Specificities of one-dimensional dissipative magnetohydrodynamics

One-dimensional dynamics of a plane slab of cold (β ? 1) isothermal plasma accelerated by a magnetic field is studied in terms of the MHD equations with a finite constant conductivity. The passage to the limit β → 0 is analyzed in detail. It is shown that, at β = 0, the character of the solution depends substantially on the boundary condition for the electric field at the inner plasma boundary. The relationship between the boundary condition for the pressure at β > 0 and the conditions for the electric field at β = 0 is found. The stability of the solution against one-dimensional longitudinal perturbations is analyzed. It is shown that, in the limit β → 0, the stationary solution is unstable if the time during which the acoustic wave propagates across the slab is longer than the time of magnetic field diffusion. The growth rate and threshold of instability are determined, and results of numerical simulation of its nonlinear stage are presented.     

Nonlinear dynamics of Kelvin-Helmholtz instability in a finite-width plasma flow

The nonlinear stage of Kelvin-Helmholtz (KH) instability in a finite-width plane-parallel plasma flow is analyzed. The analysis is performed by means of two-dimensional numerical simulations with the use of ideal magnetohydrodynamic equations describing isothermal plasma flows propagating along the magnetic field. The influence of the magnetic field strength, the plasma temperature, and the ratio of the flow width to the width of the transition layer on the formation of vortex layers and large-scale flow perturbations is investigated. It is shown that, if the wavelength of periodic perturbations is shorter than the flow width, the symmetric and antisymmetric modes develop in a qualitatively similar manner. For waves with wavelengths longer than the flow width, the development of such modes is very different due to the mutual influence of the flow boundaries. Analysis of the development of instability at different values of the Alfvén Mach number M _A shows that long-lived vortices with a characteristic scale length on the order of the flow width appear in a weak magnetic field for both symmetric and antisymmetric modes; however, the vortex geometries for these modes are different. In a strong magnetic field, M _A ～ 5, the phase of vortex decay for both types of modes occurs faster than in a weak field; however, in the case of an antisymmetric mode, large-scale perturbations of the flow boundary are retained for a longer time. Analysis of the evolution of the initial disturbance produced by an ensemble of random small perturbations (noise) at different plasma temperatures shows that, for a flow width comparable with the width of the transition region, the development of KH instability is always antisymmetric in character and leads to well-developed large-scale perturbations of the flow as a whole. For a cold plasma with C _S < 0.5U (where C _S is the speed of sound and U is the flow velocity), in contrast to hot plasma with C _S > 0.5U, the development of KH instability leads to the growth of the antisymmetric mode even if the flow width is much larger than the width of the transition region.     

Generation of zonal flows and large-scale magnetic fields by drift-Alfvén turbulence

The possibility of generating zonal perturbations by drift-Alfvén turbulence in a plasma with a finite pressure (1>β>m_e/m_i) is investigated. A set of coupled equations is derived that includes the equation for the spectral function of the turbulence and the averaged equations for zonal perturbations. It is shown that, in particular cases, the equation for the spectral function possesses action invariants; i.e., it takes the form of a conservation law for some quantities that are proportional to the spectral function of turbulence. Two types of instability of the zonal perturbations are revealed. The first type of instability generates only a zonal flow. Two regimes of this instability—resonant and hydrodynamic regimes—are examined, and the corresponding instability growth rates are determined. The second type of instability takes place when the resonant interaction of drift-Alfvén waves with electrons is taken into account. Because of this instability, the generation of a zonal magnetic field is inevitably accompanied by the generation of a zonal flow. It is found that the growth rate of the second type of instability is slower than that of the first type.     

Kelvin-Helmholtz instability in a bounded plasma flow

Kelvin-Helmholtz instability in a three-layer plane geometry is investigated theoretically. It is shown that, in a three-layer system (in contrast to the traditionally considered case in which instability develops at the boundary between two plasma flows), instability can develop at an arbitrary ratio of the plasma flow velocity to the ion-acoustic velocity. Perturbations with wavelengths on the order of the flow thickness or longer can increase even at a zero temperature. The system can also be unstable against long-wavelength perturbations if the flow velocity at one of the boundaries is lower than the sum of the Alfvén velocities in the flow and the ambient plasma. The possibility of applying the results obtained to interpret the experimental data acquired in the framework of the CLUSTER multisatellite project is discussed. It follows from these data that, in many cases, the propagation of an accelerated particle flow in the plasma-sheet boundary layer of the Earth’s magnetotail is accompanied by the generation of magnetic field oscillations propagating with a velocity on the order of the local Alfvén velocity.     

