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.     

Distributions of the ion temperature,ion pressure,and electron density over the current sheet surface

The distributions of the ion temperature, ion pressure, and electron density over the width (the major transverse dimension) of the current sheet have been studied for the first time. The current sheets were formed in discharges in argon and helium in 2D and 3D magnetic configurations. It is found that the temperature of argon ions in both 2D and 3D magnetic configurations is almost uniform over the sheet width and that argon ions are accelerated by the Ampère force. In contrast, the distributions of the electron density and the temperature of helium ions are found to be substantially nonuniform. As a result, in the 2D magnetic configuration, the ion pressure gradient across the sheet width makes a significant contribution (comparable with the Ampère force) to the acceleration of helium ions, whereas in the 3D magnetic configuration, the Ampère force is counterbalanced by the pressure gradient.     

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.     

Kinetic theory of the positive column of a low-pressure discharge in a transverse magnetic field

The influence of a transverse magnetic field on the characteristics of the positive column of a planar low-pressure discharge is studied theoretically. The motion of magnetized electrons is described in the framework of a continuous-medium model, while the ion motion in the ambipolar electric field is described by means of a kinetic equation. Using mathematical transformations, the problem is reduced to a secondorder ordinary differential equation, from which the spatial distribution of the potential is found in an analytic form. The spatial distributions of the plasma density, mean plasma velocity, and electric potential are calculated, the ion velocity distribution function at the plasma boundary is found, and the electron energy as a function of the magnetic field is determined. It is shown that, as the magnetic field rises, the electron energy increases, the distributions of the plasma density and mean plasma velocity become asymmetric, the maximum of the plasma density is displaced in the direction of the Ampère force, and the ion flux in this direction becomes substantially larger than the counter-directed ion flux.     

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.     

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.     

Adiabatic Heating of Electrons in the Magnetospheric Current Sheet

Electron dynamics and acceleration in an electromagnetic field configuration modeling the current sheet configuration of the Earth’s magnetotail region is investigated. A focus is made on the role of the dawn?dusk magnetic field component B_y in the convection electron heating by an electric field E_y. For numerical integration of a large number of test particle trajectories over long time intervals, the equations of motion written in the guiding center approximation are used. It is shown that the presence of a B_y ≠ 0 magnetic field significantly changes the electron heating and allows electrons with small pitch angles to gain energy much more efficiently than the equatorial electrons. As a result, the convection heating in the current sheet with B_y ≠ 0 leads to the formation of an accelerated anisotropic population of particles with energies higher than a few hundred electronvolts. The obtained results and spacecraft observations in the Earth’s magnetotail are compared, and possible limitations in the proposed model approaches are discussed.     

Suprathermal plasma flows in current sheets formed in two- and three-dimensional magnetic configurations

Dynamics of the thermal and directed motions of argon plasma ions in current sheets formed in various magnetic configurations was investigated experimentally Measurements in three-dimensional magnetic configurations with an X line were carried out for the first time. The results of these measurements were compared with the data obtained in experiments with two-dimensional magnetic configurations. The ion temperature and the energies and velocities of directed plasma flows within the current sheet were determined by analyzing the shapes of argon ion spectral lines broadened due to the Doppler effect. It is found that, under the given experimental conditions, the axial magnetic field does not affect the ion temperature and plasma acceleration in the sheet.     

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.     

On the mechanism of the formation of magnetohydrodynamic vortices in the solar plasma

Based on the magnetohydrodynamic (MHD) equations for an incompressible conductive viscous fluid, the possible mechanism of the formation of giant MHD vortices recently discovered in the solar atmosphere (chromosphere) is analyzed. It is assumed that these vortices arise in the regions of the solar surface (photosphere) with ascending flows of hot plasma that arrives from the inner regions of the Sun as a result of thermal convection and is accelerated upward under the action of the chromospheric plasma pressure gradient. It is shown that, under the assumption of plasma incompressibility and flow continuity, the ascending plasma flows induce converging radial plasma flows, which create the convective and Coriolis nonlinear hydrodynamic forces due to the nonzero initial vorticity of the chromospheric plasma caused by Sun’s rotation. The combined action of these two forces leads to the exponential acceleration of the solid-body rotation of plasma inside the ascending flow, thereby creating a vortex that generates an axial magnetic field, in agreement with astrophysical observations.     

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.     

