Torsional Alfvén waves in stratified and expanding magnetic flux tubes

The effects of both density stratification and magnetic field expansion on torsional Alfvén waves in magnetic flux tubes are studied. The frequencies, the period ratio P ₁/P ₂ of the fundamental and its first-overtone, and eigenfunctions of torsional Alfvén modes are obtained. Our numerical results show that the density stratification and magnetic field expansion have opposite effects on the oscillating properties of torsional Alfvén waves.     

Three-Dimensional MHD Wave Propagation and Conversion to Alfvén Waves near the Solar Surface. I. Direct Numerical Solution

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°.     

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)     

Incompressible MHD Turbulence

The inertial range of incompressible MHD turbulence is most conveniently described in terms of counter propagating waves. Shear Alfvén waves control the cascade dynamics. Slow waves play a passive role and adopt the spectrum set by the shear Alfvén waves. Cascades composed entirely of shear Alfvén waves do not generate a significant measure of slow waves. MHD turbulence is anisotropic with energy cascading more rapidly along k _⊥ than along k _∥. Anisotropy increases with k _⊥ such that the excited modes are confined inside a cone bounded by k _∥∝ k _perp ^2/3. The opening angle of the cone, θ(k _⊥)∝ k _⊥ ^-1/3, defines the scale dependent anisotropy. MHD turbulence is generically strong in the sense that the waves which comprise it are critically damped. Nevertheless, deep inside the inertial range, turbulent fluctuations are small. Their energy density is less than that of the background field by a factor θ²(k _⊥)≪. MHD cascades are best understood geometrically. Wave packets suffer distortions as they move along magnetic field lines perturbed by counter propagating wave packets. Field lines perturbed by unidirectional waves map planes perpendicular to the local field into each other. Shear Alfvén waves are responsible for the mapping's shear and slow waves for its dilatation. The former exceeds the latter by θ^-1(k _⊥)≫ 1 which accounts for dominance of the shear Alfvén waves in controlling the cascade dynamics. This revised version was published online in July 2006 with corrections to the Cover Date.     

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.     

Mhd Study of Coronal Waves: A Numerical Approach

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. This revised version was published online in July 2006 with corrections to the Cover Date.     

The Plasma and Magnetic Field Characteristics of a Double Discontinuity in Interplanetary Space

A double discontinuity is a rarely observed compound structure composed of a slow shock layer and an adjoining rotational discontinuity layer in the downstream region. In this paper, we report the observations of a double discontinuity detected by Wind on May 15, 1997. This double discontinuity is found to be the front boundary of a magnetic cloud boundary layer. We strictly identify the shock layer and the rotational discontinuity layer by using the high-resolution plasma and magnetic field data from Wind. The observed jump conditions of the upstream and downstream region of the slow shock layer are in good agreement with the Rankine – Hugoniot relations. The flow speeds in the shock frame U _n <V _Acos θ _Bn on both sides of the slow shock layer. In the upstream region, the slow Mach number M _s1=U _n1/V _s1 is 1.95 (above unity), and in the downstream region, the slow Mach number M _s2=U _n2/V _s2 is 0.31 (below unity). Here V _A and V _s represent the Alfvén speed and the local slow magnetosonic speed, respectively, and θ _Bn is the angle between the direction of the magnetic field and the shock normal. The magnetic cloud boundary layer observed by Wind was also detected by Geotail 48 min later when the spacecraft was located outside the bow shock of the magnetosphere. However, Geotail observations showed that its front boundary was no longer a double discontinuity and the rotational discontinuity layer disappeared, indicating that this double discontinuity was unstable when propagating from Wind to Geotail.     

Hydromagnetic waves in structured magnetic fields

Although the inhomogeneous nature of solar magnetic fields is now well established, most theoretical analyses of hydromagnetic wave propagation assume infinite homogeneous fields. Here we reformulate the hydromagnetic wave problem for magnetic fields which vary in one direction perpendicular to the field. The permitted modes of small amplitude hydromagnetic oscillations are considered, first in the case of a single interface between semi-infinite magnetic and non-magnetic compressible regions, and secondly for a magnetic flux sheath of given thickness imbedded in a nonmagnetic region. It is shown that, for small values of R (the ratio of the Alfvén to the sound speed), an acoustic or p-mode wave front passes through the flux sheath with only minor deformation. However, for large R, the transmitted acoustic wave is attenuated and, depending upon the thickness of the flux sheath and the angle of incidence, a hydromagnetic wave may be effectively trapped and guided along the flux sheath. It is also shown that, for the symmetric vibration of the flux sheath in the absence of incident acoustic waves, only slow mode type waves are permitted. Thus, in compressible regions for which R > 1 the Alfvénic-type fast mode is not a permitted mode of free vibration of a flux sheath.     