On the growth rate of aperiodic instability in plasma with an anisotropic bi-Maxwellian electron velocity distribution

The growth rate of aperiodic instability of transverse and longitudinal-transverse electromagnetic field perturbations in plasma with an anisotropic bi-Maxwellian electron velocity distribution is studied. The boundaries of the instability domains in wave vector space are found, and the growth rates of field perturbations with configurations different from that corresponding to the maximum growth rate are determined.     

Magnetorotational instability of a weakly ionized accretion disk with vertical and azimuthal magnetic fields

Magnetorotational instability of a weakly ionized accretion disk with an admixture of charged dust grains in a magnetic field with the axial and toroidal components is analyzed. The dispersion relation for perturbations perpendicular to the disk plane is derived with allowance for both the Hall current and the finite transverse plasma conductivity. It is shown that dust grains play an important role in the disk magnetic dynamics. Due to the effect of dust grains, the Hall current can reverse its direction as compared to the case of electron-ion plasma. As a result, the instability threshold shifts toward the short-wavelength range. Under certain conditions, electromagnetic fluctuations of any length can become unstable. It is established that the instability criterion for waves of any scale length is satisfied within a finite interval of the density ratio between the dust and electron plasma components. The width of this interval and the instability growth rate as functions of the plasma parameters and the configuration of the magnetic field in the disk are analyzed.     

Ponderomotive force of the low-frequency field and modulational instability of drift waves

A study is made of the processes that occur in an inhomogeneous nonisothermal plasma in a strong external magnetic field and whose characteristic frequencies are lower than the ion Langmuir frequency but higher than the collision frequency. An expression for the ponderomotive force of the low-frequency field is derived. The excitation of a long-wavelength low-frequency drift wave during the development of the modulational instability of a drift pump wave is investigated. The growth rates of the instability are obtained, and the conditions for its onset are determined. The possible relation of the modulational instability to the formation of structures in the plasma is discussed.     

Decay instability of a laser pulse propagating in a transverse direction in a magnetized plasma

The decay instability of a lser pulse propagating across an external magnetic field in a subscritical plasma is investigated analytically and numerically. It is shown that, when the relaxation of the pulse is taken into account, the hydrodynamic growth rate of the decay instability is slower than that obtained earlier in the constant-amplitude pump wave approximation. The results of numerical simulations by a particle-in-cell method demonstrate that an increase in the amplitude of the parametrically excited waves is accompanied by a decrease in their group velocity; in this case, up to 85% of the laser energy is converted into the energy of the plasma particles. It is found that, under resonance conditions, the magnetic field acts to increase the energy of the accelerated ions that escape from the plasma slab through its front boundary.     

MHD stabilization by the magnetic hill at a small rotational transform

The effect of very small rotational transform on the plasma stability in three-dimensional closed magnetic configurations with closed magnetic field lines, stabilized by the magnetic hill (i.e., by the plasma compressibility), is considered using ideal MHD theory. It is shown that, for infinitely small values of the rotational transform, the Suydam-Mercier criterion predicts the onset of acoustic instability with a finite growth rate, provided that the Bernstein-Kadomtsev criterion is satisfied. Consequently, for a vanishingly small rotational transform, the limiting transition from the Suydam-Mercier criterion to the Bernstein-Kadomtsev criterion is impossible. Taking into account the finite Larmor radius allows this limiting transition to be made. The Bernstein-Kadomtsev criterion ensures MHD stability at rotational transform values below a certain critical value determined by the ratio of the ion Larmor radius to the plasma minor radius. Under experimental conditions, this critical value is larger than that expected to be produced by the actual magnetic perturbations.     

Stability of a quasi-flute mode under the Bernstein-Kadomtsev condition in a toroidal confinement system

It is shown that the growth rate of the MHD instability in toroidal configurations is slower in a situation in which the Bernstein-Kadomtsev condition is satisfied while the Mercier stability criterion is not. Under the Bernstein-Kadomtsev condition, Alfvénic Mercier modes are not excited, but quasi-flute acoustic Mercier modes develop instead. In confinement systems with closed magnetic field lines, the Bernstein-Kadomtsev condition ensures MHD stability; however, a small rotational transform produced by magnetic perturbations can give rise to a quasi-flute acoustic instability whose growth rate is proportional to the perturbation amplitude, in which case the fastest growing oscillations are those with the shortest wavelengths.     

