Asymmetric configurations of a thin current sheet with a constant normal magnetic field component

A possible mechanism for the formation of a quasi-equilibrium asymmetric current sheet in the magnetospheric tail due to the asymmetry of peripheral plasma sources is analyzed using a self-consistent particle- in-cell model of a thin collisionless current sheet with a constant normal magnetic field component. For the case in which the current sheet is produced by only one source, quasi-equilibrium sheet configurations with maximum possible asymmetry are obtained for different input parameters of the model. In such configurations, the equilibrium force balance is satisfied with high accuracy and the shape of the current density profile remains nearly symmetric, but the current sheet itself is slightly shifted from the source as compared to the symmetric case. The configurations obtained using numerical simulations are compared with those calculated using the previous analytical model of a thin current sheet. It is found that the results provided by these models agree well both qualitatively and quantitatively.     

Time Evolution of the Macroscopic Characteristics of a Thin Current Sheet in the Course of Its Formation in the Earth’s Magnetotail

A numerical model is developed that allows tracing the time evolution of a current sheet from a relatively thick current configuration with isotropic distributions of the pressure and temperature in an extremely thin current sheet, which plays a key role in geomagnetic processes. Such a configuration is observed in the Earth’s magnetotail in the stage preceding a large-scale geomagnetic disturbance (substorm). Thin current sheets are reservoirs of the free energy released during geomagnetic disturbances. The time evolution of the components of the pressure tensor caused by changes in the structure of the current sheet is investigated. It is shown that the pressure tensor in the current sheet evolves in two stages. In the first stage, a current sheet with a thickness of eight to ten proton Larmor radii forms. This stage is characterized by the plasma drift toward the current sheet and the Earth and can be described in terms of the Chu–Goldberger–Low approximation. In the second stage, an extremely thin current sheet with an anisotropic plasma pressure tensor forms, due to which the system is maintained in an equilibrium state. Estimates of the characteristic time of the system evolution agree with available experimental data.     

Heliospheric current sheet and effects of its interaction with solar cosmic rays

The effects of interaction of solar cosmic rays (SCRs) with the heliospheric current sheet (HCS) in the solar wind are analyzed. A self-consistent kinetic model of the HCS is developed in which ions with quasiadiabatic dynamics can present. The HCS is considered an equilibrium embedded current structure in which two main plasma species with different temperatures (the low-energy background plasma of the solar wind and the higher energy SCR component) contribute to the current. The obtained results are verified by comparing with the results of numerical simulations based on solving equations of motion by the particle tracing method in the given HCS magnetic field with allowance for SCR particles. It is shown that the HCS is a relatively thin multiscale current configuration embedded in a thicker plasma layer. In this case, as a rule, the shear (tangential to the sheet current) component of the magnetic field is present in the HCS. Taking into account high-energy SCR particles in the HCS can lead to a change of its configuration and the formation of a multiscale embedded structure. Parametric family of solutions is considered in which the current balance in the HCS is provided at different SCR temperatures and different densities of the high-energy plasma. The SCR densities are determined at which an appreciable (detectable by satellites) HCS thickening can occur. Possible applications of this modeling to explain experimental observations are discussed.     

Thin current sheets in collisionless plasma: Equilibrium structure,plasma instabilities,and particle acceleration

The review is devoted to plasma structures with an extremely small transverse size, namely, thin current sheets that have been discovered and investigated by spacecraft observations in the Earth’s magnetotail in the last few decades. The formation of current sheets is attributed to complicated dynamic processes occurring in a collisionless space plasma during geomagnetic perturbations and near the magnetic reconnection regions. The models that describe thin current structures in the Earth’s magnetotail are reviewed. They are based on the assumption of the quasi-adiabatic ion dynamics in a relatively weak magnetic field of the magnetotail neutral sheet, where the ions can become unmagnetized. It is shown that the ion distribution can be represented as a function of the integrals of particle motion—the total energy and quasi-adiabatic invariant. Various modifications of the initial equilibrium are considered that are obtained with allowance for the currents of magnetized electrons, the contribution of oxygen ions, the asymmetry of plasma sources, and the effects related to the non-Maxwellian particle distributions. The theoretical results are compared with the observational data from the Cluster spacecraft mission. Various plasma instabilities developing in thin current sheets are investigated. The evolution of the tearing mode is analyzed, and the parameter range in which the mode can grow are determined. The paradox of complete stabilization of the tearing mode in current sheets with a nonzero normal magnetic field component is thereby resolved based on the quasi-adiabatic model. It is shown that, over a wide range of current sheet parameters and the propagation directions of large-scale unstable waves, various modified drift instabilities—kink and sausage modes—can develop in the system. Based on the concept of a turbulent electromagnetic field excited as a result of the development and saturation of unstable waves, a mechanism for charged particle acceleration in turbulent current sheets is proposed and the energy spectra of the accelerated particles are obtained.     

