Correlation of longitudinal currents with Alfvén wave generation in the solar atmosphere

Current instability of Alfvén waves in coronal loops is considered. Such a mechanism of Alfvén wave generation is shown to be very efficient, and it can give rise to low-frequency perturbations even in the case of very weak currents, thus fostering the reconnection of magnetic fields and development of a flare. The low-frequency turbulence which arises in the process can be favorable to the heating and acceleration of particles.     

Kinetic Alfvén waves in preflare plasma

Low‐frequency instabilities of plasma waves in the arch structures in solar active regions have been investigated before a flare. In the framework of mechanism of “direct initiation” of instability by slowly increasing (quasi‐static) large‐scale electric field in a loop the dispersion relation has been studied for the perturbations which propagate almost perpendicularly to the magnetic field of the loop. The case has been considered, when amplitude of weak (“subdreicer”) electric field sharply increases before a flare, low‐frequency instability develops on the background of ion‐acoustic turbulence and thickness of this turbulent plasma layer plays the role of mean characteristic scale of inhomogeneity of plasma density. If the values of the main plasma parameters, i.e. temperature, density, magnetic field amplitude allow to neglect the influence of the shear of magnetic strength lines on the instability development, then two types of the waves can be generated in preflare plasma: the kinetic Alfvén waves and some new kind of the waves from the range of slowly magneto‐acoustic ones. Instability of kinetic Alfvén waves has clearly expressed threshold character with respect to the amplitude of “subdreicer” electric field. This fact seems to be useful for the short‐time prediction of a flare in arch structure. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Energy Flux of Alfvén Waves in Weakly Ionized Plasma and Coronal Heating of the Sun

The influence of collisions between neutrals and ions on the energy flux of Alfvén-type waves in partially ionized plasma based on the three-fluid equations is considered. It has been shown that amplitudes of Alfvén waves that are generated or propagating in the solar photosphere do not depend on the ionization ratio, if the wave periods are much larger than 10⁻⁴ s. This contradicts results of Vranjes et al. (Astron. Astrophys. 478, 553, 2008) and is explained by the strong coupling due to ion–neutral collisions. Alfvén waves can be effectively excited in the photosphere of the Sun by convective motions, providing the required energy for coronal heating.     

On the storage of high-energy protons in the solar corona: The cyclotron instability

We consider the problem of long-time storage of high-energy protons, accelerated in the process of a flare, in coronal magnetic traps. From the viewpoint of the storage, one of the most important plasma instabilities is the kinetic cyclotron instability of the Alfvén waves. We carry out a detailed theoretical analysis of the instability for typical conditions of the solar corona. It is the refraction of the Alfvén waves in combination with a drastic decrease of the instability growth rate with an increase of the angle between the directions of the wave vector and the stationary magnetic field that leads to the possibility of the long-term storage of the flare protons. Sufficient conditions of the storage are determined.     

On the role of transition region on the Alfvén wave phase mixing in solar spicules

Alfvénic waves are thought to play an important role in coronal heating and solar wind acceleration. Here we investigate the dissipation of standing Alfvén 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 Alfvén waves, standing Alfvén waves dissipate in time rather than in space. Density gradients and sheared magnetic fields can enhance damping due to phase mixing. Damping times deduced from our numerical calculations are in good agreement with spicule lifetimes. Since spicules are short living and transient structures, such a fast dissipation mechanism is needed to transport their energy to the corona.     

Currents over the auroral arc

The three-dimensional current system over an enhanced conductivity strip identified with an auroral arc is calculated for the case of the magnetospheric plasma convection across this strip. The strip produces a stationary Alfvén wave which propagates along magnetic field lines and is carried simultaneously by the convecting plasma. The Alfvén wave generation corresponds to an appearance of field-aligned currents over the arc. The three-dimensional current system generated over the arc is studied, taking into account reflection of the waves from the ionosphere of the opposite hemisphere. The correspondence of the theory with the experimental results is found.     

