The solar atmosphere is structured and inhomogeneous both horizontally and vertically. The omnipresence of coronal magnetic loops implies gradients of the equilibrium plasma quantities like the density, magnetic field and temperature. These gradients are responsible for the excitation of drift waves that grow both within the two-component fluid description (in the presence of collisions and without it) and within the two-component kinetic descriptions (due to purely kinetic effects). In the present work the effects of the density gradient in the direction perpendicular to the magnetic field vector are investigated within the kinetic theory, in both electrostatic and electromagnetic regimes. The electromagnetic regime implies the coupling of the gradient-driven drift wave with the Alfven wave. The growth rates for the two cases are calculated and compared. It is found that, in general, the electrostatic regime is characterized by stronger growth rates, as compared with the electromagnetic perturbations. Also discussed is the stochastic heating associated with the drift wave. The released amount of energy density due to this heating should be more dependent on the magnitude of the background magnetic field than on the coupling of the drift and Alfven waves. The stochastic heating is expected to be much higher in regions with a stronger magnetic field. On the whole, the energy release rate caused by the stochastic heating can be several orders of magnitude above the value presently accepted as necessary for a sustainable coronal heating.
We have developed a numerical model of flare heating due to the dissipation of Alfvénic waves propagating from the corona to the chromosphere. With this model, we present an investigation of the key parameters of these waves on the energy transport, heating, and subsequent dynamics. For sufficiently high frequencies and perpendicular wave numbers, the waves dissipate significantly in the upper chromosphere, strongly heating it to flare temperatures. This heating can then drive strong chromospheric evaporation, bringing hot and dense plasma to the corona. We therefore find three important concl…
We investigate in more detail the origin of chromospheric Alfven waves that give rise to the separation of ions and neutrals, the First Ionization Potential Effect (FIP), through the action of the ponderomotive force. In open field regions, we model the dependence of fractionation on the plasma upflow velocity through the chromosphere for both shear (or planar) and torsional Alfven waves of photospheric origin. These differ mainly through their parametric coupling to slow mode waves. Shear Alfven waves appear to reproduce observed fractionations for a wider range of model parameters, and prese…
We solve numerically the ideal MHD equations with an external gravitational field in 2D in order to study the effects of impulsively generated linear and non-linear Alfvén waves into isolated solar arcades and coronal funnels. We analyze the region containing the interface between the photosphere and the corona. The main interest is to study the possibility that Alfvén waves triggers the energy flux transfer toward the quiet solar corona and heat it, including the case that two consecutive waves can occur. We find that in the case of arcades, short or large, the transferred fluxes by Alfvén wa…
The dynamical response of the solar corona to surface and sub-surface perturbations depends on the chromospheric stratification, and specifically on how efficiently these layers reflect or transmit incoming Alfvén waves. While it would be desirable to include the chromospheric layers in the numerical simulations used to study such phenomena, that is most often not feasible. We defined and tested a simple approximation allowing the study of coronal phenomena while taking into account a parametrised chromospheric reflectivity. We addressed the problems of the transmission of the surface rotation…
M dwarf's atmosphere and wind is expected to be highly magnetized. The nonlinear propagation of Alfvén wave could play a key role in both heating the stellar atmosphere and driving the stellar wind. Along this Alfvén wave scenario, we carried out the one-dimensional compressive magnetohydrodynamic (MHD) simulation about the nonlinear propagation of Alfvén wave from the M dwarf's photosphere, chromosphere to the corona and interplanetary space. Based on the simulation results, we develop the semi-empirical method describing the solar and M dwarf's coronal temperature, stellar wind velocity, and…
The tenuous supersonic solar wind that streams from the top of the corona passes through a natural boundary -- the Alfvén surface -- that marks the causal disconnection of individual packets of plasma and magnetic flux from the Sun itself. The Alfvén surface is the locus where the radial motion of the accelerating solar wind passes the radial Alfvén speed, and therefore any displacement of material cannot carry information back down into the corona. It is thus the natural outer boundary of the solar corona, and the inner boundary of interplanetary space. Using a new and unique motion analysis …
A three-dimensional MHD model for the propagation and dissipation of Alfven waves in a coronal loop is developed. The model includes the lower atmospheres at the two ends of the loop. The waves originate on small spatial scales (less than 100 km) inside the kilogauss flux elements in the photosphere. The model describes the nonlinear interactions between Alfven waves using the reduced MHD approximation. The increase of Alfven speed with height in the chromosphere and transition region (TR) causes strong wave reflection, which leads to counter-propagating waves and turbulence in the photospheri…
