Interactions of plasmas with magnetic field boundaries

The magnetopause, the boundary layer, or current sheath, which separates the magnetosphere from the solar wind, is the particular interaction considered in this paper.The collision free electron skin depth, $\text{ξ}{}_{\mathrm{e}}\text{=}\text{c}\text{ω}{}_{\mathrm{pe}}$, where c is the velocity of light and ω_pe, is the plasma frequency, gives a classical measure of the penetration depth of a collisionless plasma by an electromagnetic field. This penetration depth is small compared with the dimensions of the magnetosphere and hence the boundary layer may be conveniently considered in one dimension.In General all one dimensional solutions lie within an order of magnitude of the value of ξ_e, the only exception being the important one, in which the electric field perpendicular to the current sheath plane is not present, either due to a particular trapped particle distribution or due to a short circuiting end effect. For this exception the thickness is increased by the factor ($\text{m}{}_{\mathrm{i}}\text{i/m}{}_{\mathrm{e}}\text{)}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$.The current sheath solutions discussed are equilibrium solutions but not necessarily stable equilibrium solutions.The extension of the models to three dimensions has a larger effect than might at first be expected. The effect may be intuitively understood as a consequence of flux conservation in the sheath. The one dimensional solutions then correspond to the current sheath profiles at the thinnest point of the three dimensional sheath.     

Relaxed magnetic field structures in multi-ion plasmas

The steady state solution of a three species magnetoplasma is presented. It is shown that relaxed magnetic field configuration results in a triple curl Beltrami equation which permits the existence of three structures. It is the consequence of inertial effects of the plasma constituents. One of the three vortices is of large scale while the remaining two relaxed structures are of small size of the order of electron skin depth. The magnetic field profiles are given for different Beltrami parameters. The study could be helpful to understand large magnetic field structures in three species plasmas found in space and laboratory.     

Two-stream instability in plasmas with arbitrary orientation of magnetic field

The problem of two-stream instability in plasmas where electrons move through ions with arbitrary orientation of the magnetic field is discussed. Electrostatic and electromagnetic instabilities have both been discussed. It is found that the strength and orientation of the magnetic field both affect the electrostatic waves propagating along the streaming direction to a considerable extent. The electromagnetic instability with a cross-field orientation is associated with a larger range of unstable wavenumber and larger growth rates compared to any other coexisting electrostatic instability.     

Rigidly rotating modes of the solar magnetic field

Discrete rigidly rotating components (modes) of the large-scale solar magnetic field have been investigated. We have used a specially calculated basic set of functions to resolve the observed magnetic field into discrete components. This adaptive set of functions, as well as the expansion coefficients, have been found by processing a series of digitized synoptic maps of the background magnetic field over a 20-year period. As a result, dependences have been obtained which describe the spatial structure and the temporal evolution of the 27-day and 28-day rigidly rotating modes of the Sun's magnetic field.The spatial structure of the modes has been compared with simulations based on the known flux-transport equation. In the simulations, the rigidly rotating modes were regarded as stationary states of the magnetic field whose rigid rotation and stability were maintained by a balance between the emergence of magnetic flux from stationary sources located at low latitudes and the horizontal transport of flux by turbulent diffusion and poleward directed meridional flow. Under these assumptions, the structure of the modes is determined solely by the horizontal velocity field of the plasma, except for the low-latitude zone where sources of magnetic flux concentrate. We have found a detailed agreement between the simulations and the results of the data analysis, provided that the amplitude of the meridional flow velocity and the diffusion constant are equal to 9.5 m s^–1 and 600 km² s^–1, respectively.The analysis of the expansion coefficients has shown that the rigidly rotating modes undergo rapid step-like variations which occur quasi-periodically with a period of about two years. These variations are caused by separate surges of magnetic flux in the photosphere, so that each new surge gives rise to a rapid replacement of old large-scale magnetic structures by newly arisen ones.     

