Hydromagnetic modes in an inhomogeneous collisionless plasma of finite pressure

The spatial structure and growth rate of hydromagnetic waves with frequencies are considered in a one-dimensional model. It is shown that the wave under consideration is an Alfvén mode modified by the inhomogeneity and anisotropy of the plasma and its finite pressure. Because of these factors, the magnetic field lines oscillate differently in the radial and azimuthal directions and the wave frequency depends on the radial wavenumber. There may be two types of mode structure in the direction across the magnetic shells. When the magnetospheric parameters vary monotonically along the radial coordinate, the mode propagates across the magnetic field lines; because of its resonance with high-energy particles, the radial wavenumber acquires a nonzero imaginary part, which vanishes at the Alfvén resonance surface. In the magnetospheric regions where the main plasma parameters (density or pressure) reach their extreme values, the mode is a standing wave in a direction transverse to the magnetic field lines. In this case, because of the instability, the eigen-frequency of the cavity has a nonzero imaginary part. Under certain, very specific conditions, there can exist drift-mirror waves in the magnetosphere. Such conditions, however, are unlikely to occur in reality. In terms of the modes to be described, it is possible to explain some types of oscillations of the geomagnetic field.     

Instability of a magnetic drift wave in the vicinity of the dust-ion hybrid resonance

Low-frequency electromagnetic waves propagating perpendicular to the gradients of the density and magnetic field in an inhomogeneous dusty plasma whose mass density is determined primarily by the dust component are analyzed. It is shown that, in analyzing the dispersion properties of inhomogeneous plasma, it is important to take into account the dynamic properties of ions in the vicinity of the dust-ion hybrid resonance. The conditions for the onset of instability of a magnetic drift wave are investigated for different relations between parameters of the inhomogeneity and the value of the Alfvén velocity. The differences from the previous results, as well as possible astrophysical applications, are discussed.     

Splitting of the spectra of MHD waves and the structure of a satellite alfvén resonance in a cold plasma in a strong axial magnetic field and a weak helical field

The possibility is demonstrated of splitting the eigenfrequencies of MHD plasma waves in a stellarator with a weakly rippled helical confining magnetic field. The distribution of the fields of an Alfvén wave in the satellite Alfvén resonance region is investigated when the influence of the helical ripple in a confining magnetic field on the resonance structure is comparable with the effects of the finite ion Larmor radius, electron inertia, and collisions between plasma particles.     

Conversion of fast magnetosonic waves into Alfvén waves in a longitudinally inhomogeneous gyrotropic plasma

A model is considered of the conversion of running fast magnetosonic waves into Alfvén waves in a longitudinally inhomogeneous gyrotropic plasma in a magnetic field with open field lines. The set of equations for the amplitudes of the interacting modes is obtained and investigated in the Wentzel-Kramers-Brillouin approximation. In the synchronization region, where the wave vectors of the two modes approach one another, most of the energy of fast magnetosonic waves is converted into the Alfvén wave energy. The phases of the waves are matched in such a way that the phase difference is most favorable for wave conversion. The fact that the conversion is resonant in nature may help to explain the onset of quasi-monochromatic signals in the Earth’s magnetosphere and in the magnetospheres of the giant planets.     

Exact solutions for oblique solitary Alfvén waves in plasma

The properties of solitary Alfvén waves are studied for different ratios between the thermal plasma pressure and the magnetic pressure. It is shown that the wave propagation is accompanied by the generation of a nonlinear ion current along the magnetic field, the contribution of which to the Sagdeev potential was previously ignored. An expression for the quasi-potential of Alfvén waves with allowance for this effect is derived. It is found that Alfvén waves are compression waves in the inertial limit, whereas kinetic Alfvén waves are rarefaction waves. In a high-pressure plasma, a solitary wave has the form of either a well or a hump in the plasma density, depending on the relations between the Mach number, angle between the wave propagation direction and the magnetic field, and the value of the plasma beta.     

Polarization splitting of the Alfvén wave spectrum in a dipole magnetosphere with a rotating plasma

Alfvén waves in a dipole magnetosphere with a rotating plasma are studied theoretically. The plasma-motion-related properties of azimuthally small-scale standing Alfvén waves having nearly poloidal or nearly toroidal polarization are analyzed. Equations are obtained that describe the longitudinal (along the magnetic field) structure and spectra of the waves having such polarizations. The equations obtained are then solved both analytically (in the Wentzel-Kramers-Brillouin approximation) and numerically. Attention is focused on the polarization splitting of the spectrum—the difference between the eigenfrequencies of the toroidally and poloidally polarized Alfvén waves. The distribution of this difference in a direction across the magnetic shells is analyzed. It is shown that, unlike in the models in which the plasma is assumed to be at rest, taking into account rotation of the magnetosphere plasma results in an additional splitting of the spectrum of the poloidal Alfvén waves due to the difference in their azimuthal mode numbers.     

