launched upwards in a lower uniform layer. They are partially absorbed by coupling to local resonant waves in an overlying nonuniform plasma layer at the magnetic surface where the frequency of the incoming wave equals the local Alfven continuum frequency or the local slow continuum frequency. The slow magnetosonic waves can only be coupled to resonant slow continuum waves. For the fast magnetosonic waves there are three possibilities as they can be coupled to resonant Alfven continuum waves alone, resonant Alfven continuum waves combined with resonant slow continuum waves, and resonant slow continuum waves alone. The present paper focuses on the absorption of magnetosonic waves by coupling to resonant slow continuum waves either alone or in combination with resonant Alfven continuum waves. The results show that the resonant absorption of slow and fast magnetosonic waves at the slow resonance position strongly depends on the characteristics of the equilibrium model and of the driving wave. The absorption can produce efficient local heating of plasma under conditions as in the solar atmosphere. Title: MHD surface type quasi-modes of a current sheet model. Authors: Tirry, W. J.; Cadez, V. M.; Goossens, M. Bibcode: 1997A&A...324.1170T Altcode: Resonantly damped surface type quasi-modes are computed as eigenmodes of the linear dissipative MHD equations for a simple equilibrium model of a current sheet. The current sheet is modeled by a nonuniform plasma layer embedded in a uniform plasma environment. The physical equilibrium variables change in a continuous way in the nonuniform plasma layer. In particular, this is the case with both the strength and the orientation of the equilibrium magnetic field resulting from an electric current in the nonuniform plasma layer. The equilibrium layer can be viewed as a model for a reconnection site in the solar atmosphere or for current sheets in the Earth's magnetosphere. Two surface type eigenmodes (kink and sausage) are numerically found that can propagate along the nonuniform plasma layer. The phase speeds of these eigenmodes are smaller than the Alfven speed in the uniform environment. For oblique propagation to the equilibrium magnetic field, the eigenmodes resonantly couple to localized Alfven waves leading to damped quasi-modes. It is shown that the wave damping is strongly anisotropic and that the dependence of the relative damping rate on the angle of propagation is different for the sausage and the kink type eigenmodes Title: Temporal evolution of resonant absorption in coronal loops. Excitation by footpoint motions normal to the magnetic surfaces. Authors: Tirry, W. J.; Berghmans, D.; Goossens, M. Bibcode: 1997A&A...322..329T Altcode: In this paper we study the temporal evolution of linear MHD waves excited by footpoint motions using an ideal, pressureless slab model for coronal loops. We choose the footpoint motions to be polarised normal to the magnetic flux surfaces such that only fast waves are driven directly, including the so-called quasi-modes. We have derived a formal analytical solution as a superposition of eigenmodes describing the system as a function of time. The corresponding eigenvalue problem is solved numerically. This enables us to study the influence of the characteristics of the footpoint motion on the excitation of the quasi-modes. On the magnetic flux surface where the frequency of these quasi-modes equals the local Alfven frequency, wave energy is transferred from the quasi-modes towards Alfven waves. We investigate the time evolution of this process in which small scale dissipative features are generated which can be relevant in the context of coronal heating. Special attention is given to the question whether this generation of small scale dissipative features takes place on time scales shorter than typical life times of coronal loops. Expressing the dissipation time scale as function of the length scale corresponding to the resonances, an estimate for the time when dissipation becomes important and when our ideal MHD simulation stops to be valid, can be derived. For typical dissipation coefficients and length scales, dissipation becomes important in the resonance layer in a time comparable to the life time of coronal loops. Title: MHD Study of Coronal Waves: A Numerical Approach Authors: Parhi, S.; Pandey, B. P.; Goossens, M.; Lakhina, G. S.; de Bruyne, P. Bibcode: 1997Ap&SS.250..147P Altcode: The solar corona, modelled by a low β, resistive plasma slab sustains MHD wave propagations due to footpoint motions in the photosphere. The density, magnetic profile and driver are considered to be neither very smooth nor very steep. The numerical simulation presents the evolution of MHD waves and the formation of current sheet. Steep gradients in slow wave at the slab edges which are signature of resonance layer where dissipation takes place are observed. Singularity is removed by the inclusion of finite resistivity. Dissipation takes place around the resonance layer where the perturbation develops large gradients. The width of the resonance layer is calculated. The thickness of the Alfvén resonance layer is more than that of the slow wave resonance layer. Attempt is made to distinguish between slow and Alfvén wave resonance layers. Fast waves develop into kink modes. As plasma evolves the current sheets which provide the heating at the edges gets distorted and fragment into two current sheets at each edge which in turn come closer when the twist is enhanced. Title: Direct excitation of resonant torsional Alfven waves by footpoint motions. Authors: Ruderman, M. S.; Berghmans, D.; Goossens, M.; Poedts, S. Bibcode: 1997A&A...320..305R Altcode: The present paper studies the heating of coronal loops by linear resonant Alfven waves that are excited by the motions of the photospheric footpoints of the magnetic field lines. The analysis is restricted to torsionally polarised footpoint motions in an axially symmetric system so that only torsional Alfven waves are excited. For this subclass of footpoint motions, the Alfven and cusp singularities are absent from the analysis which means that resonant coupling between global modes of the loop and localised oscillations is avoided. Instead, the focus is on the resonances due to the finite extent of the loop in the longitudinal direction: at the radii where Alfven waves travelling back and forth along the length of the loop are in phase with the footpoint motions, the oscillations grow unbounded in ideal MHD. Inclusion of electrical resistivity and viscosity as dissipation mechanisms prevents singular growth and we can look at the steady state in which the energy injected at the photospheric part of the loop is balanced by the energy dissipated at the dissipative layer around the resonance. In this sense, we show that the direct excitation of Alfven waves by torsionally polarised footpoint motions leads to a very efficient heating mechanism for coronal loops, even without resonant coupling to global modes. Title: MHD wave heating of coronal loops Authors: Poedts, S.; Tirry, W.; Berghmans, D.; Goossens, M. Bibcode: 1997jena.confE..54P Altcode: The possibility of heating coronal loops by phase-mixing and resonant absorption of MHD waves is discussed. The focus is on the efficiency and time scales of the conversion of the wave energy to heat for typical coronal loop parameter values. Both the sideways excitation of loops by incident waves and the footpoint driving by convective motions are discussed. First, the mechanisms of phase-mixing and resonant absorption are explained in a simple set-up. Next, linear MHD results on solar coronal loop applications are reviewed. In sideways excited loops (by incident waves), `quasi-modes' (or `collective modes') play the crucial role of energy carrier from the external region {through the flux surfaces} to the resonant layers. The quasi-modes are required to obtain a reasonable efficiency unless the resonances are located in the outer region of the loop. In footpoint driven loops, on the other hand, resonant Alfven can be excited directly and the efficiency depends of the polarization of the driving source. Recent results take the variation of plasma density and magnetic field strength {along the loop} into account. For typical coronal loop parameters, the MHD wave heating mechanism turns out to be very efficient, i.e. the coupling of the loop plasma to the external driver is very good and the time scales for dissipation are much smaller than the typical life time of a loop. However, the dynamics in the resonant layers is very nonlinear in the hot (very well conducting) coronal plasma. Computer simulations show that the shear flow in these layers can become unstable. It will be shown that the Kelvin-Helmholtz-like instabilities may destroy the resonant layers and lead to a turbulent state. Finally, some observational results and consequences are discussed. This brings us to the problems of the discrepancy between the observed and the required power spectrum of MHD waves and the distinction between different candidate heating mechanisms. Scientific visualization of the observational consequences of the computer simulated results may lead to different observable features for different candidate heating mechanisms and, hence, to the identification of the mechanism responsible for the heating of the coronal loops. Title: Nonlinear development of MHD waves in coronal loops Authors: Parhi, S.; Pandey, B. P.; Goossens, M.; Lakhina, G. S.; de Bruyne, P. Bibcode: 1997AdSpR..19.1891P Altcode: The solar corona, modelled by a low beta, resistive plasma slab sustains MHD wave propagations due to footpoint motions in the photosphere. The numerical simulation presents the evolution of MHD waves and the formation of current sheets. Steep gradients at the slab edges, which are signatures of resonance layers are observed. Singularities are removed by the inclusion of finite resistivity. The fast waves develop kink modes. As the plasma evolves the current sheets which provide heating at the edges fragment into two current sheets at each edge which in turn come closer when the twist is enhanced. Title: Quasi-Modes as Dissipative Magnetohydrodynamic Eigenmodes: Results for One-dimensional Equilibrium States Authors: Tirry, W. J.; Goossens, M. Bibcode: 1996ApJ...471..501T Altcode: No abstract at ADS Title: The Footpoint-driven Coronal Sausage Wave Authors: Berghmans, David; de Bruyne, Peter; Goossens, Marcel Bibcode: 1996ApJ...472..398B Altcode: We study the excitation of MHD waves in a coronal loop as its field line footpoints are forced to follow the photo spheric convective motions. By focussing on the specific case of cylindrically symmetric footpoint motions, the original problem is reduced to one in which fast waves and Alfvén waves are decoupled. This allows for a full analytical treatment of the photo spheric excitation of both sausage waves and of torsional Alfvén waves. Previously, Berghmans & De Bruyne considered the case of torsional Alfvén waves. In the present paper we extend that analysis to sausage waves that are excited by radially polarized footpoint motions (e.g., typical for granules). The time-dependent solution that we obtain is written as a superposition of body and leaky eigenmodes whose excitation is easily determined from the imposed footpoint motion. This provides analytical insight into the dynamics and energetics of both impulsively and periodically driven sausage waves. In each case, we explain the time evolution of the generated waves and discuss typical "signatures" that can be looked for in numerical simulations and possibly in solar observations. Title: Slow Resonant MHD Waves in One-dimensional Magnetic Plasmas with Anisotropic Viscosity and Thermal Conductivity Authors: Ruderman, M. S.; Goossens, M. Bibcode: 1996ApJ...471.1015R Altcode: Slow resonant MHD waves are studied in a compressible plasma with strongly anisotropic viscosity and thermal conductivity. It is shown that anisotropic viscosity and/or thermal conductivity removes the slow singularity which is present in the linear ideal MHD equations. Simple analytical solutions to the linear dissipative MHD equations are obtained which are valid in the dissipative layer and in two overlap regions to the left and the right of the dissipative layer. Asymptotic analysis of the dissipative solutions enables us to obtain connection formulae specifying the variations or jumps of the different wave quantities across the dissipative layer. These connection formulae coincide with those obtained previously for plasmas with isotropic viscosity and finite electrical conductivity. The thickness of the dissipative layer is inversely proportional to the Reynolds number, in contrast to the case of isotropic dissipative coefficients, where it is inversely proportional to the cube root of the Reynolds number. The behavior of the perturbations in the dissipative layer is described in terms of elementary functions of complex argument. Title: Trapped waves in open stellar atmospheres. Authors: Pintér, B.; Čadež, V. M.; Goossens, M. Bibcode: 1996POBeo..54...59P Altcode: Linear MHD waves whose energy remains localized in an unbounded stellar atmosphere are considered analytically and numerically. The atmosphere is modelled by a stratified fully ionized plasma with both the gravity force and the gradient of the unperturbed fluid quantities aligned along the vertical z-axis. The temperature is taken to have a linear profile while the magnetic field is assumed horizontal and homogeneous. The atmosphere is semi-infinite with a solid boundary at its bottom (the stellar photosphere). In such a system, the authors are looking for solutions localized in space and that could be treated as eigenmodes. Title: Dissipative instability of the MHD tangential discontinuity in magnetized plasmas with anisotropic viscosity and thermal conductivity Authors: Ruderman, M. S.; Verwichte, E.; Erdélyi, R.; Goossens, M. Bibcode: 1996JPlPh..56..285R Altcode: The stability of the MHD tangential discontinuity is studied in compressible plasmas in the presence of anisotropic viscosity and thermal conductivity. The general dispersion equation is derived, and solutions to this dispersion equation and stability criteria are obtained for the limiting cases of incompressible and cold plasmas. In these two limiting cases the effect of thermal conductivity vanishes, and the solutions are only influenced by viscosity. The stability criteria for viscous plasmas are compared with those for ideal plasmas, where stability is determined by the Kelvin—Helmholtz velocity VKH as a threshold for the difference in the