Inertia driven tearing modes in electron-positron plasmas

It is shown that the particle inertia can cause a tearing instability in an electron-positron collisionless plasma with sheared magnetic fields. An approximate analytical expression for the growth rate is obtained. It characterizes the magnetic reconnection timescale in a magnetized electronpositron plasma.     

Electromagnetic ion waves in cold relativistic plasmas

The high-energy processes which occur in many astrophysical objects have motivated recent studies (e.g., Tsintsadze and Tsikarishvili, 1976; Ferrariet al., 1978; Sweeney and Stewart, 1978) of large amplitude wave propagation in plasmas. Such investigations are also of interest for laboratory experiments where strong laser radiation interacts with a high-density target. In the present paper we shall show that even rather small amplitude waves in the presence of an external magnetic field can induce particle velocities which are comparable to the velocity of light. In this ultrarelativistic limit we shall demonstrate that two completely new types of circularly polarized waves appear and that under certain conditions, modulational instabilities occur. Finally we look at the possibility to relate the amplitudes and wavelengths of such waves to pulsar data.     

Excitation of non-axially symmetric modes of the Sun's mean magnetic field

The kinematic dynamo equations for the mean magnetic field are solved with an asymptotic method of the WKB type. The excitation conditions and main characteristics of the non-axially symmetric modes for a given distribution of the sources are obtained. Utilization of the helioseismologic data on the Sun's internal rotation permits an explanation, within the framework of dynamo theory, of the excitation of the main non-axially symmetric modes revealed in the Sun's magnetic field sector structure.     

Wave processes in nonlinear beams during propagation of waves in pulsar plasmas with different magnetic field orientations

The propagation of nonlinear three-dimensional waves in the form of gaussian beams in pulsars is examined. The defining equations for the wave motion of a plasma with high particle velocities, high electrical conductivity, high wave frequency, and high magnetic fields are the standard equations of magnetogas dynamics. Nonlinear, time-dependent equations are derived for relatively small perturbations of the medium and the orders of magnitude of the parameters of motion such that all the terms in the time-dependent equation are of the same order are written down. Various directions of the unperturbed magnetic field and of the wave propagation which may arise during plasma motion in quasars are considered. In a number of cases a closed analytic solution can be constructed for the propagation of axially symmetric gaussian beams. __________ Translated from Astrofizika, Vol. 49, No. 3, pp. 409–417 (August 2006).     

Influence of a chromospheric magnetic field on solar acoustic modes

This paper studies the effect of a magnetic atmosphere on the global solar acoustic oscillations in a simple Cartesian model. First, the influence of the ratio of the coronal and the photospheric temperature τ and the strength of the magnetic field at the base of the corona B_c on the oscillation modes is studied for a convection zone-corona model with a true discontinuity. The ratio τ seems to be an important parameter. Subsequently, the discontinuity is replaced by an intermediate chromospheric layer of thickness L and the effect of the thickness on the frequencies of the acoustic waves is studied. In addition, nonuniformity in the magnetic field, plasma density and temperature in the transition layer gives rise to continuous Alfvén and slow spectra. Modes with characteristic frequencies lying within the range of the continuum may resonantly couple to Alfvén and/or slow waves.     

Anomalous magnetic viscosity in accretion disks with q-distributed plasmas

Based on the equations of the self-generated magnetic field in the q-distributed plasmas, the studies show that the magnetic field is modulationally unstable by the perturbation method and the equations have self-similar collapse solution. The anomalous magnetic viscosity of accretion disks generates from highly spatially intermittent flux of the self-generated magnetic field. In addition, the anomalous viscosity coefficient is 8 orders more than the molecular viscosity and is modified by the adjustable index q, which may preferably explain the observations.     