Velocity-Space Proton Diffusion in the Solar Wind Turbulence

We study the velocity-space quasi-linear diffusion of the solar wind protons driven by oblique Alfvén turbulence at proton kinetic scales. Turbulent fluctuations at these scales possess the properties of kinetic Alfvén waves (KAWs) that are efficient in Cherenkov-resonant interactions. The proton diffusion proceeds via Cherenkov kicks and forms a quasi-linear plateau – the nonthermal proton tail in the velocity distribution function (VDF). The tails extend in velocity space along the mean magnetic field from 1 to (1.5?–?3) V _A, depending on the spectral break position, on the turbulence amplitude at the spectral break, and on the spectral slope after the break. The most favorable conditions for the tail generation occur in the regions where the proton thermal and Alfvén velocities are about equal, V _Tp/V _A≈1. The estimated formation times are within 1?–?2 h for typical tails at 1 AU, which is much shorter than the solar wind expansion time. Our results suggest that the nonthermal proton tails, observed in situ at all heliocentric distances >?0.3 AU, are formed locally in the solar wind by the KAW turbulence. We also suggest that the bump-on-tail features – proton beams, often seen in the proton VDFs, can be formed at a later evolutional stage of the nonthermal tails by the time-of-flight effects.     

Compound Effect of Alfvén Waves and Ion-Cyclotron Waves on Heating/Acceleration of Minor Ions via the Pickup Process

A scenario is proposed to explain the preferential heating of minor ions and differential-streaming velocity between minor ions and protons observed in the solar corona and in the solar wind. It is demonstrated by test-particle simulations that minor ions can be nearly fully picked up by intrinsic Alfvén-cyclotron waves observed in the solar wind based on the observed wave energy density. Both high-frequency ion-cyclotron waves and low-frequency Alfvén waves play crucial roles in the pickup process. A minor ion can first gain a high magnetic moment through the resonant wave–particle interaction with ion-cyclotron waves, and then this ion with a large magnetic moment can be trapped by magnetic mirror-like field structures in the presence of the low-frequency Alfvén waves. As a result, the ion is picked up by these Alfvén-cyclotron waves. However, minor ions can only be partially picked up in the corona because of the low wave energy density and low plasma β. During the pickup process, minor ions are stochastically heated and accelerated by Alfvén-cyclotron waves so that they are hotter and flow faster than protons. The compound effect of Alfvén waves and ion-cyclotron waves is important in the heating and acceleration of minor ions. The kinetic properties of minor ions from simulation results are generally consistent with in-situ and remote features observed in the solar wind and solar corona.     

3D MHD Coronal Oscillations about a Magnetic Null Point: Application of WKB Theory

This paper is a demonstration of how the WKB approximation can be used to help solve the linearised 3D MHD equations. Using Charpit’s method and a Runge?–?Kutta numerical scheme, we have demonstrated this technique for a potential 3D magnetic null point, B=[x,ε y,?(ε+1)z]. Under our cold-plasma assumption, we have considered two types of wave propagation: fast magnetoacoustic and Alfvén waves. We find that the fast magnetoacoustic wave experiences refraction towards the magnetic null point and that the effect of this refraction depends upon the Alfvén speed profile. The wave and thus the wave energy accumulate at the null point. We have found that current buildup is exponential and the exponent is dependent upon ε. Thus, for the fast wave there is preferential heating at the null point. For the Alfvén wave, we find that the wave propagates along the field lines. For an Alfvén wave generated along the fan plane, the wave accumulates along the spine. For an Alfvén wave generated across the spine, the value of ε determines where the wave accumulation will occur: fan plane (ε=1), along the x-axis (0<ε<1) or along the y-axis (ε>1). We have shown analytically that currents build up exponentially, leading to preferential heating in these areas. The work described here highlights the importance of understanding the magnetic topology of the coronal magnetic field for the location of wave heating.     