System of Kinetic Equations for Collisionless Space Plasma in the Approximation of Field-Aligned Force Equilibrium for Electrons

A system of kinetic equations describing relatively slow large-scale processes in collisionless magnetoplasma structures with a spatial resolution on the order of the proton thermal gyroradius is derived. The system correctly takes into account the electrostatic effects in the approximation of field-aligned force equilibrium for electrons. The plasma is considered quasineutral, and the magnetic field is described by the Ampère equation. The longitudinal component of the electric field is found explicitly from the equality of the field-aligned component of the electric force acting on plasma electrons and the divergence of the electron pressure tensor. The electric field component orthogonal to the magnetic field is determined by the distributions of the number densities, current densities, and stress tensors of all plasma species in the instantaneous long-range approximation described by a system of time-independent elliptic equations. Versions of the system of equations adapted to the case of magnetized electrons described by the Vlasov equation in the drift approximation, as well as to the case in which all plasma species are magnetized, are derived. The resulting systems of equations allow creating numerical models capable of describing large-scale processes in nonuniform collisionless space plasma.     

Model of Solar Wind in the Heliosphere at Low and High Latitudes

The spatial distributions of the magnetic field, plasma density, and current at distances of (20–400)R_S from the Sun (where R_S is the solar radius) are investigated within a stationary axisymmetric MHD model of the solar wind (SW) at all latitudes in the inertial frame of reference with the origin at the center of the Sun. The model takes into account differential (with respect to the heliolatitude) rotation of the Sun and full corotation of plasma inside a boundary sphere of radius 20RS, which breaks down beyond this sphere. Self-consistent distributions of the plasma density, current, and magnetic field in the SW are obtained by numerically solving a set of time-independent MHD equations in spherical coordinates. It is demonstrated that the calculated results do not contradict observational data and describe a gradual transition from the fast SW at high heliolatitudes to the slow SW at low heliolatitudes, as well as the steepening of the profiles of the main SW characteristics with increasing distance from the Sun. The obtained dependences extend understanding of the SW structure at low and high latitudes and agree with the well-known Parker model in the limit of a small Ampère force.     

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.     

Three-dimensional MHD simulations of forced magnetic reconnection

Results are presented from MHD simulations of three-dimensional flows of a high-conductivity plasma in the vicinity of a null point of a magnetic field. The excitation of an electric current at the boundary of the computation region results in self-consistent plasma flows and change in the structure of the magnetic field. Generally, in the vicinity of a null point, an MHD singularity arises that manifests itself in the formation of locally plane current sheets. It is shown that the current sheet can be oriented either along the separatrix surface of a magnetic configuration or perpendicular to it, except for axisymmetric configurations (or close to them), when the excitation of an electric current in the direction orthogonal to the separatrix surface does not lead to the formation of a current sheet.     

Generation and interaction of intense counterpropagating plasma flows

Results are presented from experimental studies of the parameters of two counterpropagating (colliding) plasma flows generated by discharges in crossed electric and magnetic fields. It is shown that the conversion efficiency of the energy deposited in the discharges into the energy of directed plasma flows is 0.3–0.6. For discharge current pulses with a duration of ∼10 μs, the energy flux density in the plasma flow reaches ∼10 J/cm² and the total energy of the flow is on the order of 300 J. The density of deuterons in the flows is ∼10¹⁵ cm⁻³, and the flow velocity is ≤2×10⁷ cm/s. The total number of particles carried by the flows is about 10¹⁹. The possibility of using counterpropagating plasma flows to study reactions involving light nuclei (dd, pd, dt, and dHe reactions) in the range of ultralow collision energies is discussed. __________ Translated from Fizika Plazmy, Vol. 29, No. 8, 2003, pp. 714–721. Original Russian Text Copyright ? 2003 by Dudkin, Nechaev, Padalko, Bystritsky, Stolupin, Bystritskii, Voznyak.     

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.     

Dark Current and Photocurrent in Retinal Rods

The interstitial voltages, currents, and resistances of the receptor layer of the isolated rat retina have been investigated with arrays of micropipette electrodes inserted under direct visual observation by infrared microscopy. In darkness a steady current flows inward through the plasma membrane of the rod outer segments. It is balanced by equal outward current distributed along the remainder of each rod. Flashes of light produce a photocurrent which transiently reduces the dark current with a waveform resembling the PII and a-wave components of the electroretinogram. The photocurrent is produced by a local action of light within 12 μm of its point of absorption in the outer segments. The quantum current gain of the photocurrent is greater than 10⁶. The electrical space constant of rat rods is greater than 25 μm, so that the electrical effects of the photocurrent are large enough at the rod synapses to permit single absorbed photons to be detected by the visual system. The photocurrent is apparently the primary sensory consequence of light absorption by rhodopsin.