Kinetic theory of acoustic-like modes in nonextensive pair plasmas

The low-frequency acoustic-like modes in a pair plasma (electron-positron or pair-ion) is studied by employing a kinetic theory model based on the Vlasov and Poisson’s equations with emphasizing the Tsallis’s nonextensive statistics. The possibility of the acoustic-like modes and their properties in both fully symmetric and temperature-asymmetric cases are examined by studying the dispersion relation, Landau damping and instability of modes. The resultant dispersion relation in this study is compatible with the acoustic branch of the experimental data (Oohara et al. in Phys. Rev. Lett. 95:175003, 2005) in which the electrostatic waves have been examined in a pure pair-ion plasma. Particularly, our study reveals that the occurrence of growing or damped acoustic-like modes depends strongly on the nonextensivity of the system as a measure for describing the long-range Coulombic interactions and correlations in the plasma. The mechanism that leads to the unstable modes lies in the heart of the nonextensive formalism yet, the mechanism of damping is the same developed by Landau. Furthermore, the solutions of acoustic-like waves in an equilibrium Maxwellian pair plasma are recovered in the extensive limit (q→1), where the acoustic modes have only the Landau damping and no growth.     

Kinetic Alfven wave driven by density and magnetic field inhomogeneities in plasmas of finite β

On the basis of an analysis of the instability of drift caused by density and magnetic field inhomogeneities in plasmas with finite β, the effect of the instability on the excitation of kinetic Alfven wave (KAW) is probed. In the kinetic theory, which correctly treats the effect of the finite Larmor radius and the wave-particle resonant interaction, the motion of the ions is described with the Vlasov equation and the motion of electrons, with the kinetic drift equation. Comparing the effects by inhomogeneities in the density and in the magnetic field in plasmas with finite β, we found that the drift instability is more easily excited by the former, and in the instability so excited, the energy transfer is more intense. This energy transfer provides the physical basis for the excitation of KAW. As shown by numerical solutions, KAWs can be widely excited and produced in the magnetosphere, especially in the cusp of the magnetosphere, in the magnetopause and in the boundary layers of plasma sheets, where inhomogeneities are obvious. The results of the present work further illustrate that the KAW plays an important role in the energy transfer in magnetospheric regions.     

The instability of the electromagnetic ordinary modes in counterstreaming and counterrotating plasmas

The instability of a linearly-polarised electromagnetic ordinary mode in counterrotating plasmas and propagating perpendicular to a uniform magnetic field caused by a counterstreaming of electrons along the latter is studied using a cold-plasma model. It is found that: (i) In the presence of either a streaming or a rotation or both, the ordinary-wave propagation is possible even for frequencies less than the plasma frequency; (ii) the Coriolis forces like the applied magnetic field stabilise the ordinary modes.     

Oblique solitary Alfvén modes in relativistic electron-positron plasmas

In electron-positron plasmas the charge-to-mass ratio is the same for both species. This leads for different waves to the vanishing of certain coefficients in the dispersion laws and nonlinear evolution equations, and also to the decoupling of some of the plasma modes. In particular, there is a low-frequency mode which exists at all angles of propagation with respect to the static magnetic field, corresponding at parallel propagation to a degenerate case of circularly polarized waves, and at perpendicular propagation to part of the extraordinary mode. The nonlinear evolution of this generalizedX-mode is governed by a Korteweg-de Vries equation, valid at all angles of propagation except strictly parallel propagation, for which a different approach had been given already. The nonlinearity is strongest at perpendicular propagation.     

The conditions for the existence of the electric field opposite to the current along the magnetic field lines in the thin plasma

The flow of the current along the magnetic field lines in the thin plasma directed opposite to the electric field is considered. The particles moving to the equatorial plane are supposed to have mirror points above the region of absorption (the ionosphere) and the particles moving to the ionosphere are supposed to have mirror points below the region of absorption. The current, therefore, flows. The functions of the distribution of the electrons and ions are considered to be mono-energetic. The energies of the electrons and the ions and their densities on the boundary of absorption are estimated for the potential difference and for the current density which are typical for the auroral field lines.     

Electromagnetic field in the structure of space-time

In this paper we make an attempt to show that electromagnetic field appears to be a phenomenon caused by the presence of a dilatational degree of freedom which is attributed to the whole matter of the Universe. For this attempt we used Weyl's generalization of the Riemannian geometry and tried to show that Einstein's basic objection to the Weyl theory can in this case be removed.