Phase mixing of standing Alfvén waves with shear flows in solar spicules

Alfvénic waves are thought to play an important role in coronal heating and solar wind acceleration. Here we investigate the dissipation of such waves due to phase mixing at the presence of shear flow and field in the stratified atmosphere of solar spicules. The initial flow is assumed to be directed along spicule axis and to vary linearly in the x direction and the equilibrium magnetic field is taken 2-dimensional and divergence-free. It is determined that the shear flow and field can fasten the damping of standing Alfvén waves. In spite of propagating Alfvén waves, standing Alfvén waves in Solar spicules dissipate in a few periods. As height increases, the perturbed velocity amplitude does increase in contrast to the behavior of perturbed magnetic field. Moreover, it should be emphasized that the stratification due to gravity, shear flow and field are the facts that should be considered in MHD models in spicules.     

Stationary incompressible MHD perturbationsgenerated by a current source in a moving plasma

We consider the inductive interaction between a conducting body and a magnetizedincompressible plasma in relative uniform motion, which has application to the Io–Jupitersystem, for example. An incompressible plasma only supports one mode of propagation, namelythe Alfvén mode. In the case of free oscillations, this mode propagates the perturbations in themagnetic field and in the plasma velocity unattenuated along the direction of the backgroundfield, while the plasma pressure balances the magnetic pressure. The situation changes in thepresence of source currents and in a flowing plasma. In particular, the parallel plasma vorticityand parallel plasma current are propagated unattenuated along the familiar Alfvéncharacteristics, while the field and velocity perturbations suffer Laplacian decay in the near field.We study these perturbations in the frame of the body and compare them to the case of no sourceterms.     

Excess heating of corona and chromosphere above magnetic regions by non-linear Alfvén waves

Excess heating of the active region solar atmosphere is interpreted by the decay of MHD slow-mode waves produced in the corona through the non-linear coupling of Alfvén waves supplied from subphotospheric layers. It is stressed that the Alfvén-mode waves may be very efficiently generated directly in the convection layer under the photosphere in magnetic regions, and that such magnetic regions, at the same time, provide the ‘transparent windows’ for Alfvén waves in regard to the Joule and frictional dissipations in the photospheric and subphotospheric layers. Though the Alfvén waves suffer considerable reflection in the chromosphere and in the transition layer, a certain fraction of this large flux is propagated out to the corona, and a large velocity amplitude exceeding the local Alfvén velocity is attained during the propagation along the magnetic tubes of force into a region of lower density and weaker magnetic field. The otherwise divergence-free velocity field in Alfvén waves gets involved in such a case with a compressional component (slow-mode waves) which again is of considerable velocity amplitude relative to the local acoustic velocity when estimated by using the formulation for non-linear coupling between MHD wave modes derived by Kaburaki and Uchida (1971). Therefore, the compressional waves thus produced through the non-linear coupling of Alvén waves will eventually be thermalized to provide a heat source. The introduction of this non-linear coupling process and the subsequent thermalization of thus produced slow-mode waves may provide means of converting the otherwise dissipation-free Alfvén mode energy into heat in the corona. The liberated heat will readily be redistributed by conduction along the magnetic lines of force, with higher density as a consequence of increased scale height, and thus the loop-like structure of the coronal condensations (or probably also the thread-like feature of the general corona) may be explained in a natural fashion.     

Nonlinear excitation of small-scale Alfvén waves by fast waves and plasma heating in the solar atmosphere

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/B ₀∼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.     

The Alfvén wave parallel electric field in non-uniform space plasmas

We suggest a two-step mechanism for the generation of the parallel electric field at the Alfvén wave. At the first step, the coupling with the compressional mode due to the magnetic field non-uniformity and finite plasma pressure provides the parallel magnetic field of Alfvén wave. At the second step, the compressional mode acquires the parallel electric field due to coupling with the electrostatic mode as required by the quasi-neutrality condition in kinetics. The parallel electric field acquired by the Alfvén mode is considerably larger than that due to the single-step coupling between the Alfvén and electrostatic modes in kinetics.     