A simple model of a periodic ensemble of closely packed flux tubes sitting atop a vertically stratified layer reveals that an incident fast wave from below preferentially converts almost immediately to Alfvén waves in the flux tubes, with kink waves restricted to at most a very few Fourier modes. This suggests that observations of coronal kink modes in such structured systems may greatly underestimate the net wave energy flux being transported into and through the corona, much of which may reside in harder-to-observe Alfvén waves. The processes of mode conversion/resonant absorption and Alfvén…
Super-Alfvénic shock waves associated with coronal mass ejections (CMEs) can produce radio emission known as Type II bursts. In the absence of direct imaging, accurate estimates of coronal electron densities, magnetic field strengths and Alfvén speeds are required in order to calculate the kinematics of shocks. To date, 1D radial models have been used, but these are not appropriate for shocks propagating in non-radial directions. Here, we study a coronal shock wave associated with a CME and Type II radio burst using 2D electron density and Alfvén speed maps to determine the locations that shoc…
Physical processes which may lead to solar chromospheric heating are analyzed using high-resolution 1.5D non-ideal MHD modelling. We demonstrate that it is possible to heat the chromospheric plasma by direct resistive dissipation of high-frequency Alfvén waves through Pedersen resistivity. However this is unlikely to be sufficient to balance radiative and conductive losses unless unrealistic field strengths or photospheric velocities are used. The precise heating profile is determined by the input driving spectrum since in 1.5D there is no possibility of Alfvén wave turbulence. The inclusion o…
Context. We address the heating of the solar chromosphere and the related generation of plasma inflows and outflows. Aims. We attempt to detect variations in ion temperature and vertical plasma flows, which are driven by impulsively excited two-fluid Alfvén waves. We aim to investigate the possible contribution of these waves to solar chromosphere heating and plasma outflows. Methods. We performed numerical simulations of the generation and evolution of Alfvén waves with the use of the JOANNA code, which solves the two-fluid equations for ions+electrons and neutrals, coupled by collision terms…
We have performed MHD simulations of Alfven wave propagation along an open flux tube in the solar atmosphere. In our numerical model, Alfven waves are generated by the photospheric granular motion. As the wave generator, we used a derived temporal spectrum of the photospheric granular motion from G-band movies of Hinode/SOT. It is shown that the total energy flux at the corona becomes larger and the transition region height becomes higher in the case when we use the observed spectrum rather than white/pink noise spectrum as the wave generator. This difference can be explained by the Alfven wav…
Many cool stars possess complex magnetic fields [1] that are considered to undertake a central role in the structuring and energising of their atmospheres [2]. Alfvénic waves are thought to make a critical contribution to energy transfer along these magnetic fields, with the potential to heat plasma and accelerate stellar winds [3] [4] [5]. Despite Alfvénic waves having been identified in the Sun's atmosphere, the nature of the basal wave energy flux is poorly understood. It is generally assumed that the associated Poynting flux is generated solely in the photosphere and propagates into the co…
We perform magnetohydrodynamic (MHD) simulations to investigate the propagation of Alfven wave in magnetic chromosphere. We use the 1.5-dimensional expanding flux tube geometry setting and transverse perturbation at the bottom to generate the Alfven wave. Compared with previous studies, our expansion is that we include the radiative loss term introduced by Carlsson & Leenaarts (2012). We find that when an observation based transverse wave generator is applied, the spatial distribution of the time-averaged radiative loss profile in our simulation is consistent with that in the classic atmospher…
Recent observations have demonstrated that waves which are capable of carrying large amounts of energy are ubiquitous throughout the solar corona. However, the question of how this wave energy is dissipated (on which time and length scales) and released into the plasma remains largely unanswered. Both analytic and numerical models have previously shown that Alfvénic turbulence may play a key role not only in the generation of the fast solar wind, but in the heating of coronal loops. In an effort to bridge the gap between theory and observations, we expand on a recent study [De Moortel et al., …
Phase-mixing of Alfvén waves in the solar corona has been identified as one possible candidate to explain coronal heating. While this scenario is supported by observations of ubiquitous oscillations in the corona carrying sufficient wave energy and by theoretical models that have described the concentration of energy in small scale structures, it is still unclear whether this wave energy can maintain the million degree solar corona. The aim of this work is to assess how much energy can be converted by a phase-mixing process triggered by the propagation of Alfvénic waves in a cylindric coronal …
M dwarf's atmosphere is expected to be highly magnetized. The magnetic energy can be responsible for heating the stellar chromosphere and corona, and driving the stellar wind. The nonlinear propagation of Alfvén wave is the promising mechanism for both heating stellar atmosphere and driving stellar wind. Based on this Alfvén wave scenario, we carried out the one-dimensional compressive magnetohydrodynamic (MHD) simulation to reproduce the stellar atmospheres and winds of TRAPPIST-1, Proxima Centauri, YZ CMi, AD Leo, AX Mic, as well as the Sun. The nonlinear propagation of Alfvén wave from the …