equilibrium velocities. Viscosity turns out to have a destabilizing influence when the viscosity coefficient takes different values at the two sides of the discontinuity. Viscosity lowers the threshold velocity V below the ideal Kelvin—Helmholtz velocity VKH, so that there is a range of velocities between V and VKH where the overstability is of a dissipative nature. Title: Effects of flow on resonant absorption of MHD waves in viscous MHD. Authors: Erdelyi, R.; Goossens, M. Bibcode: 1996A&A...313..664E Altcode: The effect of an equilibrium flow on resonant absorption of linear MHD waves in cylindrical magnetic flux tubes is studied in compressible viscous MHD. We treat the problem numerically with an application of the FEM combined with the Galerkin technique. The singularities of the ideal MHD equations are removed by incorporating a dissipative effect, namely the classical viscosity. We show that an equilibrium shear flow can significantly influence the absorption suffered by the incoming driving waves. The presence of an equilibrium flow may therefore be very determinant for resonant absorption. A parametric analysis shows that there are values of the equilibrium velocity field for which the absorption rate becomes zero, even for rather small velocity shears. We also found negative absorption of wave power which apparently can be attributed to the resonant instability found by Hollweg et al. (1990). For other values of the equilibrium flow we find that the resonant absorption can be strongly enhanced, even up to total absorption of the incoming wave. Title: Unified theory of damping of linear surface Alfvén waves in inhomogeneous incompressible plasmas Authors: Ruderman, M. S.; Goossens, M. Bibcode: 1996JPlPh..56..107R Altcode: The viscous damping of surface Alfvén waves in a non-uniform plasma is studied in the context of linear and incompressible MHD. It is shown that damping due to resonant absorption and damping on a true discontinuity are two limiting cases of the continuous variation of the damping rate with respect to the dimensionless number Rg = Δλ2Re, where Δ is the relative variation of the local Alfvén velocity, λ is the ratio of the thickness of the inhomogeneous layer to the wavelength, and Re is the viscous Reynolds number. The analysis is restricted to waves with wavelengths that are long in comparison with the extent of the non-uniform layer (λ 1), and to Reynolds numbers that are sufficiently large that the waves are only slightly damped during one wave period. The dispersion relation is obtained and first investigated analytically for the limiting cases of very small (Rg 1) and very large (Rg 1) values of Rg, For very small values of Rg, the damping rate agrees with that found for a true discontinuity, while for very large values of Rg, it agrees with the damping rate due to resonant absorption. The dispersion relation is subsequently studied numerically over a wide range of values of Rg, revealing a continuous but nonmonotonic variation of the damping rate with respect to Rg. Title: Numerical Simulations of Driven MHD Waves in Coronal Loops Authors: Parhi, S.; De Bruyne, P.; Murawski, K.; Goossens, M.; Devore, C. R. Bibcode: 1996SoPh..167..181P Altcode: The solar corona, modeled by a low-β, resistive plasma slab, sustains MHD wave propagations due to footpoint motions in the photosphere. Simple test cases are undertaken to verify the code. Uniform, smooth and steep density, magnetic profile and driver are considered. The numerical simulations presented here focus on the evolution and properties of the Alfvén, fast and slow waves in coronal loops. The plasma responds to the footpoint motion by kink or sausage waves depending on the amount of shear in the magnetic field. The larger twist in the magnetic field of the loop introduces more fast-wave trapping and destroys initially developed sausage-like wave modes. The transition from sausage to kink waves does not depend much on the steep or smooth profile. The slow waves develop more complex fine structures, thus accounting for several local extrema in the perturbed velocity profiles in the loop. Appearance of the remnants of the ideal singularities characteristic of ideal plasma is the prominent feature of this study. The Alfvén wave which produces remnants of the ideal x−1 singularity, reminiscent of Alfvén resonance at the loop edges, becomes less pronounced for larger twist. Larger shear in the magnetic field makes the development of pseudo-singularity less prominent in case of a steep profile than that in case of a smooth profile. The twist also causes heating at the edges, associated with the resonance and the phase mixing of the Alfvén and slow waves, to slowly shift to layers inside the slab corresponding to peaks in the magnetic field strength. In addition, increasing the twist leads to a higher heating rate of the loop. Remnants of the ideal log ¦x¦ singularity are observed for fast waves for larger twist. For slow waves they are absent when the plasma experiences large twist in a short time. The steep profiles do not favour the creation of pseudo-singularities as easily as in the smooth case. Title: Quasi-modes as dissipative MHD eigenmodes : results for 1-dimensional equilibrium states Authors: Tirry, W. J.; Goossens, M. Bibcode: 1996AAS...188.3609T Altcode: 1996BAAS...28..874T Quasi-modes which are important for understanding the MHD wave behavior of solar and astrophysical magnetic plasmas are computed as eigenmodes of the linear dissipative MHD equations. This eigenmode computation is carried out with a simple numerical scheme which is based on analytical solutions to the dissipative MHD equations in the quasi-singular resonance layer. Non-uniformity in magnetic field and plasma density gives rise to a continuous spectrum of resonant frequencies. Global discrete eigenmodes with characteristic frequencies lying within the range of the continuous spectrum may couple to localised resonant Alfven waves. In ideal MHD these modes are not eigenmodes of the Hermitian ideal MHD operator, but are found as a temporal dominant global exponentially decaying response to an initial perturbation. In dissipative MHD they are really eigenmodes with damping becoming independent of the dissipation mechanism in the limit of vanishing dissipation. An analytical solution of these global modes is found in the dissipative layer around the resonant Alfvenic position. Using the analytical solution to cross the quasi-singular resonance layer the required numerical effort of the eigenvalue scheme is limited to the integration of the ideal MHD equations in regions away from any singularity. The presented scheme allows for a straightforward parametric study. The method is checked with known ideal quasi-mode frequencies found for a 1-D box model for the Earth's magnetosphere (Zhu & Kivelson 1988). The agreement is excellent. The dependence of the oscillation frequency on the wavenumbers for a 1-D slab model for coronal loops found by Ofman, Davila, & Steinolfson (1995) is also easily recovered. Title: MHD Surface Waves in a Complex (Longitudinal + Sheared) Magnetic Field Authors: Zhelyazkov, I.; Murawski, K.; Goossens, M. Bibcode: 1996SoPh..165...99Z Altcode: We study the dispersion characteristics of fast MHD surface waves travelling on a plasma slab immersed in a complex magnetic field consisting of a large longitudinal B0z component and a small sheared B0y component. The analysis shows that for typical coronal conditions both the sausage and kink waves are generally pseudo-surface waves. The tangential magnetic field, B0y, modifies the dispersion curves, and for sufficiently large sheared fields there is a transition from pseudo-surface to pure-surface fast kink waves. Title: Numerical simulations of MHD wave excitation in bounded plasma slabs Authors: Murawski, K.; DeVore, C. R.; Parhi, S.; Goossens, M. Bibcode: 1996P&SS...44..253M Altcode: Numerical simulations are performed in the framework of nonlinear resistive 2.5-dimensional magnetohydrodynamics to investigate the response of a coronal loop to shearing motions of the footpoints. A simple slab plasma with straight magnetic field lines is used to model the coronal loop, with the photospheric ends represented by impermeable walls. The hot, dense loop plasma is approximated by smoothed step-function profiles. The results show that an initially excited Alfvén wave reveals a 1/ x-type singularity, which is characteristic of the linear Alfvén resonances, smoothed by the resistive dissipation. Both fast and slow magnetosonic waves are driven by the nonlinear Alfvén wave. The slow magnetosonic waves concentrate their energies in resonance layers, and their associated flows exhibit singularities of the 1/ x-type. The Alfvén resonances, which are absent from the system in the case of linear waves, develop late in time as the Alfvén-wave amplitude grows into the nonlinear regime, and their development is accelerated for larger-amplitude driving forces. The resultant heating associated with the resonances phase mixing of the waves is concentrated in the region of large Alfvén-speed gradients. Title: Numerical Simulation of Driven MHD Waves in Twisted Coronal Loops Authors: de Bruyne, P.; Parhi, S.; Goossens, M. Bibcode: 1996ApL&C..34..163D Altcode: No abstract at ADS Title: MHD waves in magnetic flux tubes. Authors: Goossens, M.; Ruderman, M. Bibcode: 1996ASIC..481...61G Altcode: This review is concerned with a recent development in the analytic theory of resonant Alfvén waves in nonuniform magnetic flux tubes in the solar atmosphere. It discusses how an analytic study of simplified versions of the dissipative MHD equations for plasmas with high Reynolds numbers leads to the fundamental conservation law and simple analytic solutions for resonant Alfvén waves. Asymptotic analysis of the analytic solutions gives jump conditions that connect the solutions across the dissipative layer. Title: The Linear Spectrum of Twisted Magnetic Flux Tubes in Viscous MHD Authors: Pintér, B.; Erdélyi, R.; Goossens, M. Bibcode: 1996ApL&C..34..169P Altcode: No abstract at ADS Title: Numerical Model for the Study of Wave-Mean Flow Interactions in Solar Magnetohydrodynamics Authors: Ghizaru, Mihai S.; Goossens, Marcel Bibcode: 1996RoAJ....6...21G Altcode: A 2D MHD model in cylindrical geometry is developed for the study of the behaviour of MHD waves incident on critical layers in the presence of shearing in magnetic and velocity fields in the solar plasma The MHD code described in this paper is based on the resistive MHD equations written in (r,z) coordinates. The non-divergence constraint for the magnetic field is satisfied by using a vector potential. For the time advancing, an operator splitting procedure is performed when including the different physical effects, as well as for alternating direction in the advection terms. The rotating cone test is used for numerical experiments with different advenction schemes. The model equations are integrated on an Arakawa b grid, with Bø in the cell center and Aø in the velocity points. Second order schemes are used for the mass, momentum and energy advection with a monotonicity maintaining scheme applied periodically. Implicit methods, treated by gaussian elimination are used for the toroidal and poloidal magnetic field diffusion. Title: Dissipative MHD solutions for resonant Alfvén waves in two-dimensional poloidal magnetoplasmas Authors: Tirry, W. J.; Goossens, M. Bibcode: 1995JGR...10023687T Altcode: The resonant excitation of Alfvén waves is considered in a resistive warm plasma embedded in a purely poloidal field. The magnetostatic equilibrium is invariant in the y direction. The driven problem is studied in the asymptotic state, so we can assume that all wave fields vary as exp[i(λy-ωt)]. Resistive solutions are derived in the vicinity of the resonance with the aid of an asymptotic expansion procedure. We find that the zeroth-order functions of the flux coordinate have to satisfy differential equations analogous to those obtained by Goossens et al. [1995] for the resistive one-dimensional systems. Applied to the two-dimensional box model for the Earth's magnetosphere, we recover the results found by Thompson and Wright [1993] in ideal MHD, but in addition, we obtain the behavior in the dissipative layer in the asymptotic state. Title: Analytic solutions for resonant Alfvén waves in 1D magnetic flux tubes in dissipative stationary MHD Authors: Erdélyi, Róbert; Goossens, Marcel; Ruderman, Michael S. Bibcode: 1995SoPh..161..123E Altcode: Resonantly driven Alfvén waves are studied in non-uniform stationary magnetic flux tubes. Analytic dissipative MHD solutions are obtained for the Lagrangian displacement and the Eulerian perturbation of the total pressure. These analytic solutions are valid in the dissipative layer and in the two overlap regions to the left and the right of the dissipative layer. From these analytic solutions we obtain the fundamental conservation law and the jump conditions for resonantly driven Alfvén waves in magnetic flux tubes with an equilibriun flow. The fundamental conservation law and the jump conditions depend on the equilibrium flow in a more complicated way than just a Doppler shift. The effects of an equlibrium flow are not to be predicted easily in general terms with the exception that the polarization of the driven Alfvén waves is still in the magnetic surfaces and perpendicular to the magnetic field lines as it is in a static flux tube. Title: A simple numerical scheme for the computation of resonant Alfvén waves Authors: Stenuit, Hilde; Erdélyi, Róbert; Goossens, Marcel Bibcode: 1995SoPh..161..139S Altcode: The present paper discusses the implementation of the SGHR method (Sakurai, Goossens, and Hollweg, 1991; Goossens, Ruderman, and Hollweg, 1995) in a numerical scheme for determining resonantly driven Alfvén waves in nonuniform magnetic flux tubes. This method is based on jump conditions over the dissipative layer which are obtained from an asymptotic analysis of analytical solutions to simplified versions of the linear non-ideal MHD equations in this dissipative layer. The emphasis is on the computational simplicity and the accuracy of the method. The method derives its computational simplicity from the fact that it circumvents the numerical integration of the non-ideal MHD equations. The implementation only requires the numerical integration of the ideal MHD equations away from the resonant position. There is no need for a special integration scheme and a PC suffices as a hardware tool. Title: Non-stationary resonant Alfvén surface waves in one-dimensional magnetic plasmas Authors: