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.     

Propagation of MHD waves in a plasma in a sheared magnetic field with straight field lines

The propagation of MHD plasma waves in a sheared magnetic field is investigated. The problem is solved using a simplified model: a cold plasma is inhomogeneous in one direction, and the magnetic field lines are straight. The waves are assumed to travel in the plane perpendicular to the radial coordinate (i.e., the coordinate along which the plasma and magnetic field are inhomogeneous). It is shown that the character of the singularity at the resonance surface is the same as that in a homogeneous magnetic field. It is found that the shear gives rise to the transverse dispersion of Alfvén waves, i.e., the dependence of the radial component of the wave vector on the wave frequency. In the presence of shear, Alfvén waves are found to propagate across magnetic surfaces. In this case, the transparent region is bounded by two turning points, at one of which, the radial component of the wave vector approaches infinity and, at the other one, it vanishes. At the turning point for magnetosonic waves, the electric and magnetic fields are finite; however, the radial component of the wave vector approaches infinity, rather than vanishes as in the case with a homogeneous field.     

A hall dynamo effect driven by two-fluid tearing instability

A quasi-linear prediction of the two-fluid dynamo effect is analyzed with the use of tearing eigenfunctions obtained for force-free equilibrium. In the range of parameters of practical interest, the basic shear Alfvén mode is decoupled from fast compressional Alfvén and slow magneto-acoustic modes. Kinetic Alfvén modification of the shear Alfvén wave drives an instability with a growth rate ∝δ^1/3ρ _s ^2/3 , where δ is the electron skin depth and ρ_s is the ion-sound gyroradius. A net dynamo effect parallel to the magnetic field is calculated at ρ _s ?δ for large values of the stability factor \(\Delta '\rho _s^{{1 \mathord{\left/ {\vphantom {1 3}} \right. \kern-\nulldelimiterspace} 3}} \delta ^{{1 \mathord{\left/ {\vphantom {1 3}} \right. \kern-\nulldelimiterspace} 3}} \gg 1\). The dynamo effect caused by the j×B Hall term dominates the contribution from the v×B term (the alpha effect) by a factor ∝(ρ_s/δ)² in the narrow electron layer, while in the broader ion layer these contributions are comparable. The results are compared with the case of a strong guiding field where ρ _s ?δ and the tearing instability is described by resistive MHD.     

Coronal oscillations and internal loop structure

The transverse oscillations of a coronal magnetic loop whose ends are rigidly fixed in the photosphere are investigated. The loop is assumed to be inhomogeneous and to comprise two internal structural components: a central dense hot filament and a coaxial rarefied shell around it, in which the plasma density is lower than the density of the surrounding coronal plasma. The Alfvén speed in the shell, V_Am, is higher than that in the central filament and in the corona: V_Am>V_Ae>V_Ai. It is shown that, in the perfectly conducting plasma approximation, such a loop can generate two fast magnetosonic waves. The higher velocity wave is emitted in a radial direction, thereby ensuring the effect of the radiative damping of oscillations at the frequency of the m=1 cylindrical mode. The results of calculating the effect of radiative losses show that, for typical loop parameters (corresponding to those of the loops observed in the solar corona), the quality factor of oscillations may be fairly low (Q≈40). Under the conditions in question, the second (lower velocity) fast magnetosonic wave is not emitted (in contrast to the first) but rather turns out to be trapped in the magnetic flux tube.     

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.     

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.     

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.     

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.     

Resonant excitation of the magnetosphere by stochastic and unsteady hydromagnetic waves

The effect of the magnetospheric MHD cavity on the excitation of the magnetosphere by stochastic and unsteady hydromagnetic waves incident from the solar wind is investigated theoretically by using a one-dimensional nonuniform model of the medium. It is shown that most of the energy of stochastic waves is reflected from the magnetopause and that the only waves that penetrate into the magnetosphere are those with frequencies in narrow spectral ranges near the eigenfrequencies of the cavity. These waves lead to steadystate excitation of the eigenmodes of the cavity, the energy of which is determined by the spectral density of the energy flux of the incident waves at the corresponding eigenfrequencies. The energy of the eigenmodes penetrates through the opacity barrier in the vicinity of the Alfvén resonance points (each corresponding to a particular mode), where the perturbation amplitude is sharply amplified, so the total energy localized close to the Alfvén resonance point is much higher than the total energy of the corresponding eigenmode. In the vicinities, the perturbation energy is dissipated by the finite conductivity of the ionosphere, the dissipation power being equal to the energy flux of the incident waves that penetrates into the magnetosphere. The case of unsteady waves is analyzed by considering a wave pulse as an example. It is shown that most of the energy of the wave pulse is reflected from the magnetopause. The portion of the incident perturbation that penetrates into the magnetosphere leads to unsteady excitation of the eigenmodes of the magnetospheric cavity, which are then slowly damped because part of the energy of the cavity is emitted through the magnetopause back to the solar wind while the other part penetrates into the vicinities of the Alfvén resonance points. In the vicinities, the perturbation is an Alfvén wave standing between magnetically conjugate ionospheres and its energy is dissipated by the finite conductivity of the ionosphere at a rate slower than the damping rate of the eigenmodes of the cavity.     

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.     