Alfvén waves are responsible for the transfer of magnetic energy in the magnetized plasma. They are involved in heating solar atmosphere and driving solar wind through various nonlinear processes. Since the magnetic field configurations directly affect the nonlinearity of Alfvén waves, it is important to investigate how they relate to the solar atmosphere and wind structure through the nonlinear propagation of Alfvén waves. In this study, we carried out the one-dimensional magnetohydrodynamic simulations to realize the above relation. The results show that when the nonlinearity of Alfvén waves…
We use MHD simulations to detect the nonlinear effects of torsional Alfvén wave propagation in a potential magnetic field with exponentially divergent field lines, embedded in a stratified solar corona. In Paper I we considered solutions to the linearised governing equations torsional Alfvén wave propagation and showed, using a finite difference solver we developed named WiggleWave, that in certain scenarios wave damping is stronger than what would be predicted by our analytic solutions. In this paper we consider whether damping would be further enhanced by the presence of nonlinear effects. W…
In this study, we investigate the spatial distribution of highly varying plasma composition around one of the largest sunspots of solar cycle 24. Observations of the photosphere, chromosphere, and corona are brought together with magnetic field modelling of the sunspot in order to probe the conditions which regulate the degree of plasma fractionation within loop populations of differing connectivities. We find that in the coronal magnetic field above the sunspot umbra, the plasma has photospheric composition. Coronal loops rooted in the penumbra contain fractionated plasma, with the highest le…
Coronal seismology is a diagnostic tool used in solar physics for measuring parameters that are otherwise hard to measure; of these parameters, magnetic field values are arguably the most important. The parameters are inferred by combining observations of waves with magnetohydrodynamic (MHD) wave theory. To date, coronal seismology has successfully been applied to various single-oscillation events. Such events are relatively rare, resulting in rare occasions to use diagnostics. Ubiquitous waves in the solar atmosphere might, however, allow for the possibility of dynamic coronal seismology, whi…
We used our newly developed magnetohydrodynamic (MHD) code to perform 2.5D simulations of a fast-mode MHD wave interacting with coronal holes (CH) of varying Alfvén speed which result from assuming different CH densities. We find that this interaction leads to effects like reflection, transmission, stationary fronts at the CH boundary and the formation of a density depletion that moves in the opposite direction to the incoming wave. We compare these effects with regard to the different CH densities and present a comprehensive analysis of morphology and kinematics of the associated secondary wa…
Kink oscillations of a coronal loop are observed and studied in detail because they provide a unique probe into the structure of coronal loops through MHD seismology and a potential test of coronal heating through the phase-mixing of Alfvén waves. In particular, recent observations show that standing oscillations of loops often involve also higher harmonics, beside the fundamental mode. The damping of these kink oscillations is explained by mode coupling with Alfvén waves. We investigate the consequences for wave-based coronal heating of higher harmonics and what coronal heating observational …
Phase mixing of Alfvén waves has been studied extensively as a possible coronal heating mechanism but without the full thermodynamic consequences considered self-consistently. It has been argued that in some cases, the thermodynamic feedback of the heating could substantially affect the transverse density gradient and even inhibit the phase mixing process. In this paper, we use MHD simulations with the appropriate thermodynamical terms included to quantify the evaporation following heating by phase mixing of Alfvén waves in a coronal loop and the effect of this evaporation on the transverse de…
Static distributions of temperature and wind velocity at the transition region are calculated within the framework of magnetohydrodynamics (MHD) of completely ionized hydrogen plasma. The numerical solution of the derived equations gives the width of the transition layer between the chromosphere and the corona as a self-induced opacity of high-frequency Alfven waves (AW). The domain wall is direct consequence of the self-consistent MHD treatment of AW propagation. The low-frequency MHD waves coming from the Sun are strongly reflected by the narrow transition layer, while the high-frequency wav…
Torsional Alfvén waves are promising candidates for transport of energy across different layers of the solar atmosphere and have been theoretically predicted for decades. Previous detections of Alfvén waves so far have however mostly relied on indirect signatures. We present a first direct observational evidence of a fully resolved torsional Alfvén oscillation of a large-scale structure occurring at coronal heights. We analyse IRIS imaging and spectral observation of a surge resulting from magnetic reconnection between active region prominence threads and surrounding magnetic fieldlines. The I…
Chandra [1] made an attempt to show that the work of Dwivedi and Srivastava [2] (hereinafter DS) can be investigated even analytically and their results are erroneous. Dwivedi and Srivastava [3] picked up some values of Chandra [1] and tried to show that they are not physically acceptable. Some results of Chandra [1] are not physically acceptable, as these are the outcome of the wrong approach of DS. However, the results are numerically correct whereas the results of DS are numerically wrong.