Ruderman, M. S.; Tirry, W.; Goossens, M. Bibcode: 1995JPlPh..54..129R Altcode: This paper uses incompressible visco-resistive MHD to study the propagation of linear resonant waves in an inhomogeneous plasma. The background density and magnetic field are assumed to depend only on one spartial Cartesian coordinate, and the magnetic field is taken to be unidirectional and perpendicular to the direction of inhomogeneity. The equation that governs the component of the velocity normal to the plane formed by the direction of the inhomogeneity and the magnetic field is derived under the assumption that the coefficients of viscosity and resistivity are sufficiently small that dissipation of energy is confined to a narrow dissipative layer. The solutions to this equation are obtained in the form of decaying normal surface modes with wavelengths much larger than the characteristic scale of the inhomogeneity. The effect of non-stationarity inside the dissipative layer is taken into account, and valid solutions are found even when the ratio of the thickness of the dissipative layer to the inhomogeneity length scale is of the order of or smaller than the ratio of the inhoinogeneity length scale to the wavelength. These solutions are the generalization of the solutions obtained by Mok and Einaudi, which are only valid when the first ratio is much larger than the second. The rate of wave damping is shown to be independent of the values of the viscosity and the resistivity. However, the behaviour of the solutions in the dissipative layer depends strongly on the viscosity and the resistivity. In the case that the effect of dissipation dominates the effect of non-stationarity, the solutions behave in the dissipative layer as found by Mok and Einaudi. When the effect of dissipation is steadily decreased in comparison with the effect of nonstationarity, the solutions become more and more oscillatory, and their amplitudes grow very rapidly in the dissipative layer. Eventually, when nonstationarity dominates dissipation, the amplitudes of the solutions become so large in the dissipative layer in comparison with those outside the dissipative layer that practically all the energy of the perturbations is concentrated in the dissipative layer. Title: Surface Alfvén waves of negative energy Authors: Ruderman, M. S.; Goossens, M. Bibcode: 1995JPlPh..54..149R Altcode: The stability of an MHD tangential discontinuity is studied in an incompressible plasma where viscosity is taken into account at one side of the discontinuity. When the shear velocity is smaller than the threshold value for the onset of the Kelvin-Helmholtz (KH) instability, two surface waves can propagate along the discontinuity. There is a critical value for the shear velocity, which is smaller than the threshold value for the onset of the KH instability. When the shear velocity is smaller than the critical value, the two surface waves propagate in Opposite directions. When the shear velocity is larger than the critical velocity, the two waves propagate in the same direction, and the wave with smaller phase velocity is a negative-energy wave. Viscosity causes this negative-energy wave to be unstable, and the instability increment is proportional to the viscosity coefficient. Title: Study of nonlinear MHD equations governing the wave propagation in twisted coronal loops Authors: Parhi, S.; Debruyne, P.; Goossens, M.; Zhelyazkov, I. Bibcode: 1995sowi.conf...28P Altcode: The solar corona, modelled by a low beta, resistive plasma slab, sustains MHD wave propagations due to shearing footpoint motions in the photosphere. By using a numerical algorithm the excitation and nonlinear development of MHD waves in twisted coronal loops are studied. The plasma responds to the footpoint motion by sausage waves if there is no twist. The twist in the magnetic field of the loop destroys initially developed sausage-like wave modes and they become kinks. The transition from sausage to kink modes is analyzed. The twist brings about mode degradation producing high harmonics and this generates more complex fine structures. This can be attributed to several local extrema in the perturbed velocity profiles. The Alfven wave produces remnants of the ideal 1/x singularity both for zero and non-zero twist and this pseudo-singularity becomes less pronounced for larger twist. The effect of nonlinearity is clearly observed by changing the amplitude of the driver by one order of magnitude. The magnetosonic waves also exhibit smoothed remnants of ideal logarithmic singularities when the frequency of the driver is correctly chosen. This pseudo-singularity for fast waves is absent when the coronal loop does not undergo any twist but becomes pronounced when twist is included. On the contrary, it is observed for slow waves even if there is no twist. Increasing the twist leads to a higher heating rate of the loop. The larger twist shifts somewhat uniformly distributed heating to layers inside the slab corresponding to peaks in the magnetic field strength. Title: Dissipative MHD solutions for resonant AlfvÉn waves in 1-dimensional magnetic flux tubes Authors: Goossens, Marcel; Ruderman, Michail S.; Hollweg, Joseph V. Bibcode: 1995SoPh..157...75G Altcode: The present paper extends the analysis by Sakurai, Goossens, and Hollweg (1991) on resonant Alfvén waves in nonuniform magnetic flux tubes. It proves that the fundamental conservation law for resonant Alfvén waves found in ideal MHD by Sakurai, Goossens, and Hollweg remains valid in dissipative MHD. This guarantees that the jump conditions of Sakurai, Goossens, and Hollweg, that connect the ideal MHD solutions forξr, andP' across the dissipative layer, are correct. In addition, the present paper replaces the complicated dissipative MHD solutions obtained by Sakurai, Goossens, and Hollweg forξr, andP' in terms of double integrals of Hankel functions of complex argument of order with compact analytical solutions that allow a straightforward mathematical and physical interpretation. Finally, it presents an analytical dissipative MHD solution for the component of the Lagrangian displacement in the magnetic surfaces perpendicular to the magnetic field linesξ⊥ which enables us to determine the dominant dynamics of resonant Alfvén waves in dissipative MHD. Title: Resonant absorption of Alfven waves in coronal loops in visco-resistive MHD. Authors: Erdelyi, R.; Goossens, M. Bibcode: 1995A&A...294..575E Altcode: This paper uses numerical simulations in linear visco-resistive MHD for determining the dominant dissipative mechanism for the stationary state of resonant absorption of MHD waves in coronal loops. The full Braginskii viscous stress tensor with five viscosity coefficients and electrical resistivity are included in the MHD equations. The coronal loops are approximated by straight, cylindrical, axisymmetric plasma columns with equilibrium quantities which vary only in the radial direction. The simulations are carried out with a numerical code that uses finite elements for the spatial discretization combined with the Galerkin method. Computations in viscous MHD (in the absence of electrical resistivity) show that shear viscosity produces the largest contribution to the absorption and that the contributions due to the compressive and perpendicular components of the viscous stress tensor can be neglected for all practical purposes. Computations in visco-resistive MHD reveal that on the whole it is not possible to distinguish between shear viscosity and electrical resistivity as the most efficient dissipative mechanism for resonant absorption. The relative importance of these two dissipative mechanisms depends on the equilibrium conditions of density and magnetic field strength so that there are situations in which either electrical resisitivity or shear viscosity is the most effective mechanism and in which both mechanisms are equally efficient. Title: Conservation laws and connection formulae for resonant MHD waves Authors: Goossens, Marcel; Ruderman, Michael S. Bibcode: 1995PhST...60..171G Altcode: This paper reviews a recent development in the theory of resonant MHD waves in non-uniform plasmas. An asymptotic analysis of the equations for MHD waves in plasmas with high magnetic Reynolds numbers has shown that resonant slow and Alfvén waves obey conservation laws and jump conditions across the dissipative layer. These conservation laws specify the dominant dynamics of the resonant MHD waves. In combination with the jump conditions they enable us to understand the basic physics of resonant MHD waves and also help us with the interpretation of results of large scale numerical simulations in resistive MHD. They also can be used to design an accurate and computationally simple methods for numerical studying resonant MHD waves in non-uniform plasmas.

Conservation laws and jump conditions for resonant MHD waves are first discussed in linear MHD for 1-dimensional equilibrium states. Subsequently the generalization of these results to 2-dimensional equilibrium state in linear MHD and to nonlinear MHD is reviewed. The interaction of sound waves with an inhomogeneous plasma is discussed as an application of the theory. Firstly the results of linear theory are used to consider the interaction of sound waves with 1-dimensional magnetic tubes. The phenomenon of total resonant absorption is discussed. Secondly the nonlinear theory of cusp dissipative layers is used to study the interaction of sound waves with 1-dimensional inhomogeneous plasmas in planar geometry. New effects that owe their existence to nonlinearity in the cusp dissipative layer are reviewed. Title: Multiple Scattering and Resonant Absorption of p-Modes by Fibril Sunspots Authors: Keppens, R.; Bogdan, T. J.; Goossens, M. Bibcode: 1994ApJ...436..372K Altcode: We investigate the scattering and absorption of sound waves by bundles of magnetic flux tubes. The individual flux tubes within the bundle have thin nonuniform boundary layers where the thermodynamic and magnetic properties change continuously to their photospheric levels. In these nonuniform layers, resonant absorption converts some of the incident acoustic wave energy into heat and thus the flux-tube bundle appears as a sink of acoustic power. For a fixed amount of magnetic flux, we find that composite ('spaghetti') sunspots absorb much more wave energy than their monolithic counterparts, although both sunspots scatter comparable amounts of the incident acoustic wave energy. The extra energy drainage results from the interplay of the wave scattering back and forth between the tubes and the incremental loss of acoustic power at each interaction with an individual tube due to the resonant absorption in its boundary layer. The scattering cross section is not similarly enhanced because the multiply scattered waves generally interfere destructively in the far field. Another interesting consequence of the lack of axisymmetry is that composite sunspots may show acoustic emission for some multipole components, and absorption for others. The net absorption cross section is however never negative, and is nonzero only when the projection of the wave phase speed along the flux-tube bundle is less than the maximal value of the Alfven speed. Whereas composite sunspots composed of uniformly magnetized flux tubes posses narrow scattering resonances, the analogous bundle of nonuniform fibrils instead exhibits corresponding broad absorption resonances, resulting from the incremental loss of power on successive scatters. These broad absorption resonances correspond to leaky (MHD radiating) eigenmodes of the composite structure. When progressively more flux tubes are clustered, additional oscillation eigenmodes appear grouped in a complicated band structure characterized by a (nearly) common speed of propagation along the bundle. Title: Book Review: Solar wind seven / Pergamon Press, 1992 Authors: Goossens, M. Bibcode: 1994SSRv...69..207M Altcode: No abstract at ADS Title: Operator splitting for multidimensional magnetohydrodynamics Authors: Murawski, K.; Goossens, M. Bibcode: 1994JGR....9911569M Altcode: Operator splitting and direct time integration of the ideal MHD equations are compared by using a finite difference flux-corrected transport method. The comparison is made for impulsively generated nonlinear waves in a coronal plasma. It suggests that operator splitting and direct time integration both lead to physically acceptable results and provide a good agreement with results obtained with the fast Fourier transform method. Title: Flux corrected transport method for MHD plasma: description of the numerical algorithm and tests Authors: Murawski, K.; Goossens, M. Bibcode: 1994A&A...286..943M Altcode: This paper gives a detailed description of an MHD code for the simulation of 2D flows and waves in magnetic astrophysical plasmas. The code uses the flux corrected transport method with Zalesak's flux limiter for the spatial integration and a predictor-corrector method for the direct time integration. Results of test problems are presented in order to assess the numerical accuracy and performance of the code. The test problems deal with the numerical simulations of impulsively generated nonlinear MHD waves in coronal density interfaces and slabs. At present the code uses Cartesian coordinates and the MHD equations for a (β=0) pressureless ideal plasma. The extension to more complicated geometries and non-zero β plasmas is straightforward. Title: Excitation of nonlinear MHD waves by foot-point motions Authors: Murawski, K.; Goossens, M. Bibcode: 1994A&A...286..952M Altcode: Numerical simulations are performed to investigate the excitation of magnetohydrodynamic waves in coronal loops by photospheric shearing motions. In the simulations the solar coronal loop is modelled as a straight slab of enhanced gas density. The plasma is described by magnetohydrodynamic equations that include finite gas pressure effects and magnetic diffusivity. The Alfven wave is artificially suppressed from the system. MHD waves are excited by imposing oscillations at one end of the plasma slab. A plasma responds to a foot-point motion by kink or sausage waves in dependence on the polarization of a driver. The foot-point motion induces a growth in the parallel velocity. The growth occurs in a resonant layer on a time scale which is much less than a typical life time of a loop. The heating associated with the resonant absorption of the waves is very small and can thus not be considered as relevant for the coronal heating mechanism. The nonlinearity of the MHD equations gives rise to a distorted plasma flow, introducing an asymmetry in the system, and speeds up the occurrence of the resonant layer. Title: Alfvén wave heating Authors: Goossens, M. Bibcode: 1994SSRv...68...51G Altcode: This review discusses Alfvén wave heating in non-uniform plasmas as a possible means for explaining the heating of the solar corona. It focusses on recent analytical results that enable us to understand the basic physics of Alfvén wave heating and help us with the interpretation of results of numerical simulations. First we consider the singular wave solutions that are found in linear ideal MHD at the resonant magnetic surface where the frequency of the wave equals the local Alfvén frequency. Next, we use linear resistive MHD for describing the waves in the dissipative region and explain how dissipation modifies the singular solutions found in linear ideal MHD. Title: Modulations of slow sausage surface waves travelling along a magnetized slab Authors: Zhelyazko, I.; Murawski, K.; Goossens, M.; Nenovaki, P.; Roberts, B. Bibcode: 1994JPlPh..51..291Z Altcode: In this paper we consider a set of nonlinear MHD equations that admits in a linear approximation a solution in the form of a slow sausage surface wave travelling along an isolated magnetic slab. For a wave of small but finite amplitude, we investigate how a slowly varying amplitude is modulated by nonlinear self-interactions. A stretching transformation shows that, at the lowest order of an asymptotic expansion, the original set of equations with appropriate boundary conditions (free interfaces) can be reduced to the cubic nonlinear Schrödinger equation, which determines the amplitude modulation. We study analytically and numerically the evolution of impulsively generated waves, showing a transition of the initial states into a train of solitons and periodic waves. The possibility of the existence of solitary waves in the solar atmosphere is also briefly discussed. 