Formation of a steady-state shock front of a fast magnetosonic wave in a turbulent plasma

The question of the existence of a steady-state shock front of a fast magnetosonic wave propagating across the magnetic field against the background of turbulent Alfvén waves is considered. It is shown that the steady-state shock front can form as a result of energy transfer from the turbulent Alfvén wave to the fast magnetosonic wave.     

Numerical analysis of the safety factor and effective ion mass in a tokamak plasma with the help of the discrete alfvén wave spectrum

Numerical aspects of the method for diagnosing a tokamak plasma with the help of the discrete Alfvén wave spectrum are considered. It is shown that this diagnostics should be supported with highly accurate computational tools. A code suitable for implementing the relevant calculation scheme is developed, which makes it possible to identify the eigenmodes numerically with the desired accuracy. The code can also provide recommendations for performing tokamak experiments and can be used to study the possibility of auxiliary plasma heating by Alfvén waves. The discrete Alfvén wave spectrum, radial profiles of the energy deposited in the plasma, and the dependence of the Alfvén mode frequencies on the damping rate and on the class of the current-density profiles chosen are calculated for the first time for the T-10 tokamak. It is also shown that the diagnostic method proposed makes it possible to obtain reliable information about the plasma parameters.     

On the possibility of reflection of Alfvén waves in a curvilinear magnetic field

The propagation of Alfvén waves in a plasma immersed in a curvilinear magnetic field is investigated by using a 2D model. The waves are described by a 1D equation that formally coincides with the equation for the case of a quasi-uniform straight magnetic field with a modified Alfvén velocity that takes into account the longitudinal dependence of the Lame coefficients. It is shown that toroidal and poloidal Alfvén modes depend differently on the magnetic-field geometry. In the case of a 2D plane-parallel configuration of the magnetic field, poloidal modes are efficiently reflected from regions where the magnetic field lines sharply converge or diverge. This effect can result in the formation of open-field-line Alfvén quasi-resonators.     

Plasma heating in a variable magnetic field

The problem of particle acceleration in a periodically variable magnetic field that either takes a zero value or passes through zero is considered. It is shown that, each time the field [0]passes through zero, the particle energy increases abruptly. This process can be regarded as heating in the course of which plasma particles acquire significant energy within one field period. This mechanism of plasma heating takes place in the absence of collisions between plasma particles and is analogous to the mechanism of magnetic pumping in collisional plasma considered by Alfvén.     

Reversal of the hall current and amplification of the magnetorotational instability in a weakly ionized plasma

A criterion for the development of a magnetorotational instability in a weakly ionized dusty plasma is considered. A dispersion relation for the wavenumber and the growth rate of an unstable perturbation is derived for an arbitrary angle between the wave vector and magnetic field. It is shown that the presence of dust grains can reverse the direction of the Hall current in the plasma and can shift the instability threshold to shorter wavelengths. Under certain conditions, Alfvén fluctuations of arbitrary scale can be unstable. The Hall current reversal is found to have a strong effect on the development of a magnetorotational instability when the Alfvén resonance frequency in a weakly ionized plasma is close to the rotation frequency of the accretion disk.     

ICRF heating in magnetic mirror plasmas

Waves in the ion cyclotron range of frequency are efficiently used to produce and heat magnetic mirror plasmas. In relatively low-density (lower than 10¹⁸ m^?3) plasmas, the fast Alfvén eigenmodes are formed in radial and axial directions and the excitation of these modes is strongly affected by the density. The slow Alfvén waves are also effectively used for plasma heating. The ion temperature above 10 keV is achieved, which is confirmed by the detection of fusion neutrons. The excitation of Alfvén eigenmodes is studied in the GAMMA 10 tandem mirror.     

Viscous damping of Alfvén surface waves in the solar atmosphere

The dispersion relation for the propagation of viscous Alfvén surface waves along viscous plasmaplasma interface has been derived. Two modes of Alfvén surface waves are found to propagate with their characteristics depend on the interface parameters like magnetic field, density ratio, viscosity, etc. The viscous damping of Alfvén surface waves has been studied in the astrophysical point of view. The damping length of Alfvén surface waves due to viscosity in the solar atmosphere has been estimated.     

Emission of alfvén waves from a nonuniform MHD waveguide

The efficiency of the wave energy loss from a nonuniform MHD waveguide due to the conversion of the trapped magnetosonic waveguide modes into runaway Alfvén waves is estimated theoretically. It is shown that, if the waveguide parameters experience a jumplike change along the waveguide axis, the interaction between the waveguide modes and Alfvén waves occurs precisely at this “jump.” This effect is incorporated into the boundary conditions. A set of coupled integral equations with a singular kernel is derived in order to determine the transmission and reflection coefficients for the waveguide modes. The poles in the kernels of the integral operators correspond to the surface waves. When the jump in the waveguide parameters is small, analytic expressions for the frequency dependence of the transformation coefficients are obtained by using a model profile of the Alfvén velocity along the magnetic field. For the jump characterized by the small parameter value ε=0.3, the wave-amplitude transformation coefficient can amount to 5–10%. Under the phase synchronization condition (when the phase velocities of the waveguide modes on both sides of the jump are the same), the wave-energy transformation coefficient is much higher: it increases from a fraction of one percent to tens of percent. The transformation of fast magnetosonic waves into Alfvén waves is resonant in character, which ensures the frequency and wavelength filteringof the emitted Alfvén perturbations.     