We present a new insight into the propagation, attenuation and dissipation of two-fluid, torsional Alfvén waves in the context of heating of the lower solar atmosphere. By means of numerical simulations of the partially-ionized plasma, we solve the set of two-fluid equations for ion plus electron and neutral fluids in three-dimensional (3D) Cartesian geometry. We implement initially a current-free magnetic field configuration, corresponding to a magnetic flux-tube that is rooted in the solar photosphere and expands into the chromosphere and corona. We put the lower boundary of our simulation r…
The solar atmosphere may be heated by Alfven waves that propagate up from the convection zone and dissipate their energy in the chromosphere and corona. To further test this theory, we consider wave heating in an active region observed on 2012 March 7. A potential field model of the region is constructed, and 22 field lines representing observed coronal loops are traced through the model. Using a three-dimensional (3D) reduced magneto-hydrodynamics (MHD) code, we simulate the dynamics of Alfven waves in and near the observed loops. The results for different loops are combined into a single for…
Whilst there are observational indications that transverse MHD waves carry enough energy to maintain the thermal structure of the solar corona, it is not clear whether such energy can be efficiently and effectively converted into heating. Phase-mixing of Alfvén waves is considered a candidate mechanism, as it can develop transverse gradient where magnetic energy can be converted into thermal energy. However, phase-mixing is a process that crucially depends on the amplitude and period of the transverse oscillations, and only recently have we obtained a complete measurement of the power spectrum…
The discovery of ubiquitous low-frequency (3-5mHz) Alfvenic waves in the solar chromosphere (with Hinode/SOT), and corona (with CoMP and the Solar Dynamics Observatory, SDO) has provided some insight into the non-thermal energy content of the outer solar atmosphere. However, many questions remain about the true magnitude of the energy flux carried by these waves. Here we explore the apparent discrepancy in the resolved coronal Alfvenic wave amplitude (~0.5km/s) measured by the Coronal Multi-channel Polarimeter (CoMP) compared to those of the Hinode and the SDO near the limb (~20km/s). We use a…
Context. We diagnose the properties of the plume and interplume regions in a polar coronal hole and the role of waves in the acceleration of the solar wind. Aims. We attempt to detect whether Alfven waves are present in the polar coronal holes through variations in EUV line widths. Methods. Using spectral observations performed over a polar coronal hole region with the EIS spectrometer on Hinode, we study the variation in the line width and electron density as a function of height. We use the density sensitive line pairs of Fe xii 186.88 A & 195.119 A and Fe xiii 203.82 A & 202.04 A . Results.…
It has been shown in a previous work that torsional Alfvén waves can drive turbulence in nonuniform coronal loops with a purely axial magnetic field. Here we explore the role of the magnetic twist. We model a coronal loop as a transversely nonuniform straight flux tube, anchored in the photosphere, and embedded in a uniform coronal environment. We consider that the magnetic field is twisted and control the strength of magnetic twist by a free parameter of the model. We excite the longitudinally fundamental mode of standing torsional Alfvén waves, whose temporal evolution is obtained by means o…
Both observations and numerical simulations suggest that Alfvenic waves may carry sufficient energy to sustain the hot temperatures of the solar atmospheric plasma. However, the thermalization of wave energy is inefficient unless very short spatial scales are considered. Phase mixing is a mechanism that can take energy down to dissipation lengths, but it operates over too long a timescale. Here, we study how turbulence, driven by the nonlinear evolution of phase-mixed torsional Alfven waves in coronal loops, is able to take wave energy down to the dissipative scales much faster than the theory…
We investigate off-limb active region and quiet Sun corona using spectroscopic data. Active region is clearly visible in several spectral lines formed in the temperature range of 1.1--2.8 MK. We derive electron number density using line ratio method, and non-thermal velocity in the off-limb region up to the distance of 140 Mm. We compare density scale heights derived from several spectral line pairs with expected scale heights as per hydrostatic equilibrium model. Using several isolated and unblended spectral line profiles, we estimate non-thermal velocities in active region and quiet Sun. Non…