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: Viscous computations of resonant absorption of MHD waves in flux tubes by fem Authors: Erdelyi, R.; Goossens, M. Bibcode: 1994Ap&SS.213..273E Altcode: A numerical code is presented for computing the stationary state of resonant absorption of MHD waves in cylindrical flux tubes in linear, compressible, and viscous MHD. The full viscosity stress tensor is included in the code with the five viscosity coefficients as given by Braginskii (1965). Also non-zero plasma pressure effects are taken into account, and the finite elements discretization with the Galerkin method has been used. The implementation of the stress tensor and the numerical accuracy of the tensorial viscous MHD code are scrutinized in test case. The test case involves the absorption of waves in cylindrical flux tubes considered by Lou (1990) and Goossens and Poedts (1992) in the context of absorption of acoustic oscillations. The results for the absorption rates obtained with the tensorial viscous code agree completely with the results obtained by Lou in a scalar viscous MHD and by Goossens and Poedts in resistive MHD. This verifies not only the complicated tensor viscous code but again proves that the absorption rate is independent of the actual dissipation mechanism. Title: Linear Visco-Resistive Computations of Magnetohydrodynamic Waves II. Viscous Effects Authors: Erdelyi, R.; Goossens, M. Bibcode: 1994scs..conf..506E Altcode: 1994IAUCo.144..506E Resonant absorption of MHD waves in coronal loops is studied in linear, viscous MHD. Shear viscosity produces absorption and is a viable candidate for heating coronal loops. Title: Linear Visco-Resistive Computations of Magnetohydrodynamics Waves I. The Code and Test Cases Authors: Erdelyi, R.; Goossens, M.; Poedts, S. Bibcode: 1994scs..conf..503E Altcode: 1994IAUCo.144..503E The stationary state of resonant absorption of linear, MHD waves in cylindrical magnetic flux tubes is studied in viscous, compressible MHD with a numerical code using finite element discretization. The full viscosity tensor with the five viscosity coefficients as given by Braginskii is included in the analysis. The computations reproduce the absorption rates obtained by Lou in scalar viscous MHD and Goossens and Poedts in resistive MHD, which guarantee the numerical accuracy of the tensorial viscous MHD code. Title: Random velocity field corrections to the f-mode. 3: A photospheric random flow and chromospheric magnetic field Authors: Murawski, K.; Goossens, M. Bibcode: 1993A&A...279..225M Altcode: The combined effect of a photospheric random flow and a chromospheric magnetic field on the frequencies of the f-mode is studied for a simple model of the photosphere and chromosphere. The photosphere and chromosphere are approximated as inviscid fluids with constant mass densities rho1 and rho2. The photosphere is taken to be free of a magnetic field and subject to a random flow and the chromosphere is in static equilibrium but permeated by a horizontal magnetic field. Numerical solutions show that the frequencies of the f-mode depart from the parabola omega2 = gk(rho1 - rho2)/rho1 + rho 2) + k2(VA exp 2 rho2/(rho1 + rho2) at high wavenumbers k. Title: Total Resonant Absorption of Acoustic Oscillations in Sunspots Authors: Stenuit, Hilde; Poedts, Stefaan; Goossens, Marcel Bibcode: 1993SoPh..147...13S Altcode: The question of total resonant absorption of acoustic oscillations in sunspots is studied for cylindrical 1-D flux tubes that are stratified only in the radial direction and surrounded by a uniform, non-magnetic plasma. The numerical investigation of Goossens and Poedts (1992) in linear resistive MHD is taken further by increasing the strength of the azimuthal magnetic field in the equilibrium flux tubes. For relatively strong azimuthal magnetic fields, total absorption is found over a relatively wide range of spot radii. Title: Resonant Behaviour of Magnetohydrodynamic Waves on Magnetic Flux Tubes - Part Four Authors: Goossens, Marcel; Hollweg, Joseph V. Bibcode: 1993SoPh..145...19G Altcode: Resonant absorption of MHD waves on a nonuniform flux tube is investigated as a driven problem for a 1D cylindrical equilibrium. The variation of the fractional absorption is studied as a function of the frequency and its relation to the eigenvalue problem of the MHD radiating eigenmodes of the nonuniform flux tube is established. The optimal frequencies producing maximal fractional absorption are determined and the condition for total absorption is obtained. This condition defines an impedance matching and is fulfilled for an equilibrium that is fine tuned with respect to the incoming wave. The variation of the spatial wave solutions with respect to the frequency is explained as due to the variation of the real and imaginary parts of the dispersion relation of the MHD radiating eigenmodes with respect to the real driving frequency. Title: Non-adiabatic discrete Alfvén waves in coronal loops and prominences Authors: Keppens, Rony; van der Linden, Ronald A. M.; Goossens, Marcel Bibcode: 1993SoPh..144..267K Altcode: Discrete Alfvén waves in coronal loops and prominences are investigated in non-ideal magnetohydrodynamics. The non-ideal effects included are anisotropic, thermal conduction, and optically thin radiation. The classic ideal Alfvén continuum is not altered by these non-ideal effects, but the discrete Alfvén modes, which exist under certain conditions above or below the Alfvén continuum in ideal MHD, are shown to be influenced by non-adiabatic effects. Title: Nonlinearity effects on resonant absorption of surface Alfvén waves in incompressible plasmas Authors: Ruderman, M. S.; Goossens, Marcel Bibcode: 1993SoPh..143...69R Altcode: The resonant absorption of small amplitude surface Alfvén waves is studied in nonlinear incompressible MHD for a viscous and resistive plasma. The reductive perturbation method is used to obtain the equation that governs the spatial and temporal behaviour of small amplitude nonlinear surface Alfvén waves. Numerical solutions to this equation are obtained under the initial condition that att = 0 the spatial variation is purely sinusoidal. The numerical results show that nonlinearity accelerates the wave damping due to resonant absorption. Resonant absorption is a more efficient wave damping mechanism than can be anticipated on the basis of linear theory. 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: The magnetothermal stability of radially stratified line-tied coronal loops. Authors: Vanderlinden, Ronald A. M.; Goossens, M. Bibcode: 1992ESASP.348..269V Altcode: 1992cscl.work..269V The influence of the photospheric anchoring of the magnetic field lines (line-tying) on the magnetic and thermal (or "magnetothermal") stability of radially stratified coronal loops is studied. The anchoring of the magnetic field lines in the photosphere is modelled by line-tying boundary conditions. Using a simple force-free equilibrium, it is shown that line-tying has a much stronger influence on a magnetic instability than on a thermal instability. Thus, line-tying can lead to loops that are magnetically stable but thermally unstable. In such loops, condensations can form due to a thermal instability. This may be of relevance in the context of the formation and eruption of prominences in the solar corona. 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: Total Absorption of Sound Waves by Solar Magnetic Flux Tubes Authors: Hollweg, J. V.; Goossens, M. Bibcode: 1992AAS...180.1702H Altcode: 1992BAAS...24R.753H No abstract at ADS Title: Resonant Behaviour of Magnetohydrodynamic Waves on Magnetic Flux Tubes - Part Three Authors: Goossens, Marcel; Hollweg, Joseph V.; Sakurai, Takashi Bibcode: 1992SoPh..138..233G Altcode: The resonances that appear in the linear compressible MHD formulation of waves are studied for equilibrium states with flow. The conservation laws and the jump conditions across the resonance point are determined for 1D cylindrical plasmas. For equilibrium states with straight magnetic field lines and flow along the field lines the conserved quantity is the Eulerian perturbation of total pressure. Curvature of the magnetic field lines and/or velocity field lines leads to more complicated conservation laws. Rewritten in terms of the displacement components in the magnetic surfaces parallel and perpendicular to the magnetic field lines, the conservation laws simply state that the waves are dominated by the parallel motions for the modified slow resonance and by the perpendicular motions for the modified Alfvén resonance. Title: Linear Resistive Magnetohydrodynamic Computations of Resonant Absorption of Acoustic Oscillations in Sunspots Authors: Goossens, Marcel; Poedts, Stefaan Bibcode: 1992ApJ...384..348G Altcode: A numerical study of the resonant absorption of p-modes by sunspots is performed in linear resistive MHD. A parametric evaluation shows that the efficiency of the absorption mechanism depends significantly on both the equilibrium model and the characteristics of the p-modes. Results from this numerical study of the relevant parameter domain indicate that the resonant absorption of p-modes is more efficient in larger sun spots with twisted magnetic fields. This is particularly true for p-modes with higher azimuthal wave numbers. Title: Modelling stellar surface magnetic fields. I. Search strategies and uniqueness. Authors: Stift, M. J.; Goossens, M. Bibcode: 1991A&A...251..139S Altcode: Within the framework of the Rigid Rotator hypothesis, an elaborate procedure for the modeling of stellar magnetic surface fields aimed at ensuring the uniqueness of the final models by means of appropriate search strategies is proposed. Two different field geometries are considered for this purpose. Using a sufficiently dense grid, the entire 6D or 4D parameter space for those models that best predict the observed integrated longitudinal field and integrated scalar field strength is explored. In a second step, detailed calculations of Stokes profiles for a few selected transitions make it possible to pick out the most promising starting models for the final iterative line profile modeling procedure, often leading simultaneously to the resolution of the ambiguity between obliquity angle and inclination in axisymmetric models. Illustrating the method with the analysis of the magnetic variations of four well-observed Ap stars it is shown that the starting models derived are in reasonable agreement with the published spectra. Title: The Thermal Continuum in Coronal Loops - Instability Criteria and the Influence of Perpendicular Thermal Conduction Authors: van der Linden, R. A. M.; Goossens, M. Bibcode: 1991SoPh..134..247V Altcode: The linear MHD spectrum is investigated for cylindrical equilibrium models under typical coronal conditions. Non-ideal effects are included and attention is focussed on the thermal instability and the influence of perpendicular thermal conduction. It is shown that, when thermal conduction across magnetic field lines is neglected, the `classic' Alfvén and slow continua are supplemented by a new `thermal' continuum. Surprisingly, the existence of this non-ideal continuous spectrum appears to have been overlooked for a very long time. Unlike the (still purely oscillatory) Alfvén continuum modes and the slow continuum modes (overstable or damped), the thermal continuum modes are exponentially growing or decaying in time. As with the Alfvén and slow continua, discrete modes may be present above or below the thermal continuum, depending upon the choice of equilibrium parameters. These modes are localized using a simple WKB approach. The knowledge of the thermal subspectrum is then exploited to find necessary and sufficient conditions for instability. Title: On Poloidal Mode Coupling in the Continuous Spectrum of 2d Equilibria Authors: Poedts, Stefaan; Goossens, Marcel Bibcode: 1991SoPh..133..281P Altcode: The continuous spectrum of linear ideal MHD is determined analytically in 2D magnetostatic models for coronal loops and arcades by means of a perturbation expansion. Poloidal mode coupling, induced by non-circularity of the cross-sections of the magnetic surfaces and/or variation of the plasma density along the magnetic field lines, is shown to occur in first order. The coupling is most pronounced on and near rational surfaces for particular poloidal and toroidal mode numbers and produces gaps in the continuous spectrum of ideal MHD. Title: Resonant Behaviour of Magnetohydrodynamic Waves on Magnetic Flux Tubes - Part One Authors: Sakurai, Takashi; Goossens, Marcel; Hollweg, Joseph V. Bibcode: 1991SoPh..133..227S Altcode: A basic procedure is presented for dealing with the resonance problems that appear in MHD of which resonant