Kinetic models of current sheets with a sheared magnetic field

Thin current sheets, whose existence in the Earth’s magnetotail is confirmed by numerous spacecraft measurements, are studied analytically and numerically. The thickness of such sheets is on the order of the ion Larmor radius, and the normal component of the magnetic field (B _z ) in the sheet is almost constant, while the tangential (B _x ) and shear (B _y ) components depend on the transverse coordinate z. The current density in the sheet also has two self-consistent components (j _x and j _y , respectively), and the magnetic field lines are deformed and do not lie in a single plane. To study such quasi-one-dimensional current configurations, two kinetic models are used, in particular, a numerical model based on the particle-in-cell method and an analytical model. The calculated results show that two different modes of the self-consistent shear magnetic field B _y and, accordingly, two thin current sheet configurations can exist for the same input parameters. For the mode with an antisymmetric z profile of the B _y component, the magnetic field lines within the sheet are twisted, whereas the profiles of the plasma density, current density component j _y , and magnetic field component B _x differ slightly from those in the case of a shearless magnetic field (B _y = 0). For the symmetric B _y mode, the magnetic field lines lie in a curved surface. In this case, the plasma density in the sheet varies slightly and the current sheet is two times thicker. Analysis of the dependence of the current sheet structure on the flow anisotropy shows that the sheet thickness decreases significantly with decreasing ratio between the thermal and drift plasma velocities, which is caused by the dynamics of quasi-adiabatic ions. It is shown that the results of the analytical and numerical models are in good agreement. The problems of application of these models to describe current sheets at the magnetopause and near magnetic reconnection regions are discussed.     

Numerical simulations of plasma equilibrium in a one-dimensional current sheet with a nonzero normal magnetic field component

The force balance in a thin collisionless current sheet in the Earth’s magnetotail with a given constant magnetic field component B _z across the sheet is numerically studied for the first time in a self-consistent formulation of the problem. The current sheet is produced by oppositely directed plasma flows propagating from the periphery of the sheet toward the neutral plane. A substantially improved version of a macroparticle numerical model is used that makes it possible to simulate on the order of 10⁷ macroparticles even with a personal computer and to calculate equilibrium configurations with a sufficiently low discrete noise level in the first-and second-order moments of the distribution function, which determine the stress tensor elements. Quasisteady configurations were calculated numerically for several sets of plasma parameters in some parts of the magnetotail. The force balance in the sheet was checked by calculating the longitudinal and transverse pressures as well as the elements of the full stress tensor. The stress tensor in the current sheet is found to be nondiagonal and to differ appreciably from the gyrotropic stress tensor in the Chew-Goldberger-Low model, although the Chew-Goldberger-Low theory and numerical calculations yield close results for large distances from the region of reversed magnetic field.     

Energy of Plasma Flows Accelerated in a Current Sheet as a Function of the Current Flowing through the Sheet

The energy of directed plasma flows accelerated in a current sheet is studied experimentally as a function of the current flowing through the sheet. It is found that the plasma flow energy rapidly increases with increasing current amplitude, nearly according to a power law with an exponent of 1.8–1.9. Using relations for the neutral current sheet and the concept of plasma acceleration under action of the Ampère forces, the energy of directed plasma flows is estimated as a function of the total current flowing through the sheet. It is shown that, as the current rises, the ion energy grows due to an increase in both the Ampère forces and the width of the current sheet within which plasma is accelerated.     