The solar wind emanates from the hot and tenuous solar corona. Earlier studies using 1.5 dimensional simulations show that Alfvén waves generated in the photosphere play an important role in coronal heating through the process of non-linear mode conversion. In order to understand the physics of coronal heating and solar wind acceleration together, it is important to consider the regions from photosphere to interplanetary space as a single system. We performed 2.5 dimensional, self-consistent magnetohydrodynamic simulations, covering from the photosphere to the interplanetary space for the firs…
We present a new version of the Alfven Wave Solar Model (AWSoM), a global model from the upper chromosphere to the corona and the heliosphere. The coronal heating and solar wind acceleration are addressed with low-frequency Alfven wave turbulence. The injection of Alfven wave energy at the inner boundary is such that the Poynting flux is proportional to the magnetic field strength. The three-dimensional magnetic field topology is simulated using data from photospheric magnetic field measurements. This model does not impose open-closed magnetic field boundaries; those develop self-consistently.…
We study the impulsively generated non-linear Alfvén waves in the solar atmosphere, and describe their most likely role in the observed non-thermal broadening of some spectral lines in solar coronal holes. We solve numerically the time-dependent magnetohydrodynamic equations to find temporal signatures of large-amplitude Alfvén waves in the model atmosphere of open and expanding magnetic field configuration, with a realistic temperature distribution. We calculate the temporally and spatially averaged, instantaneous transversal velocity of non-linear Alfvén waves at different heights of the mod…
We present numerical simulations of reduced magnetohydrodynamic (RMHD) turbulence in a magnetic flux tube at the center of a polar coronal hole. The model for the background atmosphere is a solution of the momentum equation, and includes the effects of wave pressure on the solar wind outflow. Alfvén waves are launched at the coronal base, and reflect at various heights due to variations in Alfvén speed and outflow velocity. The turbulence is driven by nonlinear interactions between the counter-propagating Alfvén waves. Results are presented for two models of the background atmosphere. In the f…
In the solar atmosphere, Alfvén waves are believed to play an important role in the transfer of energy from the photosphere to the corona and solar wind, and in the heating of the chromosphere. We perform numerical computations to investigate energy transport and dissipation associated with torsional Alfvén waves propagating in magnetic flux tubes that expand from the photosphere to the corona in quiet-Sun conditions. We place a broadband driver at the photosphere that injects a wave energy flux of $10^7$ erg cm$^{-2}$ s$^{-1}$ and consider Ohm's magnetic diffusion and ion-neutral collisions a…
We take stock of recent observations that identify the episodic plasma heating and injection of Alfvenic energy at the base of fast solar wind (in coronal holes). The plasma heating is associated with the occurrence of chromospheric spicules that leave the lower solar atmosphere at speeds of order 100km/s, the hotter coronal counterpart of the spicule emits radiation characteristic of root heating that rapidly reaches temperatures of the order of 1MK. Furthermore, the same spicules and their coronal counterparts ("Propagating Coronal Disturbances"; PCD) exhibit large amplitude, high speed, Alf…
There is observational evidence of the presence of small-amplitude transverse magnetohydrodynamic (MHD) waves with a wide range of frequencies in the threads of solar prominences. It is believed that the waves are driven at the photosphere and propagate along the magnetic field lines up to prominences suspended in the corona. The dissipation of MHD wave energy in the partially ionized prominence plasma is a heating mechanism whose relevance needs to be explored. Here we consider a simple 1D model for a non-uniform thin thread and investigate the heating associated with dissipation of Alfven wa…