absorption of waves at the Alfvén resonance point is the best known example in solar physics. The procedure avoids solving the full fourth-order differential equation of dissipative MHD by using connection formulae across the dissipation layer. Title: Resonant Behaviour of Magnetohydrodynamic Waves on Magnetic Flux Tubes II. Absorption of Sound Waves by Sunspots Authors: Sakurai, Takashi; Goossens, Marcel; Hollweg, Joseph V. Bibcode: 1991SoPh..133..247S Altcode: The absorption of solar five-min oscillations by sunspots is interpreted as the resonant absorption of sound waves by a magnetic cylinder. The absorption coefficient is calculated both analytically under certain simplifying assumptions, and numerically under more general conditions. The observed magnitude of the absorption coefficient, which is up to 0.5 or even more, can be explained for suitable ranges of parameters. Limitations in the present model are also discussed. Title: The Visco Resistive Stability of Arcades in the Corona of the Sun Authors: Bogaert, E.; Goossens, M. Bibcode: 1991SoPh..132..109B Altcode: The stability of ballooning modes in coronal arcades is studied using linear visco-resistive MHD. Rigid wall conditions are adopted for modelling the photospheric line-tying of the magnetic field. The full Braginskii viscosity stress tensor is used and particular attention is given to the effect of the viscosity coefficient η3 which was left out of an earlier investigation by Van der Linden, Goossens, and Hood (1987, 1988). The numerical results for shearless arcades show that the coefficient η3 has a stabilizing effect. However, for realistic values of the equilibrium quantities the stabilizing effect by η3 can be neglected in comparison with the strong stabilizing effect of the perpendicular viscosity. The effect of magnetic field strength and mode number on stability are determined. In particular it is found that there exists a critical field strength for every mode number such that the mode is stable for weaker fields and unstable for stronger fields. Title: Analytical study of plasma heating by resonant absorption of the modified external kink mode Authors: van Eester, D.; Goossens, M.; Poedts, S. Bibcode: 1991JPlPh..45....3V Altcode: A simplified analytic description is used to understand recent results of large-scale numerical simulations of resonant absorption and to disentangle the basic physics. It is shown that very efficient absorption takes place at frequencies where a discrete external kink and an Alfvén continuum mode merge into a modified external kink mode. The relation between this ‘hybrid’ mode and ‘pure’ continuum or discrete spectrum modes is discussed. Title: Thermal instability in slab geometry in the presence of anisotropical thermal conduction Authors: van der Linden, R. A. M.; Goossens, M. Bibcode: 1991SoPh..131...79V Altcode: Prominences and filaments are thought to arise as a consequence of a magnetized plasma undergoing thermal instability. Therefore, the thermal stability of a magnetized plasma is investigated under coronal conditions. The equilibrium structure of the plasma is approximated by a 1-D slab configuration. This is investigated in thermal instability taking into account optically thin plasma radiation and anisotropic thermal conduction. The thermal conduction perpendicular to the magnetic field is taken to be small but non-zero. Title: Resonant Absorption of MHD Waves in Magnetic Loops in the Solar Corona Authors: Goossens, M. Bibcode: 1991mcch.conf..480G Altcode: No abstract at ADS Title: Magnetohydrodynamic waves and wave heating in non-uniform plasmas. Authors: Goossens, M. Bibcode: 1991gamp.conf..137G Altcode: The present review will not try to give a complete description of the present status of MHD waves in the solar atmosphere. Instead it will attempt to outline basic properties of MHD waves in nonuniform plasmas and will focus on those aspects of MHD waves that are important for understanding wave heating theories of the solar corona. Title: Magnetohydrodynamic Waves and Wave Heating in Nonuniform Plasmas Authors: Goossens, M. Bibcode: 1991assm.conf..137G Altcode: No abstract at ADS Title: On the Efficiency of Coronal Loop Heating by Resonant Absorption Authors: Poedts, Stefaan; Goossens, Marcel; Kerner, Wolfgang Bibcode: 1990ApJ...360..279P Altcode: The heating of solar coronal loops by resonant absorption of Alfven waves is investigated in the framework of linearized compressible resistive MHD. The resonant absorption of the waves incident on the coronal loops is numerically simulated in straight cylindrical, axisymmetric loop models externally excited by a periodic source. The stationary state of this driven system and the ohmic dissipation rate in this state are determined by a very accurate code based on the finite element technique. The efficiency of the heating mechanism and the energy deposition profile in this stationary state strongly depend on the characteristics of both the external driver and the equilibrium. It is shown that resonant absorption is very efficient for typical coronal loops as a considerable part of the energy supplied by the external source is actually dissipated ohmically and converted into heat. The heating rate is proportional to the square of the magnitude of the background magnetic field. Title: Temporal evolution of resonant absorption in solar coronal loops Authors: Poedts, Stefaan; Goossens, Marcel; Kerner, Wolfgang Bibcode: 1990CoPhC..59...95P Altcode: A numerical code is presented for the computation of the temporal evolution of an externally driven cylindrical plasma column in the framework of linearized compressible and resistive magnetohydrodynamics. The partial differential equations are solved with a semi-discretization method using cubic and quadratic finite elements for the spatial discretization and a fully implicit time advance. This numerical technique yields very accurate results even for small values of the resistivity. With this code it is, amongst others, possible to simulate the heating of solar coronal loops by the resonant absorption of waves that inpitch on them in order to determine the role of this dissipation mechanism in coronal heating. In particular, it is necessary to find out how the time scales of this heating mechanism compare to the life of the coronal loops.

Present address: JET Joint Undertaking, Theory Division, Abingdon, Oxfordshire OX14 3EA, England. Title: A combined finite element/Fourier series method for the numerical study of the stability of line-tied magnetic plasmas Authors: van der Linden, R. A. M.; Goossens, M.; Kerner, W. Bibcode: 1990CoPhC..59...61V Altcode: An efficient method is presented for the numerical study of the stability of line-tied coronal plasmas. This method uses a finite element discretization in the direction normal to the magnetic flux surfaces and a Fourier series analysis in the axial direction for solving the differential equations that govern linear perturbations of a static equilibrium. It has a wide range of possible applications both in ideal and non-ideal magnetohydrodynamic stability investigations.

As an example, the numerical method is used to investigate the ideal MHD stability of a straight line-tied cylindrical plasma, modelling a coronal loop. It is found that line-tying has a notable stabilizing influence on both internal and external modes in the sense that it reduces the growthrate of the unstable modes as compared to the case of an infinite or periodic cylinder. For a fixed equilibrium profile, complete stabilization is obtained as soon as the cylinder length is reduced below a critical value. Title: Linearly overstable magnetic convection in 1D compressible and non-uniform plasmas Authors: Hermans, D.; Kerner, W.; Goossens, M. Bibcode: 1990CoPhC..59..127H Altcode: The linear overstable magnetic convection in a non-uniform and compressible plasma slab is computed using a finite element eigenvalue code. Overstable modes are found to be part of the slow-gravity subspectrum and can be stabilized by increasing the magnetic field strength. The periods of overstable oscillations are determined by the isothermal frequency. Results for two different sequences of equilibrium configurations are presented. Title: Numerical simulation of the stationary state of periodically driven coronal loops Authors: Poedts, Stefaan; Goossens, Marcel; Kerner, Wolfgang Bibcode: 1990CoPhC..59...75P Altcode: The heating of solar coronal loops by resonant absorption of Alfvén waves is studied in the framework of linearized, compressible, resistive MHD by means of numerical simulations in which the loops are approximated by straight cylindrical, axisymmetric plasma columns with equilibrium quantities varying only in the radial direction. The incident waves that excite the loops are modelled by a periodic external source. The stationary state of this driven system is determined numerically with a finite element code. The finite element technique is extremely suitable to compute the nearly-singular solutions and yields very accurate results. The efficiency of the heating mechanism and the energy deposition profile in this stationary state strongly depend on the characteristics of both the external driver and the equilibrium. A numerical survey of the relevant parameter space shows that resonant absorption is very efficient for typical coronal parameter values and appears to be a viable candidate heating mechanism for solar loops.

Present address: JET Joint Undertaking, Theory Division, Abingdon, Oxfordshire OX14 3EA, England. Title: Problems in the numerical modelling of plasmas. Contributed papers. 4. European Workshop on Problems in the Numerical Modelling of Plasmas (NUMOP 89), Spitzingsee (Germany, F.R.), 1 - 5 Oct 1989. Authors: Goossens, M.; Kerner, W. Bibcode: 1990CoPhC..59.....G Altcode: For the invited review papers of this workshop see the main entry 012.063. Title: Problems in the numerical modelling of plasmas. Invited review papers. 4. European Workshop on Problems in the Numerical Modelling of Plasmas (NUMOP 89), Spitzingsee (Germany, F.R.), 1 - 5 Oct 1989. Authors: Goossens, M.; Kerner, W. Bibcode: 1990CoPhR..12.....G Altcode: For the contributed papers of this workshop see the main entry 012.093. Title: Overstable slow-gravity modes in a thermally conducting MHD plasma-slab Authors: Hermans, D.; Goossens, M.; Kerner, W. Bibcode: 1990A&A...231..259H Altcode: A study of the spectrum of linear motions of a compressible and thermally conducting plasma slab with a horizontal magnetic field and a constant vertical gravity field is conducted in order to obtain a clear picture of overstable linear motions. A numerical scheme is used based on a finite element discretization which allows for the rigorous inclusion of the compressibility of the plasma and the nonuniformity of the equilibrium configuration. It is found that the overstable linear modes are part of the slow-gravity subspectrum that also contains the isothermal continuum and two groups of purely exponentially growing modes, determined by thermal and gravitational effects. The oscillatory frequencies of the overstable modes are always smaller than the maximum value of the isothermal frequency, so that the characteristic periods of the overstable modes are larger than those obtained in the Boussinesq approximation which are linked to the Alfven frequency. Title: Thermal Instability in Planar Solar Coronal Structures Authors: van der Linden, R. A. M.; Goossens, M. Bibcode: 1990LNP...363..276V Altcode: 1990doqp.coll..276V; 1990IAUCo.117..276V Prominentes and filaments are thought to arise as a consequence of a magnetized plasma undergoing thermal instability. Therefore the thermal stability of a magnetized plasma is investigated under coronal conditions. The equilibrium structure of the plasma is approximated by a 1-D slab configuration. This is investigated on thermal instability taking into account optically thin plasma radiation and anisotropical thermal conduction. The thermal conduction perpendicular to the magnetic field is taken to be small but non-zero. The classical rigid wall boundary conditions which are often applied in the litterature, either directly on the plasma or indirectly through some other medium, are replaced by a more physical situation in which the plasma column is placed in a low-density background stretching towards infinity. Results for a uniform equilibrium structure indicate the major effect of this change is on the eigenfunctions rather than on the growthrate. Essentially, perpendicular thermal conduction introduces field-aligned fine-structure. It is also shown that in the presence of perpendicular thermal conduction, thermal instability in a slab model is only possible if the inner plasma has the shortest thermal instability time-scale. Title: Dynamic stabilization of unstable gravity modes by magnetic fields in non-uniform and compressible plasma Authors: Hermans, D.; Goossens, M. Bibcode: 1989A&A...225..569H Altcode: The dynamic stabilization of unstable gravity modes by magnetic fields is investigated for nonuniform and compressible plasmas. This is done by studying the spectrum of linear motions of 1D horizontal plasmas in the presence of a horizontal sheared magnetic field and an external vertical gravity field. In case of a compressible plasma the slow subspectrum is the relevant part of the spectrum for the dynamic stabilization of unstable gravity modes. Because of the nonuniformity of the basic state this slow subspectrum consists of a discrete part and a continuous part, with the latter defined by the range of the cusp frequency. The slow subspectrum is computed for three sequences of basic states which differ by the profiles of the frequency of Brunt-Vaisala, the frequency of Alfven, and the cusp frequency. The magnetic field has a stabilizing effect and complete stability can be obtained under certain conditions for strong enough fields. The stabilizing effect of the magnetic field is determined by the variation of the cusp frequency, and, thus by the slow continuous part of the spectrum. The discrete slow subspectrum hangs on the slow continuous spectrum, so to speak, and stability can be obtained by transition of unstable regular normal modes either to stable regular modes below the slow continuum or into the slow continuum. 