Alfvén node-free vibrations of white dwarf in the model of solid star with toroidal magnetic field

In the context of white dwarf asteroseismology, we investigate the vibrational properties of a non-convective solid star with an axisymmetric purely toroidal intrinsic magnetic field of two different shapes. Focus is laid on the regime of node-free global Lorentz-force-driven vibrations about the symmetry axis at which material displacements have one and the same form as those for nodeless spheroidal and torsional vibrations restored by Hooke’s force of elastic shear stresses. Particular attention is given to the even-parity poloidal Alfvén modes whose frequency spectra are computed in analytic form, showing how the purely toroidal magnetic fields completely buried beneath the star surface can manifest itself in seismic vibrations of non-magnetic white dwarfs. The spectral formulae obtained are discussed in juxtaposition with those for Alfvén modes in the solid star model with the poloidal, homogeneous internal and dipolar external, magnetic field whose inferences are relevant to Alfvén vibrations in magnetic white dwarfs.     

The problem of phase mixed shear Alfvén waves in the solar corona revisited

The problem of phase mixing of shear Alfvén waves is revisited taking into account dissipative phenomena specific for the solar corona. In regions of space plasmas where the dynamics is controlled by the magnetic field, transport coefficients become anisotropic with transport mechanism having different behavior and magnitude depending on the orientation with respect to the ambient magnetic field. Taking into account realistic values for dissipative coefficients we obtain that the previous results derived in context of torsional Alfvén wave phase mixing are actually heavily underestimated so phase mixing cannot be used to explain the damping of torsional Alfvén waves and heating of open coronal structures. The presented results indicate that in order for phase mixing to still be a viable mechanism to explain heating or wave damping unrealistic assumptions have to be made. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

On the Propagation and Dissipation of Alfvén Waves in Coronal Holes

We underline the importance of Alfvén wave dissipation in the magnetic funnels through the viscous and resistive plasma. Our results show that Alfvén waves are one of the primary energy sources in the innermost part of coronal holes where the solar wind outflow starts.     

Wave propagation in a magnetic cylinder

The nature of oscillations in a magnetic cylinder embedded in a magnetic environment is investigated. It is shown that the standard slender flux tube analysis of a kink mode in a cylinder excludes the possibility of a second mode, which arises under photospheric conditions. Under coronal conditions, two widely separated classes of oscillation can be freely sustained, one on an acoustic time-scale and the other on an Alfvénic time-scale. The acoustic-type oscillations are always present, but the much shorter period, Alfvénic-type, oscillations arise only in high density (strictly, low Alfvén velocity) loops. An application to waves in fibrils is also given, and suggests (following Wentzel, 1979) that they are fast kink waves propagating in a density enhancement.     

Reflection of Alfvén waves by non-uniform ionospheres

Magnetospheric Alfvén waves are reflected by the ionosphere. We investigate the effect of horizontally varying ionospheric conductivity on the process of Alfvén wave reflection. Four idealised ionospheric models are considered in detail. We find that the reflection process is strongly dependent on the orientation of the wave electric field vector with respect to the boundary between high and low conductivities, and under certain conditions subsidiary Alfvén waves are generated. The field-aligned currents in the subsidiary Alfvén waves serve to close divergent horizontal currents resulting from the non-uniform ionospheric conductivity. The implications for ground-based pulsation studies are discussed.     

Parametric generation of acoustic-gravity waves by Alfvén waves in the solar atmosphere

Based on a plane-parallel isothermal model solar atmosphere permeated by a uniform magnetic field directed against the action of gravity, we investigate the parametric generation of acoustic-gravity disturbances by Alfvén waves propagating along the corresponding field lines. We established that for a weak linear coupling of Alfvén waves, the nonlinear interaction of Alfvén waves propagating in opposite directions (rather than in the same direction) is the predominant generation mechanism of acoustic-gravity disturbances at the difference frequency. In this case, no acoustic flow (wind) was found to emerge at a zero difference frequency in the acoustic-gravity field.