Absolute and convective instabilities of parallel propagating circularly polarized Alfvén waves: numerical results

Context.The stability of parallel propagating circularly polarized Alfvén waves (pump waves) has been studied for more than four decades with the use of normal mode analysis. It is well known that the normal mode analysis does not answer the question if a pump wave looks stable or unstable in a particular reference frame. To answer this question it is necessary to find out if the instability is absolute or convective in this reference frame. Aims.We extend our previous study of absolute and convective instabilities of pump waves with small amplitude to pump waves with arbitrary amplitude. Methods.To study the absolute and convective instabilities of pump waves with arbitrary amplitude we numerically implement Brigg's method. Results.We show that the wave is absolutely unstable in a reference frame moving with the velocity U with respect to the rest plasma if U satisfies the inequality Ul Ur) we study the signalling problem. We show that spatially amplifying waves exist only when the signalling frequency is in two symmetric frequency bands, and calculate the dependences of the boundaries of these bands on U for different values of a . We also obtain the dependences of the maximum spatial amplification rate on U for different values of a . The implication of these results on the interpretation of observational data from space missions is discussed. In particular, it is shown that circularly polarized Alfvén waves propagating in the solar wind are convectively unstable in a reference frame of any realistic spacecraft

Propagating transverse waves in soft X-ray coronal jets

Aims. The theoretical model for magnetohydrodynamic (MHD) modes guided by a field-aligned plasma cylinder with a steady flow is adapted to interpret transverse waves observed in solar coronal hot jets, discovered with Hinode/XRT in terms of fast magnetoacoustic kink modes. Methods. Dispersion relations for linear magnetoacoustic perturbations of a plasma jet of constant cross-section surrounded by static magnetised plasma are used to determine the phase and group speeds of guided transverse waves and their relationship with the physical parameters of the jet and the background plasma. The structure of the perturbations in the macroscopic parameters of the plasma inside and outside the jet, and the phase relations between them are also established. Results. We obtained a convenient expansion for the long wave-length limit of the phase and group speeds and have shown that transverse waves observed in soft-X-ray solar coronal jets are adequately described in terms of fast magnetoacoustic kink modes by a magnetic cylinder model, which includes the effect of a steady flow. In the observationally determined range of parameters, the waves are not found to be subject to either the Kelvin-Helmholtz instability or the negative energy wave instability, and hence they are likely to be excited at the source of the jet

The effect of longitudinal flow on resonantly damped kink oscillations

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-Alfv\'enic and hence comparatively slow. 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. 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. Using the small ratio of flow and Alfv\'en speeds we derive simple analytical expressions to the damping rate. The analytical expressions are in good agreement with the resistive eigenmode calculations. Under typical coronal conditions the effect of the flow on the damped kink oscillations is small when the characteristic scale of the density layer is similar or smaller 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

Kink oscillations of flowing threads in solar prominences

Recent observations by Hinode/SOT show that MHD waves and mass flows are simultaneously present in the fine structure of solar prominences. 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. 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. 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. 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.Comment: Accepted for publication in A&

Effects of Steady Flow on Magnetoacoustic-Gravity Surface Waves: I. The Weak Field Case

Magnetoacoustic gravity (MAG) waves have been studied for some time. In this article, we investigate the effect that a shear flow at a tangential discontinuity embedded in a gravitationally stratified and magnetised plasma has on MAG surface waves. The dispersion relation found is algebraically analogous to the relation of the non-flow cases obtained by Miles and Roberts (Solar Phys.141, 205, 1992), except for the introduction of a Doppler-shifted frequency for the eigenvalue. This feature, however, introduces rather interesting physics, including the asymmetric presence of forward- and backward-propagating surface waves. We find that increasing the equilibrium flow speed leads to a shift in the permitted regions of propagation for surface waves. For most wave number combinations this leads to the fast mode being completely removed, as well as more limited phase speed regimes for slow-mode propagation. We also find that upon increasing the flow, the phase speeds of the backward propagating waves are increased. Eventually, at high enough flow speeds, the wave’s direction of propagation is reversed and is in the positive direction. However, the phase speed of the forward-propagating wave remains mainly the same. For strong enough flows we find that the Kelvin–Helmholtz instability can also occur when the forward- and backward-propagating modes couple

Excitation of standing kink oscillations in coronal loops

In this work we review the efforts that have been done to study the excitation of the standing fast kink body mode in coronal loops. We mainly focus on the time-dependent problem, which is appropriate to describe flare or CME induced kink oscillations. The analytical and numerical studies in slab and cylindrical loop geometries are reviewed. We discuss the results from very simple one-dimensional models to more realistic (but still simple) loop configurations. We emphasise how the results of the initial value problem complement the eigenmode calculations. The possible damping mechanisms of the kink oscillations are also discussed

Absolute and convective instabilities in open shear layers

The present paper is the continuation of our study of absolute and convective instabilities in open shear layers [CITE]. In this paper the effects of a magnetic field are included and a series of fully non-linear ideal polytropic 2D MHD numerical simulations is carried out. The amount of mean flow required to sweep away the perturbation before it grows and destroys the whole flow is calculated for various configurations of the magnetic field. The analytical results obtained by [CITE] for a velocity discontinuity were recovered with a very good accuracy. The study focused on uniform, discontinuous and sheared magnetic fields. We found that the value of mean flow needed for a perturbation to become convectively unstable (critical mean flow) decreased with decreasing value of the plasma β. We also found that the low β value side, of a discontinuous and sheared magnetic field, is predominant in the behaviour of the instability. Finally we show the thickness of the magnetic shear layer has no effect on the value of critical mean flow