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: Alfvén-wave heating in resistive MHD Authors: Poedts, Stefaan; Kerner, Wolfgang; Goossens, Marcel Bibcode: 1989JPlPh..42...27P Altcode: Resonant absorption of Alfvén waves in tokamak plasmas is studied numerically using the linearized equations of resistive magnetohydrodynamics. A numerical code based on a finite-element discretization is used for determining the stationary state of a cylindrical plasma column that is excited by an external periodic driver. The energy dissipation rate in the stationary state is calculated and the dependence of the plasma heating on electrical resistivity, the equilibrium profiles, and the wavenumbers and frequency of the external driver is investigated. Resonant absorption is extremely efficient when the plasma is excited with a frequency near that of a so-called ‘collective mode’. The heating of a plasma by driving it at the frequencies of discrete Alfvén waves is also investigated. Title: Numerical simulation of coronal heating by resonant absorption of Alfvén waves Authors: Poedts, Stefaan; Goossens, Marcel; Kerner, Wolfgang Bibcode: 1989SoPh..123...83P Altcode: The heating of coronal loops by resonant absorption of Alfvén waves is studied in compressible, resistive magnetohydrodynamics. The loops are approximated by straight cylindrical, axisymmetric plasma columns and the incident waves which excite the coronal loops are modelled by a periodic external driver. The stationary state of this system is determined with a numerical code based on the finite element method. Since the power spectrum of the incident waves is not well known, the intrinsic dissipation is computed. The intrinsic dissipation spectrum is independent of the external driver and reflects the intrinsic ability of the coronal loops to extract energy from incident waves by the mechanism of resonant absorption. Title: Thermal Instability in Planar Solar Coronal Structures Authors: van der Linden, R. A. M.; Goossens, M. Bibcode: 1989HvaOB..13..289V Altcode: No abstract at ADS Title: Kink modes in coronal loops. Authors: Goedbloed, J. P.; Goossens, M.; Poedts, S. Bibcode: 1989plap.work..103G Altcode: Spectral theory of magnetohydrodynamic waves and instabilities has been extensively developed. With proper modifications results obtained for tokamaks can be transferred to the study of stability of coronal flux loops and heating of the corona by means of Alfvén waves. In tokamaks external kink modes are stabilized by the geometric constraint that the modes should fit into the torus. In current-carrying coronal loops the opposite problem arises, viz. the apparent absence of external kink modes, as evidenced by their long life-time, spanning many orders of magnitude of the characteristic growth-time of these instabilities. Anchoring of the foot points of the field lines in the photosphere is generally considered to be the responsible agent for stabilization. Given the overall MHD stability of a coronal magnetic loop structure, the subtle analysis of Alfvén wave heating by means of the continuous spectrum may be undertaken. Here, an additional complication is encountered which turns out to be quite beneficial though from the point of view of heating efficiency. This gives rise to improper modes which have both a global character and a non-integrable part which admits quasi-dissipation. Title: Coronal heating by resonant absorption in resistive MHD. Authors: Poedts, S.; Goossens, M.; Kerner, W. Bibcode: 1989plap.work..107P Altcode: The heating of coronal loops by the process of resonant absorption of Alfvén waves is studied in compressible, resistive magnetohydrodynamics. The authors consider a one-dimensional, cylindrical-symmetric plasma column which is excited periodically by means of an external driver. They determine the intrinsic dissipation spectrum which is independent of the external driver (whose power spectrum is not known) and yet reveals some interesting features of heating by resonant absorption. Resonant absorption is very efficient for typical coronal loop parameter values. A considerable part of the energy supplied by the external driver, is actually dissipated Ohmically and converted into heat. The energy dissipation rate is almost independent of the resistivity for the relevant values of this parameter. The efficiency of the heating mechanism strongly depends on the equilibrium profiles, the wave numbers and the frequency of the external driver. Title: Deposit of observations of beta Cephei stars in the IUA archives of unpublished photoelectric observations of variable stars. Authors: Cuypers, J.; Lampens, P.; Goossens, M. Bibcode: 1988BICDS..35..155C Altcode: No abstract at ADS 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: The continuous spectrum of MHD waves in 2-D solar loops and arcades - Parametric study of poloidal mode coupling for poloidal magnetic fields Authors: Poedts, S.; Goossens, M. Bibcode: 1988A&A...198..331P Altcode: This parametric study investigates how poloidal mode coupling of ideal MHD continuum modes of two-dimensional models for coronal loops and arcades depends on equilibrium quantities. The two physical causes for poloidal mode coupling considered are non-circularity of the cross-sections of the flux surfaces and variation of the equilibrium density along the magnetic field lines. This phenomenon of wave number coupling is typical for the continuous spectrum of MHD waves of 2D plasmas. It has two important consequences: the eigenfrequencies are modified, and the eigenfunctions tend to localize. The present parametric study is concerned with the dependence of poloidal mode coupling on the value of the plasma beta (i.e. the ratio of the plasma pressure to the magnetic pressure), the ellipticity of the cross-sections, and the variation of the equilibrium density normal to the magnetic surfaces and along the magnetic field lines. For realistic values of the parameters, it is found that the continuous spectrum is modified, the ranges of the continuum frequencies are considerably enlarged, and the derivatives of the continuum frequencies normal to the magnetic surfaces are considerably increased. Consequently, the phasemixing time is reduced, and the efficiency of phase-mixing as a heating mechanism of solar loops and arcades is increased. The dissipation of wave energy depends on two spatial coordinates and is found to be larger at the tops of the coronal loops. Title: Linear spectrum of magnetostatic and thermally conducting planar plasmas Authors: Hermans, D.; Goossens, M.; Kerner, W.; Lerbinger, K. Bibcode: 1988PhFl...31..547H Altcode: The linear spectrum of one-dimensional magnetostatic and thermally conducting plasmas is analyzed. The model and mathematical expressions for the eigenvalue problem of linear motions of a one-dimensional plasma in a gravitational field are presented. The effects of thermal conduction on the linear spectrum, the ideal slow continuous spectrum, and the isothermal slow continuous spectrum are investigated. Particular attention is given to changes in the slow and fast magnetoacoustic modes and the thermal modes of the isothermal slow continuous spectrum. It is observed that thermal conduction affects various portions of the linear spectrum of ideal MHD differently; the ideal Alfven continuous spectrum is not influenced by thermal conduction; and the isothermal slow continuous spectrum replaces the ideal slow continuous spectrum. Title: Overstable Convection in a Non-Uniform Magnetic Field Authors: Hermans, D.; Goossens, M.; Kerner, W.; Lerbinger, K. Bibcode: 1988IAUS..123..395H Altcode: The linear spectrum of a non-homogeneous, compressible and thermally conducting planar plasma with a vertical gravitational field and a sheared horizontal magnetic field is studied. It is shown that the spectrum has two continuous parts. The Alfvén continuum of linear ideal MHD is unaffected by radiative conduction, but the slow continuum is removed and replaced by a new continuous part called isothermic continuum. Purely exponentially growing and overstable normal modes have been determined numerically and the distribution of their eigenfrequencies in the complex plane has been studied. Title: The Continuous Spectrum of Magnetohydrodynamic Waves in 2d Solar Loops and Arcades - First Results on Poloidal Mode Coupling for Poloidal Magnetic Fields Authors: Poedts, S.; Goossens, M. Bibcode: 1987SoPh..109..265P Altcode: A first attempt is made to study the continuous spectrum of linear ideal MHD for 2D solar loops and to understand how 2D effects change the continuum eigenfrequencies and continuum eigenfunctions. The continuous spectrum is computed for 2D solar loops with purely poloidal magnetic fields and it is investigated how non-circularity of the cross-sections of the poloidal magnetic surfaces and variations of density along the poloidal magnetic field lines change the continuous spectrum and induce poloidal wave number coupling in the eigenfunctions. Approximate analytical results and numerical results are obtained for the eigenfrequencies and the eigenfunctions and the poloidal wave number coupling is clearly illustrated. It is found that the continuum frequencies are substantially increased, that the ranges of the continuum frequencies are considerably enlarged and that the derivatives of the continuum frequencies normal to the magnetic surfaces are substantially increased. The eigenfunctions are strongly influenced by poloidal wave number coupling. Implications of these findings for the heating mechanisms of resonant absorption and phase mixing are briefly considered. 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: Poloidal Mode Coupling of Alfvén Continuum Modes in 2D Coronal Loops Authors: Poedts, S.; Goossens, M. Bibcode: 1987rfsm.conf..272P Altcode: No abstract at ADS Title: Poloidal mode coupling of Alfvén continuum modes in 2D coronal loops. Authors: Poedts, S.; Goossens, M. Bibcode: 1987rfsm.conf..277P Altcode: Study of the continuous spectrum of two-dimensional (2D) solar loops is obviously required to see how 2D effects change the continuous spectrum and influence resonant absorption and phase mixing. The results show that the Alfvén continuum of static 2D solar loops can be changed substantially compared with the 1D plasma case. This can have important consequences for resonant absorption and phase mixing. In particular the present results indicate that density variation along magnetic field lines increases the efficiency of phase mixing of Alfvén continuum waves. Title: The Alfven-gravity spectrum of an incompressible slab Authors: Hermans, D.; Goossens, M. Bibcode: 1987A&A...172...85H Altcode: The linear spectrum of a horizontal incompressible layer in the presence of a nonuniform magnetic field is studied in order to understand the dynamic stabilization of the unstable gravity modes. Such a study is necessary to understand overstable magnetic convection. Overstable magnetoconvection has been invoked as a possible mechanism for waves and oscillations in sunspots and for rapid oscillations observed in Ap-stars. The Alfven-gravity for waves and oscillations in sunspots and for rapid oscillations observed in Ap-stars. The Alfven-gravity spectrum is computed for four sequences of equilibrium configurations that differ by the profiles of the Brunt-Vaisala frequency and the Alfven frequency, and hence by the Alfven continuum. The evolution of the spectrum is determined for increasing strength of the magnetic field. Title: Viscous Normal Modes on Coronal Inhomogeneities and Their Role as a Heating Mechanism Authors: Steinolfson, R. S.; Priest, E. R.; Poedts, S.; Nocera, L.; Goossens, M. Bibcode: 1986ApJ...304..526S Altcode: Viscous damping of Alfven surface waves is examined both analytically and numerically using incompressible MHD. Normal modes are shown to exist on discontinuous as well as continuously varying interfaces in Alfven speed. The waves experience negligible decay below the transition zone. High-frequency waves damp just above the transition region, while those of lower frequency lose energy further out. A comparison of dissipative decay rates shows that wave damping by viscosity proceeds approximately two orders of magnitude faster than by resistivity. Title: On the existence of the continuous spectrum of ideal MHD in a 2D magnetostatic equilibrium. Authors: Goossens, M.; Poedts, S.; Hermans, D. Bibcode: 1985SoPh..102...51G Altcode: The continuous spectrum of a 2D magnetostatic equilibrium with y-invariance is derived. It is shown that the continuous spectrum is given by an eigenvalue problem on each magnetic surface and is related to the different behaviour of the equilibrium quantities in different magnetic surfaces. The special case of a uniform poloidal magnetic field in a 1D equilibrium that is stratified with height, has been considered in detail and it is found that there is no continuous spectrum. It is shown that this result relies completely on the artificial property that the behaviour of the equilibrium quantities along a magnetic field line is independent of the field line considered. As a consequence the non-existence of a continuous spectrum in a 1D equilibrium with a uniform magnetic field cannot be used to argue that the continuous spectrum has no physical relevance. Title: The continuous spectrum of an axisymmetric self-gravitating and static equilibrium with a mixed poloidal and toroidal magnetic field Authors: Poedts, S.; Hermans, D.; Goossens, M. Bibcode: 1985A&A...151...16P Altcode: The continuous spectrum of the linearized equations of ideal MHD is investigated for an axisymmetric, self-gravitating equilibrium with a mixed poloidal and toroidal magnetic field. The continuous spectrum for a purely poloidal magnetic field is treated as a special case. The continuous spectrum of a purely poloidal magnetic field is given by an eigenvalue problem of two uncoupled ordinary second order differential equations along the magnetic field lines, so that there are two uncoupled continuous parts of the spectrum: an Alfvén continuum and a cusp continuum. Variational expressions for the continuum frequencies are derived for each of the two continua, and it is found that the Alfvén continuum is always on the stable side of the spectrum but the cusp continuum can be unstable. The continuous spectrum in the presence of a mixed poloidal and toroidal magnetic field is given by an eigenvalue problem of a fourth order system of coupled ordinary differential equations. A variational expression is derived for the continuum frequencies and it is found that the equilibrium gravitational field can lead to an unstable continuous spectrum. Title: Axisymmetric force-free stellar magnetospheres Authors: Goossens, M.; Hereygers, G. Bibcode: 1985A&A...149..253G Altcode: Self-consistent axisymmetric force-free magnetospheres are computed on the assumption that the toroidal component is related to the poloidal flux function