Time-Distance Seismology and the Solar Transition Region

Time-Distance ‘travel time’ perturbations (as inferred from wave phase) are calculated relative to the quiet-Sun as a function of wave orientation and field inclination in a uniform inclined magnetic field. Modelling indicates that the chromosphere-corona Transition Region (TR) profoundly alters travel times at inclinations from the vertical θ for which the ramp-reduced acoustic cutoff frequency ω _c cosθ is similar to the wave frequency ω. At smaller inclinations phase shifts are much smaller as the waves are largely reflected before reaching the TR. At larger inclinations, the shifts resume their quiet-Sun values, although with some resonant oscillatory behaviour. Changing the height of the TR in the model atmosphere has some effect, but the thickness and temperature jump do not change the results substantially. There is a strong correspondence between travel-time shifts and the Alfvén flux that emerges at the top of the modelled region as a result of fast/Alfvén mode conversion. We confirm that the TR transmission coefficient for Alfvén waves generated by mode conversion in the chromosphere is far larger (typically 30 % or more) than for Alfvén waves injected from the photosphere.     

Transmission of Alfvén waves through the rotational discontinuity at magnetopause

The reflection and refraction of MHD waves through an “open” magnetopause (rotational discontinuity) is studied. It is found that most of the incident wave energy can be transmitted through the open magnetopause. A transverse Alfvén wave (or a compressional magnetosonic wave) from the solar wind incident upon the open magnetopause would generally lead to the generation of both the transverse Alfvén and compressional magnetosonic waves in the magnetosphere. Transmission of Alfvén waves in the coplanar rotational discontinuity is studied in detail. The integral power of the Alfvén-wave transfer is found to be proportional to the open magnetic flux of the magnetosphere and is typically ～ 1% of the power of the total electromagnetic energy transfer through the open magnetopause. The transmitted wave power may contribute significantly to the geomagnetic pulsations observed on the ground, especially in the open-field-line region.     

Ion-Acoustic Wave Generation by Two Kinetic Alfvén Waves and Particle Heating

In this paper we have investigated the beat wave excitation of an ion-acoustic wave at the difference frequency of two kinetic (or shear) Alfvén waves propagating in a magnetized plasma with β<1 (β=8π n _e0 T _e/B ₀ ² , where n _e0 is the unperturbed electron number density, T _e is the electron temperature, and B ₀ is the external magnetic field). On account of the interaction between two kinetic Alfvén waves of frequencies ω ₁ and ω ₂, the ponderomotive force at the difference frequency ω ₁−ω ₂ leads to the generation of an ion-acoustic wave. Also because of the filamentation of the Alfvén waves, magnetic-field-aligned density dips are observed. In this paper we propose that the ion-acoustic wave generated by this mechanism may be one of the possible mechanisms for the heating and acceleration of solar wind particles.     

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.     

Resonant Absorption of Fast Magnetoacoustic Waves due to Coupling into the Slow and Alfvén Continua in the Solar Atmosphere

Resonant absorption of fast magnetoacoustic (FMA) waves in an inhomogeneous, weakly dissipative, one-dimensional planar, strongly anisotropic and dispersive plasma is investigated. The magnetic configuration consists of an inhomogeneous magnetic slab sandwiched between two regions of semi-infinite homogeneous magnetic plasmas. Laterally driven FMA waves penetrate the inhomogeneous slab interacting with the localised slow or Alfvén waves present in the inhomogeneous layer and are partly reflected, dissipated and transmitted by this region. The presented research aims to find the coefficient of wave energy absorption under solar chromospheric and coronal conditions. Numerical results are analysed to find the coefficient of wave energy absorption at both the slow and Alfvén resonance positions. The mathematical derivations are based on the two simplifying assumptions that i) nonlinearity is weak, and ii) the thickness of the inhomogeneous layer is small in comparison to the wavelength of the wave, i.e. we employ the so-called long wavelength approximation. Slow resonance is found to be described by the nonlinear theory, while the dynamics at the Alvén resonance can be described within the linear framework. We introduce a new concept of coupled resonances, which occurs when two different resonances are in close proximity to each other, causing the incoming wave to act as though it has been influenced by the two resonances simultaneously. Our results show that the wave energy absorption is heavily dependent on the angle of the incident wave in combination with the inclination angle of the equilibrium magnetic field. In addition, it is found that FMA waves are very efficiently absorbed at the Alvén resonance under coronal conditions. Under chromospheric conditions the FMA waves are far less efficiently absorbed, despite an increase in efficiency due to the coupled resonances.     