We derive a corrected analytical solution for the propagation and enhanced phase mixing of torsional Alfvén waves, in a potential magnetic field with exponentially divergent field lines, embedded in a stratified solar corona. Further we develop a code named TAWAS which calculates the analytic solution describing torsional Alfvén waves using IDL software language. We then use TAWAS to demonstrate that both our correction to the analytic solution and the inclusion of wave reflection have a significant impact on Alfvén wave damping. We continue to utilise TAWAS by performing a parameter study in …
How do magnetohydrodynamic waves travel from the fully ionized corona, into and through the underlying partially ionized chromosphere, and what are the consequences for solar flares? To address these questions, we have developed a 2-fluid model (of plasma and neutrals) and used it to perform 1D simulations of Alfvén waves in a solar atmosphere with realistic density and temperature structure. Studies of a range of solar features (faculae, plage, penumbra and umbra) show that energy transmission from corona to chromosphere can exceed 20% of incident energy for wave periods of one second or less…
In this paper we further develop a model for the heating of coronal loops by Alfven wave turbulence (AWT). The Alfven waves are assumed to be launched from a collection of kilogauss flux tubes in the photosphere at the two ends of the loop. Using a three-dimensional magneto-hydrodynamic (MHD) model for an active-region loop, we investigate how the waves from neighboring flux tubes interact in the chromosphere and corona. For a particular combination of model parameters we find that AWT can produce enough heat to maintain a peak temperature of about 2.5 MK, somewhat lower than the temperatures …
We present a measurement of the energy carried and dissipated by Alfvén waves in a polar coronal hole. Alfvén waves have been proposed as the energy source that heats the corona and drives the solar wind. Previous work has shown that line widths decrease with height in coronal holes, which is a signature of wave damping, but have been unable to quantify the energy lost by the waves. This is because line widths depend on both the non-thermal velocity v_nt and the ion temperature T_i. We have implemented a means to separate the T_i and v_nt contributions using the observation that at low heights…
Two of the central problems in our understanding of the solar chromosphere are how the upper chromosphere is heated and what drives spicules. Estimates of the required chromospheric heating, based on radiative and conductive losses suggest a rate of ${\sim} 0.1 \mathrm{\:erg\:cm^{-3}\:s^{-1}}$ in the lower chromosphere dropping to ${\sim} 10^{-3} \mathrm{\:erg\:cm^{-3}\:s^{-1}}$ in the upper chromosphere (\citet{Avrett1981}). The chromosphere is also permeated by spicules, higher density plasma from the lower atmosphere propelled upwards at speeds of ${\sim} 10-20 \mathrm{\:km\:s^{-1}}$, for s…
Between February 24-25, 2009, the EIS spectrometer onboard the Hinode spacecraft performed special "sit & stare" observations above the South polar coronal hole continuously over more than 22 hours. Spectra were acquired with the 1" slit placed off-limb covering altitudes up to 0.48 R$_\odot$ ($3.34\times 10^2$ Mm) above the Sun surface, in order to study with EIS the non-thermal spectral line broadenings. Spectral lines such as Fe {\sc xii} $λ$186.88, Fe {\sc xii} $λ$193.51, Fe {\sc xii} $λ$195.12 and Fe {\sc xiii} $λ$202.04 are observed with good statistics up to high altitudes and they have…
We study the heating of charged test particles in three-dimensional numerical simulations of weakly compressible magnetohydrodynamic (MHD) turbulence (``Alfvenic turbulence''); these results are relevant to particle heating and acceleration in the solar wind, solar flares, accretion disks onto black holes, and other astrophysics and heliospheric environments. The physics of particle heating depends on whether the gyrofrequency of a particle is comparable to the frequency of a turbulent fluctuation that is resolved on the computational domain. Particles with these frequencies nearly equal under…
Alfvenic waves are thought to play an important role in coronal heating and solar wind acceleration. Here we investigate the dissipation of standing Alfven waves due to phase mixing at the presence of steady flow and sheared magnetic field in the stratified atmosphere of solar spicules. The transition region between chromosphere and corona has also been considered. The initial flow is assumed to be directed along spicule axis, and the equilibrium magnetic field is taken 2-dimensional and divergence-free. It is determined that in contrast to propagating Alfven waves, standing Alfven waves dissi…