through a power law and that the emergent field has both a dipolar and a quadrupolar contribution. It is found that there is a maximum value of the toroidal magnetic field which cannot be exceeded if the magnetosphere is to be force-free, and this maximum value decreases when the quadrupolar contribution to the poloidal magnetic field becomes more important. Simple polynomial expressions are derived for the quantities that describe the variations of the magnetic field components over the stellar surface and these polynomial expressions allow magnetic observations to be modelled with axisymmetric force-free magnetic fields. Title: The Continuous Spectrum of AN Axisymmetric, Self-Gravitating Equilibrium in the Presence of a Poloidal Magnetic Field Authors: Hermans, D.; Goossens, M.; Poedts, S. Bibcode: 1984ESASP.207..297H Altcode: The continuous spectrum of oscillation frequencies is examined for an axisymmetric, self-gravitating equilibrium in the presence of a purely poloidal magnetic field. It is shown that the continuous spectrum is given by an eigenvalue problem of two uncoupled ordinary second orders differential equations along the magnetic field lines. The two decoupled continuous spectra have modes that are polarized either perpendicular or parallel to the magnetic field lines and may be called Alfven continuum and cusp continuum in analogy to the linear diffuse pinch. Curvature and toroidicity influence the two continua, but only the cusp continuum is affected by gravity and compressibility. Variational expressions for the continuum frequencies are derived and it is found that only the cusp continuum can attain negative values. The stability depends on the distribution of density, pressure, gravity, and magnetic field along the magnetic field lines. Title: The continuous spectrum of an axisymmetric equilibrium with a mixed poloidal and toroidal magnetic field and with gravity included. Authors: Poedts, S.; Goossens, M.; Hermans, D. Bibcode: 1984ESASP.220..201P Altcode: 1984ESPM....4..201P The continuous spectrum of a static, axisymmetric self-gravitating equilibrium with a mixed poloidal and toroidal magnetic field is given by an eigenvalue problem of two coupled ordinary second-order differential equations. The solutions have motions in the magnetic surfaces that are not polarized purely perpendicular and purely parallel to the magnetic field lines and show mixed properties. This coupling of the classical Alfven and cusp continuum is due to the toroidal magnetic field component and even persists in the incompressible limit. A variational expression was derived for the continuum frequencies and it is shown that the continuum frequencies can be negative. The stability depends on the distributions of density and pressure in the magnetic surfaces. Title: Light variability of sigma Scorpii. Authors: Goossens, M.; Lampens, P.; de Maerschalck, D.; Schrooten, M. Bibcode: 1984A&A...140..223G Altcode: The light variability of the spectroscopic binary and Beta Cephei star Sigma Scorpii is studied in view of Van Hoof's (1966) observations, which when subjected to period analyses in individual years reveal two oscillations whose periods and mean light curves do not exhibit any detectable year-to-year variation. Period analyses of the light observations grouped in orbital phase intervals show that the largest amplitude oscillation found in the individual years is the only oscillation in observations grouped along the binary orbit. The light variability of Sigma Sco can be modelled by two mathematically equivalent, but physically different, models: two intrinsic pulsations with constant periods and amplitudes, or one intrinsic pulsation in which mean light curve amplitude and shape are modulated by tidal action. Title: Linear incompressible magnetoconvection in a planar layer with a non-uniform horizontal magnetic field. Authors: Hermans, D.; Goossens, M.; Polfliet, R. Bibcode: 1984ESASP.220..199H Altcode: 1984ESPM....4..199H The linear stability of an incompressible planar layer in the presence of a non-uniform horizontal magnetic field is studied for three sequences of equilibrium configurations. It is found that the Alfvén continuum is fundamental for the understanding of the linear stability. Title: Linear Stability of an Incompressible Horizontal Layer with a Non-uniform Horizontal Magnetic Field Authors: Hermans, D.; Goossens, M.; Polfliet, R. Bibcode: 1984LIACo..25..387H Altcode: 1984trss.conf..387H; 1984tpss.conf..387H No abstract at ADS Title: Continuous Spectra of Oscillation Frequencies of an Axisymmetric Incompressible Equilibrium with a Poloidal Magnetic field Authors: Goossens, M.; Hermans, D.; Poedts, S. Bibcode: 1984LIACo..25..382G Altcode: 1984trss.conf..382G; 1984tpss.conf..382G No abstract at ADS Title: Light variations of Sigma Sco (conference paper) Authors: Goossens, M.; Lampens, P.; de Maerschalck, D.; Schrooten, M. Bibcode: 1983HvaOB...7..215G Altcode: The light variability of σ Sco can be represented by two mathematically equivalent but physically different models: (1) two intrinsic pulsations with constant periods and amplitudes; (2) one intrinsic pulsation of which the amplitude and the shape of the mean light curve are modulated by tidal action. Title: A singular perturbation approach to the effect of a weak magnetic field on stellar oscillations Authors: Biront, D.; Goossens, M.; Cousens, A.; Mestel, L. Bibcode: 1982MNRAS.201..619B Altcode: The effect of a weak, axisymmetric magnetic field on linear, adiabatic oscillations of a star is studied. Over the bulk of the star a regular perturbation treatment is adequate, but this breaks down near the surface if the field does not vanish there but extends into the low density exterior. Singular perturbation methods are applied to the case of a star with a polytropic atmosphere and a curl-free, dipolar field in the surface region, oscillating in a mode that is radial in the absence of the field. Deep down the motions remain nearly radial, but as the surface is approached the field ensures that the horizontal and vertical motions are of the same order, possibly affecting the interpretation of observed light and velocity curves. Title: Frequency analyses of light and radialvelocity observations of alf Lup. Authors: Lampens, P.; Goossens, M. Bibcode: 1982A&A...115..413L Altcode: Photoelectric photometric observations by Van Hoof are used to study the light variability of α Lupi. Frequency analyses of Van Hoof's observations in Y and UV light reveal the existence of only one oscillation with an amplitude larger than the noise level of the observations. The frequency of this oscillation is determined to be f = 3.848424 ± O.OOOO4Oc/d and shows no variation that can be detected with Van Hoof's observations. We show that both the light variability and the radial velocity variations can be represented by an oscillation with a constant frequency. Title: Unstable poloidal magnetic fields in stars Authors: van Assche, W.; Goossens, M.; Tayler, R. J. Bibcode: 1982A&A...109..166V Altcode: The dynamic stability of an axisymmetric star with a purely poloidal magnetic field is studied by means of the energy method. It is shown that a poloidal magnetic field is always unstable at a simple neutral point, which is encircled by the magnetic field lines. The results obtained by Wright and by Markey and Tayler for particular field geometries are thus generalized. The sigma-energy method is used to obtain the growth rates of instabilities in the neighbourhood of a simple neutral point. Numerical applications to weak poloidal fields in polytropes show that these fields are unstable with very short e-folding times. Title: The magnetic field surface structure of HD 215441 Authors: Goossens, M.; van Assche, W.; Demoitie, R.; Gadeyne, L. Bibcode: 1982Ap&SS..83..213G Altcode: The oblique rotator model with axisymmetric magnetic fields containing a toroidal component is adopted for the description of the magnetic variations observed in Ap stars. The toroidal component is taken as a non-linear function of the stream function of the poloidal component. A scheme is presented for the determination fromH e andH s observations of the parameters that describe the surface distribution of the magnetic field components. This schema is succesfully applied to the magnetic observations of HD 215441, and the existence of different magnetic field surface structures that reproduce equally well the observations has been found. The main characteristics of the different solutions are discussed. Title: Composite Boundary Layer Approximation for Adiabatic Pulsation in Stars with a Magnetic Field Authors: Biront, D.; Cousens, A.; Goossens, M.; Mestel, L. Bibcode: 1982pccv.conf..257B Altcode: No abstract at ADS Title: Frequency Analyses of Light and Radial Observations - Observations of - LUPI and - Crucis Authors: Lampens, P.; Goossens, M.; Cuypers, J. Bibcode: 1982pccv.conf..317L Altcode: No abstract at ADS Title: A contribution to the study of the stability and oscillations of stars with a magnetic field. Authors: Goossens, M. Bibcode: 1982MeBel..44...23G Altcode: No abstract at ADS Title: Frequency Analysis of Photometric Observations of the Beta-Cephei Star Nu-Eridani Authors: Cuypers, J.; Goossens, M. Bibcode: 1981A&AS...45..487C Altcode: A phase dispersion minimization method is used to perform a frequency analysis of Van Hoof's photometric observations of the β Cephei star, ν Eridani. The frequency analysis reveals the existence of four oscillations in the light variability of p Eridani. In addition to the primary largest amplitude oscillation with frequency f0 = 5.76349 c/d, three oscillations have been detected with closely spaced frequencies : f1 = 5.6373 c/d, f2 = 5.6535 c/d, f3 = 5.6201 c/d. The present numerical values of the frequencies are in good agreement with the values obtained by Saito and Kubiak from a frequency analysis of radial velocity data. Title: Additional Results for Unstable Stratified Toroidal Magnetic Fields in Stars Authors: Goossens, M.; Biront, D.; Tayler, R. J. Bibcode: 1981Ap&SS..75..521G Altcode: General conditions for adiabatic instability of weak axisymmetric toroidal magnetic fields are obtained. In particular all fields which haveH ϕ=0 and ∂H {ϕ/2}/∂δ>0 simultaneously are unstable. This includes all fields which exist near to the axis of symmetry and, indeed, any without an infinite current density anywhere. A detailed discussion is given of fields with an angular dependenceH {ϕ/2}∼|P ℓ (cos θ)|. These fields are dynamically unstable with respect to both axisymmetric and non-axisymmetric perturbations for all values of the azimuthal wave number |m|. The maximum growth rates are independent ofm and they are largest for the fields that are defined in the regions closest to the polar axis. Title: On the effective magnetic field of an oblique rotating star with an axisymmetric magnetic field Authors: Goossens, M.; Martens, L.; Gadeyne, L. Bibcode: 1981A&A....95..240G Altcode: This study considers first the theoretical determination of the effective magnetic field in an oblique rotating and magnetic star. An analytical expression for the variation of the effective field is derived for a surface distribution of a magnetic field that is axisymmetric about an axis through the stellar centre, but that is not necessarily irrotational. Subsequently, it is shown that the effective-field observations only contain partial information on the surface distribution of a magnetic field if it is assumed to be axisymmetric but not irrotational. Title: Axisymmetric and mixed poloidal-toroidal magnetic fields for HD 215441 and 53 Cam Authors: Goossens, M.; van Assche, W. Bibcode: 1981LIACo..23..277G Altcode: 1981cpsu.conf..277G A method for the construction of magnetic field geometries from the observed periodic magnetic variations in Ap stars based on the oblique rotator model is presented and applied to the stars HD 215441 and 53 Cam. The method involves the fitting of observations of the surface and effective magnetic fields with the expressions for the surface distribution of the magnetic field components for an axisymmetric magnetic field in order to determine the distribution of the toroidal and poloidal field components. The solutions obtained for various values of the angles i and beta for HD 215441 are found to be characterized by a predominant dipole-like surface structure of the poloidal component with values of the polar strength in the range 40 to 50 kGs and differences in magnetic field at the two poles in the range -40 kGs to -5 kGs. Solutions for 53 Cam are all characterized by poloidal components that have a strong quadrupole-like contribution and relatively strong toroidal components, with a smaller range in polar differences. Title: The influence of a magnetic field on the oscillations of early-type stars Authors: Biront, D.; Goossens, M.; Cousens, A.; Mestel, L. Bibcode: 1981LIACo..23..337B Altcode: 1981cpsu.conf..337B Reference is made to the contention of Weiss et al. (1981) that some early-type pulsationally unstable stars almost certainly have an intrinsic magnetic field. The intent here is to discover what effects the coupling of the magnetic field and the pulsation have. It is thought that subsequent work in this field could explain the long period variability of the light curves of some stars (Blazhko effect) as a modulation caused by the coupling between the pulsation under the influence of the magnetic field and the oblique rotation of the star. It is noted that deep down in the star the thermal pressure is much greater than the magnetic pressure; over most of the star, therefore, the effects of the field are negligible. The period, too, is little affected. An oscillation mode of the star which deep down is purely radial is considered. It is found that near the surface of the star the forces exerted by the distorted field give an angle-dependent horizontal motion comparable to the radial one. A time dependence of exp(i omega t) is assumed throughout for all perturbation quantities. Title: The Effect of a Magnetic Field on Stellar Pulsations as a Singular Perturbation Problem Authors: Goossens, M.; Biront, D. Bibcode: 1980SSRv...27..661G Altcode: 1980IAUCo..58..661G The perturbation problem that describes the effect of a weak magnetic field on stellar adiabatic oscillation is considered. This perturbation problem is singular when the magnetic field does not vanish at the stellar surface, and a regular perturbation scheme fails where the magnetic pressure is comparable to the thermodynamic pressure. The application of the Method of Matched Asymptotic Expansion is used to obtain expressions