Electron-magnetohydrodynamic description of a steady-state current flow in a plasma with a three-dimensional localized density perturbation

The problem of a steady-state current flow through a localized density perturbation is analyzed in the framework of electron magnetohydrodynamics. It is examined how the degree of localization of such a flow depends on the plasma magnetization parameter and the geometric characteristics of the density perturbation. Corrections to the unperturbed current field are found by the iteration method. It is shown that the first-order correction to the current can be determined for an arbitrary perturbation. In the case of perfectly conducting plasma, the second-order correction can be found only for dipole perturbations, for which the integral change in the density is zero. In this case, the first-order correction to the current is localized, which makes possible the existence of the second-order correction. The finite plasma conductivity also assists current localization; therefore, for sufficiently small values of the plasma magnetization parameter, both first- and second-order steady-state corrections to the current can be obtained for any moderate plasma density perturbation.     

Dynamics of the structure of electric currents and electrodynamic forces in current sheets

Specific features of the spatial distributions of the electric current and electrodynamic forces in current sheets are examined by studying the magnetic fields in them. It is shown that the j × B forces should lead to a gradual increase in the kinetic energy of the plasma accelerated along the current sheet surface. Excitation of currents directed oppositely to the main current in the central part of the sheet is observed for the first time, and the time evolution of the forward and reverse currents is investigated. Generation of reversed currents is a manifestation of the dynamic effects caused by the motion of plasma flows in the magnetic field and leading to a change in the magnetic structure of the current sheet.     

Effect of the normal component of the magnetic field on the kink instability of the Earth’s magnetospheric current sheet

The kink instability of a thin anisotropic current sheet is analyzed. It is shown that, for highly anisotropic current sheets, the instability growth rate is larger than that previously obtained using the Harris isotropic sheet model. The calculated oscillation period is a few minutes. The results of calculations are compared to the observed oscillations of the magnetotail current sheet. The results obtained indicate that kink instability can significantly contribute to large-scale variations in the structure of the Earth’s magnetotail current sheet.     

On the nature of dark spots arising in a tokamak plasma during a disruption

The sudden appearance of bright and dark spots against the background lithium emission from the central regions of the plasma column was observed during major plasma disruptions in the T-11M tokamak with a lithium limiter. The measurements were performed with the help of an AXUV photodiode array operating in the energy range 1–5000 eV. Such spots in the plasma core arise in the fast transient stage of a major disruption (during the onset of the positive pulse of the plasma current) and are rather narrowly localized over r (in particular, over the vertical axis). It is supposed that the observed dark spots are related to the development of magnetic islands induced in the plasma core by an outer MHD perturbation. This effect can be used as a tool for studying specific forms of MHD resonance.     

Experimental studies of the magnetic structure and plasma dynamics in current sheets (a review)

Based on measurements of magnetic fields in current sheets, spatial distributions of the electric current and electrodynamic forces in successive stages of the sheet evolution are determined. Two new effects manifesting themselves mostly in the late stages of the current sheet evolution have been discovered, namely, expansion of the current flow region at the periphery of the sheet and the appearance of a region with inverse currents, which gradually expands from the periphery toward the center of the sheet. Using spectroscopic methods, generation of superthermal plasma flows accelerated along the sheet width from the center toward the periphery has been revealed and investigated. The measured energies of accelerated plasma ions satisfactorily agree with the Ampère forces determined from magnetic measurements. The excitation of inverse currents additionally confirms the motion of high-speed plasma flows from the center of the current sheet toward its side edges.     

Study of the structure and dynamics of current sheets in three-dimensional magnetic configurations with an X line by holographic interferometry

Results are presented from studies of the structure and dynamics of current sheets in three-dimensional magnetic configurations with an X line by means of holographic interferometry. It is found that the efficiency of plasma compression into the sheet is reduced as the longitudinal magnetic field B _z , directed along the X line, increases. This effect is attributed to the enhancement of the longitudinal component of the magnetic field within the sheet and to the corresponding increase in the magnetic pressure. It is shown that the formation of a plasma sheet lags behind the beginning of the plasma current pulse, the delay time being close to the characteristic Alfvén time.     

Study of Current Sheets in Three-Dimensional Magnetic Fields with an X-Line by Holographic Interferometry

Results are presented from experimental studies of the spatial electron density distribution in current sheets formed in three-dimensional magnetic configurations with X-lines. The electron density is measured by using two-exposure holographic interferometry. It is shown that plasma sheets can form in a magnetic configuration with an X-line in the presence of a sufficiently strong longitudinal magnetic-field component B_∥ when the electric current is excited along the X-line. As the longitudinal magnetic-field component increases, the electron density decreases and the plasma sheet thickness increases; i.e., the plasma is compressed into a sheet less efficiently.     