Nonlinear interaction between Alfvén and acoustic-gravity 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 considered the nonlinear interaction between vertically propagating Alfvén and acoustic-gravity waves. We established that Alfvén waves are efficiently generated at the difference and sum frequencies. We ascertained that no acoustic-gravity waves are formed at the corresponding combination frequencies. A horizontal magnetohydrodynamic wind whose direction changes with height was found to be formed in the solar atmosphere at zero difference frequency.     

Modeling helioseismic modes in the magnetic atmosphere of the Sun

The pulsation of the solar surface is caused by acoustic waves traveling in the solar interior. Thorough analyses of observational data indicate that these f and p helioseismic oscillation modes are not bounced back completely at the surface but they partially penetrate into the atmosphere. Atmospheric effects and their possible observational application are investigated in one‐dimensional magnetohydrodynamic models. It is found that f and p mode frequencies are shifted of the order of μHz due to the presence of an atmospheric magnetic field. This shift varies with the direction of the wave propagation.Resonant coupling of global helioseismic modes to local Alfvén and slow waves reduce the life time of the global modes. The resulting line width of the frequency line is of the order of nHz, and it also varies with propagation angle. These features enable us to use helioseismic observations in magnetic diagnostics of the lower atmosphere. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

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.     

Influence of the Conversion Layer on the Dispersion Relation of Waves in the Solar Atmosphere

Observations carried out with the Magneto-Optical Filter at Two Heights (MOTH) experiment show upward-traveling wave packets in magnetic regions with frequencies below the acoustic cut-off. We demonstrate that the frequency dependence of the observed travel times, i.e. the dispersion relation, shows significant differences in magnetic and non-magnetic regions. More importantly, at and above the layer where the Alfvén speed equals the sound speed we do not see the dispersion relation of the slow acoustic mode with a lowered cut-off frequency. Our comparisons with theoretical dispersion relations suggest that this is not the slow acoustic wave type for the upward low-frequency wave. From this we speculate that partial mode conversion from the fast acoustic to the fast magnetic wave might take place.     

The nature of the sunspot phenomenon

This paper points out the basic relation between the conversion of thermal energy into convective fluid motion (Alfvén waves when a strong vertical magnetic field is present) and the convective transport of thermal energy. It is shown that heat transport necessarily accompanies convective driving of fluid motion. Convective motions restricted to a layer whose thickness is a small fraction of the local scale height can divert no more than the same fraction of the energy into Alfvén waves. But if the convecting layer extends over many scale heights, then the convective forces may convert more energy into fluid motion than they transport. Hence the creation of a cool sunspot requires convection extending coherently over several scale heights, at least 500 km. This requirement is basically just the familiar thermodynamic efficiency of an ideal heat engine. The calculations establish that convection need not be much less efficient than the ideal.     

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.     

Oblique propagation and dissipation of Alfvén waves in coronal holes

We investigate the effect of viscosity and magnetic diffusivity on the oblique propagation and dissipation of Alfvén waves with respect to the normal outward direction, making use of MHD equations, density, temperature and magnetic field structure in coronal holes and underlying magnetic funnels. We find reduction in the damping length scale, group velocity and energy flux density as the propagation angle of Alfvén waves increases inside the coronal holes. For any propagation angle, the energy flux density and damping length scale also show a decrement in the source region of the solar wind (< 1.05 R_⊙) where these may be one of the primary energy sources, which can convert the inflow of the solar wind into the outflow. In the outer region (> 1.21 R_⊙), for any propagation angle, the energy flux density peaks match with the peaks of MgX 609.78 Å and 624.78 Å linewidths observed from the Coronal Diagnostic Spectrometer (CDS) on SOHO and the non-thermal velocity derived from these observations, justify the observed spectroscopic signature of the Alfvén wave dissipation.