Sharpening of the front of the current through a cylindrical foil liner

Results are presented from experiments on the electromagnetic implosion of aluminum foil liners at the MIG generator with a current rise time of ≈80 ns. Plasma with a density of 10¹⁷ cm^–3 was preliminarily injected into the liner region by using a set of radial plasma guns. The Lorentz force J × B causes plasma acceleration in the radial direction. Since the magnetic field pressure is inversely proportional to the radius squared, the plasma displacement is maximum near the liner surface. As a result, plasma motion becomes two-dimensional, a gap appears between the plasma and the liner, and the generator current is switched over to the liner. The plasma velocity at the liner surface is close to the local Alfvén velocity, while the time during which the current is switched over to the liner is nearly equal to the ratio of the liner length to the Alfvén velocity. The proposed scheme allows one to decrease the rise time of the current through the liner to several nano-seconds and, as a result, to reduce the initial liner radius and improve the stability of liner implosion.     

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.     

Dynamics of a nonquasineutral plasma in a strong magnetic field

The motion of a nonquasineutral plasma in a strong magnetic field such that is analyzed. It is shown in simple examples that, when the plasma pressure and dissipation are neglected, the only dynamic process in a magnetized plasma is the evolution of the charge-separation electric field and the related magnetic field flux. The equations derived to describe this evolution are essentially the wave Grad-Shafranov equations. The solution to these equations implies that, in a turbulent Z-pinch, a steady state can exist in which the current at a supercritical level is concentrated near the pinch axis.     

Electron Landau damping in toroidal plasma with Solov’ev equilibrium

The contribution of untrapped and two groups of trapped particles to the longitudinal (with respect to the magnetic field) elements of the dielectric susceptibility is determined by solving the drift-kinetic equations for such particles in axisymmetric tokamaks with Solov’ev equilibrium. The obtained dielectric characteristics are applicable for studying linear wave processes in the frequency range of Alfvén and fast magnetosonic waves in small- and large-aspect-ratio tokamaks with circular, elliptical, and D-shaped cross sections of magnetic surfaces. The high-frequency power absorbed in plasma via electron Landau damping is estimated by summing up terms containing the imaginary parts of both diagonal and non-diagonal elements of the longitudinal susceptibility. The imaginary part of the longitudinal susceptibility is calculated numerically for spherical tokamaks in a wide range of wave frequencies and magnetic surface radii.     

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.     

Generation of ion-acoustic and magnetoacoustic waves in an RF helicon discharge

A study is made of the generation of ion-acoustic and magnetoacoustic waves in a discharge excited in an external magnetic field by an electromagnetic wave in the whistler frequency range (ω_LH ? ω ? ω_He, where ω_LH = $\sqrt {\omega _{He} \omega _{Hi} } $ and ω_He and ω_Hi are the electron and ion gyrofrequencies, respectively). The excitation of acoustic waves is attributed to the decay of a high-frequency hybrid mode forming a plasma waveguide into low-frequency acoustic waves and new high-frequency waves that satisfy both the decay conditions and the waveguide dispersion relations. The excitation of acoustic waves is resonant in character because the conditions for the generation of waveguide modes and for the occurrence of the corresponding nonlinear wave processes should be satisfied simultaneously. An unexpected effect is the generation of magnetoacoustic waves by whistlers. A diagnostic technique is proposed that allows one to determine the thermal electron velocity by analyzing decay conditions and dispersion relations for waves in the discharge channel.     

Localization of magnetized electrons in current filaments as a fundamental cause of Coulomb explosion

Mechanisms for generating current filaments in a dense plasma under the action of focused laser pulses and in a Z-pinch configuration are discussed. The main properties of current filaments with a zero and nonzero electron vorticity Ω _e =B?(c/e)?×p _e that originate at magnetic fields in the range 4πn _e m _e c²?B²?4πn _i m _i c² are investigated under the conditions of Coulomb explosion at currents below the ion Alfvén current. A study is made of the equilibrium configurations of nonquasineutral current filaments in a purely longitudinal (B_z) and a purely azimuthal (B_θ) magnetic field and also in a more general case of a helical magnetic field, having two components, under conditions such that the charge separation occurs on a spatial scale on the order of the magnetic Debye radius r_B ? |B|/(4πen_e. It is shown that strong electric fields generated in the current filaments are comparable in magnitude to the atomic field and are capable of accelerating ions to energies of several tens of megaelectronvolts. The ion dynamics in strong electric fields of the filaments is calculated numerically and is shown to lead to the formation of collisionless shock waves on time scales on the order of several inverse ion plasma frequencies ω _pi ^?1 . The possible formation of current filaments on different spatiotemporal scales is considered.     

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.     

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.     

Reconnection in photospheric-chromospheric current sheet and coronal heating

It has been observed by various ground and space based solar missions that magnetic reconnection occurs frequently in the photosphere-chromosphere region as well as in the solar corona. The purpose of this article is to examine the process of reconnection in thin current sheet formed between two oppositely directed magnetic flux tubes in photospheric-chromospheric region. Using the data of different atmospheric models for the solar photosphere and chromosphere, we have estimated the rate of magnetic reconnection in terms of Alfvénic Mach number, growth rate of tearing mode, island length scales, and energy dissipation rate necessary to heat the chromospheric plasma. It is found that magnetic Reynolds number for the current sheet in the chromosphere varies from 1.14 × 10³ to 7.14 × 10⁶ which indicates that the field lines in the photosphere and chromosphere reconnect with speed, that is, 0.00034 to 0.0297 times the Alfvén speed. Frequency of the MHD waves generated in the chromosphere reconnection region is of the order of 100 Hz, so these high-frequency waves may be the sources of coronal heating and solar wind acceleration.