Progress in theory of instabilities in a rotating plasma

A review is given of the basic results of modern theory of instabilities in a rotating plasma. Both axisymmetric and nonaxisymmetric perturbations are considered. Main attention is given to the magnetorotational instability (MRI), discovered earlier by Velikhov, and the rotational-convective instability (RCI) discussed in a number of papers of astrophysical trend. For qualitative explanation of the results, a local approach is used which, with equilibrium plasma pressure gradient and/or nonsymmetry of perturbations, requires operation with nonlocal azimuthal perturbed magnetic field. The gravity and effects of pressure anisotropy are taken into account. In addition to hydrodynamic, the electrodynamic approach is formulated. The drift effects are considered. Analyzed are the ideal instabilities and those depending on the dissipative effects: viscosity and heat conductivity. The MRI is considered at presence of the charged dust particles. Besides the local approach, the nonlocal approach is formulated for the plasma model with a steplike profile of angular rotation frequency. Alongside with perturbations which frequencies are small compared to the ion cyclotron frequency, the perturbations are analyzed with frequencies larger than the ion cyclotron frequency. The latter corresponds to the Hall regime and subregime of nonmagnetized plasma.     

Kelvin-Helmholtz instability of a cylindrical plasma flow with an arbitrary temperature

The dispersion relation for Kelvin-Helmholtz magnetohydrodynamic instability of a cylindrical plasma flow in a longitudinal magnetic field is studied with allowance for plasma compressibility. Stability of the system in a wide range of plasma parameters is thoroughly analyzed in the incompressible plasma approximation. Using the results obtained, a diagram of the system stability is constructed in terms of the magnetic field and the ratio between the plasma densities in the flow and the ambient space. It is shown by numerically solving the dispersion relation for the case of a compressible plasma that perturbations with scale lengths on the order of the flow diameter and larger can develop even at a zero temperature. For low ion-sound velocities, c _S ²/U ₀² < 0.25, the growth rate of the axisymmetric mode with m = 0 is much smaller than that of non-axisymmetric modes. It is shown that, in an incompressible plasma, the eigenmodes are damped monotonically with distance from the flow. In plasma with a finite temperature, the character of damping is oscillatory; in this case, the lower the plasma temperature, the larger the distance at which the ambient plasma is perturbed.     

Kelvin-Helmholtz instability for a bounded plasma flow in a longitudinal magnetic field

Kelvin-Helmholtz MHD instability in a plane three-layer plasma is investigated. A general dispersion relation for the case of arbitrarily orientated magnetic fields and flow velocities in the layers is derived, and its solutions for a bounded plasma flow in a longitudinal magnetic field are studied numerically. Analysis of Kelvin-Helmholtz instability for different ion acoustic velocities shows that perturbations with wavelengths on the order of or longer than the flow thickness can grow in an arbitrary direction even at a zero temperature. Oscillations excited at small angles with respect to the magnetic field exist in a limited range of wavenumbers even without allowance for the finite width of the transition region between the flow and the ambient plasma. It is shown that, in a low-temperature plasma, solutions resulting in kink-like deformations of the plasma flow grow at a higher rate than those resulting in quasi-symmetric (sausage-like) deformations. The transverse structure of oscillatory-damped eigenmodes in a low-temperature plasma is analyzed. The results obtained are used to explain mechanisms for the excitation of ultra-low-frequency long-wavelength oscillations propagating along the magnetic field in the plasma sheet boundary layer of the Earth’s magnetotail penetrated by fast plasma flows.     

Interaction of an ion bunch with a plasma slab

Charge neutralization of a short ion bunch passing through a plasma slab is studied by means of numerical simulation. It is shown that a fraction of plasma electrons are trapped by the bunch under the action of the collective charge separation field. The accelerated electrons generated in this process excite beam?plasma instability, thereby violating the trapping conditions. The process of electron trapping is also strongly affected by the high-frequency electric field caused by plasma oscillations at the slab boundaries. It is examined how the degree of charge neutralization depends on the parameters of the bunch and plasma slab.     