Generation of Alfvén waves by a plasma inhomogeneity moving in the Earth’s magnetosphere

The generation of an Alfvén wave by an azimuthally drifting cloud of high-energy particles injected in the Earth’s magnetosphere is studied analytically. In contrast to the previous studies where the generation mechanisms associated with the resonant wave-particle interaction were considered, a nonresonant mechanism is investigated in which the wave is excited by the alternating current produced by drifting particles. It is shown that, at a point with a given azimuthal coordinate, a poloidally polarized wave, in which the magnetic field lines oscillate predominantly in the radial direction, is excited immediately after the passage of the particle cloud through this point. As the cloud moves away from that point, the wave polarization becomes toroidal (the magnetic field lines oscillate predominantly in the azimuthal direction). The azimuthal wavenumber m is defined as the ratio of the wave eigenfrequency to the angular velocity of the cloud (the drift velocity of the particles). It is shown that the amplitudes of the waves so generated are close to those obtained under realistic assumptions about the density and energy of the particles.     

Two-dimensional modeling of a transverse collisionless shock wave

Transverse collisionless shock waves in a plasma in which the initial β value is equal to zero for electrons and is small but nonzero for ions are studied in the two-dimensional approximation with allowance for anomalous resistivity. A hybrid model is applied such that the ions are treated in the kinetic approximation and the electrons are described in the hydrodynamic approximation. A collisionless shock wave is generated using a piston with a small two-dimensional perturbation. The ion distribution downstream of the shock front and the effect of electron and ion heating are analyzed. It is shown that, for Alfvén-Mach numbers M _A>2, ion heating is attributed primarily to the ions that have experienced a reflection from the shock front and whose velocities downstream of the front are very high. This conclusion agrees with the results of one-dimensional calculations. Solving the problem as formulated shows that two-dimensional effects are insignificant in the range of low Alfvén-Mach numbers (M _A≤5): the direction of the magnetic field is always close to its initial direction, the ions acquire low velocities along the magnetic field, and the quantitative parameters of the plasma downstream of the shock front are close to those obtained from the one-dimensional model. In the range of higher Alfvén-Mach numbers, two-dimensional effects are more pronounced and the ion distribution function is less anisotropic.     

Small-scale Alfvén waves localized near an extremum in the finite-amplitude perturbation of the radial plasma density profile

A study is made of electromagnetic waves localized in the region where the radial plasma density profile has an extremum between two local Alfvén resonances. Analytic expressions for the eigenfrequencies and eigenmodes are obtained. It is shown that kinetic and inertial Alfvén waves can propagate in the vicinity of a maximum and a minimum in the density profile, respectively. Passage to the limiting case in which the plasma density is nonuniform and has a parabolic profile is considered.     

Stability of Alfvén modes in a collisionless anisotropic plasma confined by a highly curved magnetic field

The stability of Alfvén modes in a collisionless plasma with an anisotropic pressure in a highly curved magnetic field is studied. A linearized equation for describing longitudinally nonuniform MHD perturbations with frequencies below the bounce frequency is derived. In this equation, the perturbations of longitudinal and transverse pressures are calculated using a collisionless kinetic equation. It is shown that longitudinal fluxes of the transverse and longitudinal plasma energies give rise to pressure perturbations different from those in the Chew-Goldberger-Low collisionless hydrodynamics. The corresponding energy principle is constructed. A stability criterion for Alfvén modes is obtained and is found to be more stringent than that in the Chew-Gold-berger-Low model.     

The DNLS equation and parametric decay instability

A model that describes the interaction of nonlinear Alfvén packets propagating in opposite directions parallel to the ambient magnetic field is constructed. This model incorporates both (i) the parametric interaction of harmonics propagating in the same direction, which can be responsible for the transportation of the wave energy to the short-wavelength region of the spectrum, and (ii) the parametric interaction of Alfvén waves propagating in opposite directions, which can be responsible for the excitation of backward-propagating waves by the parametric decaylike instability of the forward-propagating fluctuations.     

Formation of shock waves in a discharge plasma in the presence of a magnetic field

The effect of an external magnetic field on the dynamics of shock waves generated in an argon plasma due to both explosive processes on the cathode and expansion of the spark channel has been studied experimentally. It is shown that the expanding plasma of the cathode spot forms a shock wave and that the application of a longitudinal magnetic field decelerates the radial expansion of the cathode plasma. It is found that the intensities of some argon spectral lines increase in the presence of a magnetic field.