Triple splitting of a thin current sheet: A new type of plasma equilibrium

A hybrid numerical model of a one-dimensional current sheet in the Earth’s magnetotail is used to calculate a new self-consistent equilibrium state in the form of a triply split current sheet composed of three thin subsheets that are located close to each other and whose thickness is on the order of the ion gyroradius. The current in the central subsheet flows in the negative direction, opposite to the direction of the currents in the side subsheets. The magnetic field of the triply split current sheet has three neutral planes, in contrast to that of a classical bell-shaped current sheet with a single neutral plane at the sheet center. The particle dynamics in a triply split current configuration is analyzed. It is shown that, within the sheet, the current carriers—untrapped ions—move along meandering trajectories and can maintain an equilibrium structure self-consistently. It is found that a triply split current sheet is stable against external perturbations. The results obtained can help to explain complex dynamic processes occurring in the Earth’s magnetotail.     

Magnetic structure of current sheets in magnetic fields with a singular X line

Direct measurements of magnetic fields in a plasma show that current sheets can form in magnetic configurations with an X line in the presence of a longitudinal magnetic field. It is found that, in a plane perpendicular to the X line and to the direction of the main current, the current sheet has two very different dimensions. The tangential and normal components of the magnetic field and current density in the sheet are determined. The influence of the initial conditions (such as the strength of the longitudinal magnetic field, the gradient of the transverse field, and the plasma ion mass) on the current sheet parameters is investigated.     

MHD waveguides in space plasma

The waveguide properties of two characteristic formations in the Earth’s magnetotail—the plasma sheet and the current (neutral) sheet—are considered. The question of how the domains of existence of different types of MHD waveguide modes (fast and slow, body and surface) in the (k, ω) plane and their dispersion properties depend on the waveguide parameters is studied. Investigation of the dispersion relation in a number of particular (limiting) cases makes it possible to obtain a fairly complete qualitative pattern of all the branches of the dispersion curve. Accounting for the finite size of perturbations across the wave propagation direction reveals new additional effects such as a change in the critical waveguide frequencies, the excitation of longitudinal current at the boundaries of the sheets, and a change in the symmetry of the fundamental mode. Knowledge of the waveguide properties of the plasma and current sheets can explain the occurrence of preferred frequencies in the low-frequency fluctuation spectra in the magnetotail. In satellite observations, the type of waveguide mode can be determined from the spectral properties, as well as from the phase relationships between plasma oscillations and magnetic field oscillations that are presented in this paper.     

Plasma acceleration in current sheets formed in helium in two- and three-dimensional magnetic configurations

The processes of heating and acceleration of plasma in current sheets formed in 2D and 3D magnetic configurations with an X-line in helium plasma have been investigated using spectroscopic methods. It is found that, in 2D magnetic configurations, plasma flows with energies of 400?C1000 eV, which are substantially higher than the ion thermal energy, are generated and propagate along the width (the larger transverse dimension) of the sheet. In 3D configurations, the influence of the longitudinal (directed along the X-line) component of the magnetic field on the plasma parameters in the current sheet has been studied. It is shown that plasma acceleration caused by the Amp??re force can be spatially inhomogeneous in the direction perpendicular to the sheet surface, which should lead to sheared plasma flows in the sheet.     

Modeling of electron heating and the spatiotemporal evolution of emission in a current-sheet plasma

Results are presented from a detailed study of the behavior of the electron temperature during the evolution of a current sheet by comparing the data from spectral measurements with the spatiotemporal evolution of the emission intensities of the atomic and ionic lines of the working gas (He) and impurities (C, O) calculated in the collisional-radiative model. It is shown that the electron temperature in the center of the sheet attains a value of T _e =110±40 eV; under these conditions, taking into account metastable states affects the calculated results only slightly. The spatial profiles of the electron temperature and the plasma emission in the spectral lines of various atoms and ions across the plasma sheet are calculated as functions of time. It is shown that as the electron temperature grows most of the spectral lines of atoms and ions of the working gas and impurities are depleted in the center of the sheet and the emission region shifts toward the periphery of the sheet. The results obtained confirm the previous conclusion that, in this regime, a hot plasma is formed in the center of the sheet.