Effect of the shear flow in the generation and self-organization of internal gravity wave structures in the dissipative ionosphere

A linear mechanism for the generation and amplification of internal gravity waves and their further nonlinear dynamics in the stably stratified dissipative ionosphere in the presence of an inhomogeneous zonal wind (shear flow) is studied. For shear flows, the operators of linear problems are non-self-conjugate and the corresponding eigenfunctions are nonorthogonal. Therefore, the canonical modal approach is poorly applicable to study such motions. In this case, the so-called nonmodal mathematical analysis is more adequate. Dynamic equations and equations for the energy transport of internal gravity perturbations in the ionosphere with shear flows are derived on the basis of the nonmodal approach. Exact analytic solutions of linear and nonlinear equations are found. The growth rate of the shear instability of internal gravity waves is determined. It is revealed that perturbations grow in time according to a power law, rather than exponentially. The frequency and wavenumber of the generated internal gravity modes depend on time; hence, a wide spectrum of wave perturbations caused by linear effects (rather than nonlinear turbulent ones) forms in the ionosphere with shear flows. The efficiency of the linear mechanism for the amplification of internal gravity waves during their interaction with the inhomogeneous zonal wind is analyzed. A criterion for the development of the shear instability of such waves in the ionospheric plasma is obtained. It is shown that, in the presence of shear instability, internal gravity waves extract the shear flow energy in the initial (linear) stage of their evolution, due to which their amplitude and, accordingly, energy increase substantially (by an order of magnitude). As the amplitude increases, the mechanism of nonlinear self-localization comes into play and the process terminates with the self-organization of strongly localized solitary nonlinear internal gravity vortex structures. As a result, a new degree of freedom of the system and a new way of the evolution of perturbations in a medium with a shear flow appear. Inductive and viscous dampings limit the lifetime of vortex internal gravity structures in the ionosphere; nevertheless, their lifetime is long enough for them to strongly affect the dynamic properties of the medium. It is revealed on the basis of the analytic solution of a set of time-independent nonlinear dynamic equations that, depending on the velocity profile of the shear flow, the nonlinear internal gravity structures can take the form of a purely monopole vortex, a dipole cyclone-anticyclone pair, a transverse vortex chain, or a longitudinal vortex path against the background of the inhomogeneous zonal wind. The accumulation of such vortices in the ionosphere can result in a strongly turbulent state.     

Quasilinear theory of the inversionless generation of electron cyclotron radiation

A study is made of the parametric generation of cyclotron radiation by a modulated electron ensemble that is stable against the generation of a monochromatic field—the classical effect characteristic of an inversionless maser. A quasilinear theory of inversionless cyclotron instability is developed. It is shown that, during quasilinear diffusion, the system of a modulated electron beam and an electromagnetic field relaxes to a certain steady state.     

Reflection of electromagnetic radiation from plasma with an anisotropic electron velocity distribution

The reflection of a test electromagnetic pulse from the plasma formed as a result of tunnel ionization of atoms in the field of a circularly polarized high-power radiation pulse is analyzed using the kinetic approach to describe electron motion. It is shown that the reflected pulse is significantly amplified due to the development of Weibel instability. The amplification efficiency is determined by the maximum value of the instability growth rate, which depends on the degree of anisotropy of the photoelectron distribution function.     

<Emphasis Type="Italic">l</Emphasis>=1 diocotron instability of single charged plasmas

The linear stability analysis of the l=1 diocotron perturbations in a low density single charged plasma confined in a cylindrical Penning trap is critically revisited. Particular attention is devoted to the instability due to the presence of one or more stationary points in the radial profile of the azimuthal rotation frequency. The asymptotic analysis of Smith and Rosenbluth for the case of a single-bounded plasma column (algebraic instability proportional to t^1/2) is generalized in a few respects. In particular, the existence of unperturbed density profiles that give rise to l=1 algebraic instabilities growing with time proportionally to t^1?1/m, m≥ 3 being the order of a stationary point in the rotation frequency profile, and even proportionally to t, is pointed out. It is also shown that smoothing the density jumps of a multistep density profile can convert algebraically growing perturbations into exponentially decaying modes. The relevant damping rates are computed. The asymptotic analysis (t → ∞) of the fundamental diocotron perturbations is then generalized to the case of a cylindrical Penning trap with an additional coaxial inner conductor. It is shown that the algebraic instability found in the case of a single-bounded plasma column becomes exponential at longer times. The relevant linear growth rate is computed by a suitable inverse Laplace transform (contour integral in the complex plane). In the particular case of an uncharged inner conductor of radius a, the growth rate is shown to scale as a^4/3 for a → 0. The theoretical results are compared with the numerical solution of the linearized two-dimensional drift Poisson equations.     

Raman scattering of laser radiation in magnetoactive plasma

Raman scattering in a subcritical plasma is simulated numerically for the case where the laser radiation propagates transversely to an external magnetic field. It is shown that, in the linear stage of Raman instability, the magnetic field decreases the instability growth rate for forward scattering and increases it for backward scattering. As the value of the magnetic field increases, the stochastic heating of plasma electrons is enhanced in the region of backscattering.