for the eigenfunctions and the eigenfrequencies. Title: On unstably stratified toroidal magnetic fields in stars Authors: Goossens, M.; Tayler, R. J. Bibcode: 1980MNRAS.193..833G Altcode: A previous discussion of the stability of stars containing an axisymmetric toroidal magnetic field is extended and it is shown that there exist continuous perturbations which give a negative value of (delta) (W to the sigma power) when one of the conditions for stability is violated; this contradicts a conclusion reached by Dicke. The main characteristics of the displacement fields that are associated with the instabilities in the special, but astrophysically relevant, case of a weak toroidal field are indicated. In particular, axisymmetric toroidal magnetic fields with a strength of 100 million G in the cores of solar-type stars produce instabilities with e-folding times of the order of a few hours. Title: Omicron-Stability Analysis of Hydromagnetic Instabilities in Stars with Toroidal Magnetic Fields Authors: Goossens, M.; Biront, D. Bibcode: 1980SSRv...27..667G Altcode: 1980IAUCo..58..667G σ-stability analysis is used to investigate the adiabatic stability of a star containing an axisymmetric toroidal magnetic field. Necessary and sufficient conditions for σ-stability are derived. Special attention is devoted to the typical hydromagnetic instabilities that can be introduced by a weak toroidal magnetic field in a star that is stably stratified in the absence of any magnetic field. An expression for the maximum growth rate of instability is derived and the basic properties of the displacement fields associated with the instabilities are indicated. Title: Periods and Photographic Mean Light Curves of 17 Long Period Variables in a Field around alpha= 17h, delta= -70d Authors: Goossens, M.; Waelkens, C. Bibcode: 1980IBVS.1828....1G Altcode: No abstract at ADS Title: Periods and Mean Light Curves of 22 Long Period Variables in a Field Centered at alpha= 13h, delta= -70d Authors: Goossens, M.; Stoop, C.; Waelkens, C. Bibcode: 1980IBVS.1760....1G Altcode: No abstract at ADS Title: -stability analysis of toroidal magnetic fields in stars Authors: Goossens, M. Bibcode: 1980GApFD..15..123G Altcode: This study uses -stability analysis to explore the hydromagnetic instabilities of a star with an axisymmetric toroidal magnetic field. Necessary and sufficient conditions for -stability are derived and are used to obtain the maximum growth rate (MGR) of instability. The concepts determining the point of MGR and the -stability line are introduced as rigorous tools to investigate the instabilities. The -stability analysis of a star with a weak toroidal magnetic field is considered in detail. It is shown that the hydromagnetic stability of a star with a weak toroidal magnetic field depends solely on the shape of the impressed toroidal magnetic field. Relevant hydromagnetic instabilities are in almost all cases due to an unstable stratification of the toroidal magnetic field with respect to the colatitude. The MGR depends on the strength of the impressed magnetic field, but important properties of the hydromagnetic instabilities, such as the extent of the instability region, the position of the point of MGR, and the shape of the -stability line, depend only on the topology of the magnetic field. The results of the -stability analysis of a star with a weak magnetic field are used to investigate the instabilities caused by admissible weak toroidal magnetic fields H = Kβ (r sin θ)2β - 1 (with β a parameter) in a polytrope n = 3. These toroidal magnetic fields are always most unstable under non-axisymmetric perturbations with |m| = 1 (for β < 2) or under axisymmetric perturbations (β ≥ 2). The growth rates of the most unstable perturbations lead to very short e-folding times when applied to real stars with weak magnetic fields. Instabilities with growth rates comparable to the MGR are primarily internal phenomena, but interesting instabilities with e-folding times still relatively short compared to the nuclear time scale may occur further out. Title: The effective magnetic field of an oblique rotating star with an irrotational and axisymmetric surface distribution of magnetic field. Authors: Goossens, M. Bibcode: 1979A&A....79..210G Altcode: Summary. This study deals with the theoretical determination of the effective field, H,, in a rigidly rotating and magnetic star. An analytical expression is derived for H, when the surface distribution of the magnetic field is irrotational and axisymmetric about an axis through the stellar center. This expression is applied to the axisymmetric and irrotational surface fields that have been considered in the literature to explain observed magnetic variations. It is shown that the expressions for these particular geometries, which were sometimes obtained by elaborate mathematical methods, can be recovered in an elegant way. Key words: magnetic stars - oblique rotator model - effective magnetic field Title: On the orientation of magnetic and rotation axes in Ap stars. II. Results. Authors: Hensberge, H.; van Rensbergen, W.; Goossens, M.; Deridder, G. Bibcode: 1979A&A....75...83H Altcode: On the assumption of a decentered magnetic dipole, models are constructed for 17 Ap stars for which the phase diagram of the effective magnetic field is known. This model involves the determination of the displacement of the dipole, the angle between the rotation axis and the line of sight, the angle between the rotation and magnetic axes, and a parameter determining the strength of the magnetic field. It is possible to determine these parameters quite accurately if the phase diagram of the mean surface magnetic field is also known. It is shown that, for a sample of 17 stars with theoretically predicted distribution functions, there is no evidence against randomly oriented magnetic axes in Ap stars. Title: Unrestricted Second-Order Tensor Virial Equations for Linear Oscillations of Magnetic Configurations Authors: Goossens, M. Bibcode: 1979Ap&SS..60..401G Altcode: This paper deals with the second-order tensor virial equations for the linear oscillations of a gaseous mass in the presence of a magnetic field. It is shown that the commonly used linearized versions of the tensor virial equations are restricted integral equations that incorporate the linearized equation of motion but not the boundary condition. These restricted equations only allow trial functions that fulfil the boundary condition and are of limited practical value. The unrestricted variational principle for the linear oscillations of a magnetic configuration is used to derive a more general formulation of the second-order tensor virial equations so that the linear trial function ξi =X ij x j can be used to study the oscillations of a configuration with a magnetic field that extends in the exterior vacuum. The unrestricted virial equations have been applied to Ferraro's model and approximate results for the eigenfrequencies and eigenfunctions have been obtained for nine oscillation modes. Title: On the Lamb Frequencies of Spherical Gaseous Star Authors: Smeyers, P.; Goossens, M. Bibcode: 1979GApFD..11..237S Altcode: No abstract at ADS Title: Hydromagnetic Instabilities in Polytropic Stars Containing Toroidal Mag- netic Fields Authors: Goossens, M.; Veugelen, R. Bibcode: 1978A&A....70..277G Altcode: Summary. This study concerns the typically hydromagnetic instabilities that occur in a polytrope n =3 that is stably stratified in the absence of any magnetic field and that contains a weak toroidal magnetic field = Kpr sin 0. It is shown that the non-axisymmetric perturbations associated with Im 1=1 are the only possible unstable perturbations and that the most unstable perturbations are localized in the immediate vicinity of the center of the polytrope. A trial function method is used to study the characteristic features of the hydromaguetic instabilities. It is inferred that the motions that are driven by the most violent hydromagnetic instabilities are characterized by small vertical wavelenths for perturbations confined close to the polar axis and by small horizontal wavelengths for other perturbations. Key words: toroidal magnetic fields - hydromagnetic instabilities Title: Application of the Method of Matched Asymptotic Expansions to the Radial Oscillations of a Magnetic Cylinder Authors: Goossens, M.; Cornette, J. Bibcode: 1978Ap&SS..58..227G Altcode: This study deals with the singular character of the perturbation introduced into the eigenvalue problem of the linear and adiabatic oscillations of a gaseous configuration by a magnetic field that is non-zero on the boundary surface of the configuration. This singular character implies that a regular perturbation scheme cannot yield uniformly valid expansion for the eigenfunctions. This investigation considers the application of the Method of Matched Asymptotic Expansions (M.M.A.E.) to the latter singular perturbation problem in order to obtain uniformly valid expansions for the eigenfunctions and first-order expressions for the eigenfrequencies. As an illustrative example, the M.M.A.E. is applied to the eigenvalue problem of the linear, radial, and adiabatic oscillations of a homogeneous cylindrical plasma with a constant longitudinal magnetic field. Title: On the Lamb frequencies of a spherical gaseous star. Authors: Smeyers, P.; Goossens, M. Bibcode: 1978GApFD..11..237S Altcode: No abstract at ADS Title: The Effect of a Poloidal Magnetic Field on the Linear and Adiabatic Oscillations of a Polytrope n=2 Authors: Goossens, M. Bibcode: 1977Ap&SS..52....3G Altcode: The frequencies of the linear and adiabatic oscillations of a gaseous polytrope with a poloidal magnetic field are determined with the aid of a perturbation method. The influence of the poloidal magnetic field on the different types of spheroidal oscillation modes is discussed. The poloidal magnetic field generally strengthens the stability of the oscillation modes and this effect is the largest in the case of the non-radialp-modes. Title: On the orientation of magnetic and rotation axes in Ap stars. Theory of the decentred magnetic dipole. Authors: Hensberge, H.; van Rensbergen, W.; Goossens, M.; Deridder, G. Bibcode: 1977A&A....61..235H Altcode: A formalism is developed for determining the angle between the magnetic and rotational axes of a magnetic star, the angle between its rotational axis and the line of sight, and the displacement of the dipole along the magnetic axis. The variation with time of the effective magnetic field and the mean surface field is analyzed for a centered oblique rotating magnetic dipole as well as for a decentered dipole. The effective field is calculated as a function of the cosine of the angle between the magnetic axis and the line of sight for positive values of the dipole displacement and various values of the limb darkening coefficient; the surface field is computed as a function of the cosine of the same angle for positive values of the dipole displacement. The results are used to evaluate the ratios between the minimum and maximum effective and surface magnetic fields. It is noted that these ratios may be employed to select possible magnetic fields and geometries for Ap stars if the variations of the two fields with phase are known. Title: Non-Radial Oscillations and Stability of a Polytrope n=3 with a Toroidal Magnetic Field Authors: Goossens, M. Bibcode: 1976Ap&SS..44..397G Altcode: A perturbation method has been applied for the determination of the frequencies of the linear and adiabatic oscillations of a gaseous polytropic configuration pervaded by a purely toroidal magnetic field. The influence of a toroidal magnetic field on the frequencies of the different types of spheroidal oscillation modes is discussed. Title: Non-Radial Oscillations and Stability of Prendergast's Model Authors: Goossens, M. Bibcode: 1976Ap&SS..43....9G Altcode: The frequencies of the linear and adiabatic oscillations of Prendergast's model are determined with the aid of a perturbation method. The influence of the magnetic field on the frequencies of the different types of spheroidal oscillation modes is discussed. Title: Stellar Oscillations and Magnetic Field Perturbations of the Boundary Conditions Authors: Goossens, M.; Smeyers, P.; Denis, J. Bibcode: 1976Ap&SS..39..257G Altcode: The effect of a weak magnetic field on the adiabatic radial and non-radial oscillations of a stellar configuration is studied by means of a perturbation method. Special attention is devoted to the perturbation of the oscillation frequencies resulting from the change of the boundary conditions caused by the magnetic field. This change is related to the fact that the introduction of a magnetic field removes the singularity at the surface of the equilibrium configuration. The perturbation method is applied to Ferraro's model and the influence of a magnetic field on the frequencies of the different types of oscillation modes is discussed. Title: Gravity Modes in Composite Polytropic Stars Authors: Goossens, M.; Smeyers, P. Bibcode: 1974Ap&SS..26..137G Altcode: We study gravity modes of composite polytropic stars which consist of two convectively stable zones separated by a convectively unstable zone. In addition to the unstable gravity modes associated with the intermediate zone, we distinguish two types of stable gravity modes, one type being mainly associated with the core, the other one being mainly associated with the envelope. We find also some accidental ‘resonances’ between the core and the envelope. Title: First Ephemerides of Five Variable Stars in Eridanus and Fornax Authors: Deurinck, R.; Goossens, M. Bibcode: 1973IBVS..792....1D Altcode: No abstract at ADS Title: Perturbation of the Radial and Non-Radial Oscillations of a Star by a Magnetic Field Authors: Goossens, M. Bibcode: 1972Ap&SS..16..386G Altcode: A generalization of the perturbation method is applied to the problem of the radial and the non-radial oscillations of a gaseous star which is distorted by a magnetic field. An expression is derived for the perturbation of the oscillation frequencies due to the presence of a weak magnetic field when the equilibrium configuration is a spheroid. The particular application to the homogeneous model with a purely poloidal field inside, due to a current distribution proportional to the distance from the axis of symmetry, and a dipole type field outside is considered in detail. The main result is that the magnetic field has a large and almost stabilizing effect on unstableg-modes, particularly on higher order modes. With the considered magnetic field the surface layers appear to have a large weight.