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 (k z 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.

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.

Abstract. Using time series of two-dimensional Dopplergrams, a temporal and spatial analysis of oscillations in a quiescent prominence has been performed. The presence of an outstanding oscillatory signal in the acquired data has allowed us to study the two-dimensional distribution of wave motions and, in particular, to detect the location of wave generation and the anisotropic propagation of perturbations from that place. Moreover, a strong damping of oscillations has been observed, with damping times between two and three times the wave period. The direction of propagation, wavelength and phase speed, together with the damping time and wave period, have been quantified and their spatial arrangement has been analysed. Thanks to the goodness of the observational data, the image alignment procedure applied during the data reduction stage and the analysis tools employed, it has been possible to carry out a novel and far-reaching observational study of prominence oscillations.

In this Letter we establish clear evidence for the resonant absorption damping mechanism by analyzing observational data from the novel Coronal Multi-Channel Polarimeter (CoMP). 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 (MHD) wave theory, they should exhibit a frequency dependent damping length due to resonant absorption, governed by the TGV relation showing that transversal plasma inhomogeneity in coronal magnetic flux tubes causes them to act as natural low-pass filters. It is found that 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 TRACE observations of standing kink modes.

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 lowfrequency 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.

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 are 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. Subject headings: Sun: oscillations -Sun: atmosphere -Sun: magnetic fields -waves -Magnetohydrodynamics (MHD) omit the intermediate steps and give the final expression of the dispersion relation, namely k ⊥,e ρ e ω 2 −k 2 z v 2 A,e K ′ m [k⊥,e(R+l/2)] K m[ k ⊥,e (R+l/2)] G e − Ξ e k ⊥,e ρ e ω 2 −k 2 z v 2 A,e K ′ m[ k ⊥,e (R+l/2)] K m[ k ⊥,e (R+l/2)] F e − Γ e

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 nonuniform 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 nonaxisymmetric 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.

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