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.     

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.     

Holographic interferometry study of two-fluid properties of the plasma in current sheets formed in heavy noble gases

Two-exposure holographic interferometry was used to study the structure of current sheets formed in three-dimensional magnetic configurations with a singular X line in heavy noble gases (Ar, Kr, and Xe). It is found that, in the presence of a longitudinal magnetic field B _Z directed along the X line, plasma sheets take on an unusual shape: they are titled and asymmetric. Their asymmetry becomes more pronounced as the mass of a plasma ion increases—a manifestation of the two-fluid properties of the plasma. The observed effects can be attributed to additional forces arising due to the interaction of the longitudinal magnetic field B _Z with Hall currents excited in a plane perpendicular to the X line. A qualitative model describing plasma dynamics with allowance for the Hall effect and accounting for most of the experimentally observed effects is proposed.     

Time evolution of the plasma spatial structure during the formation of a current sheet in argon according to holographic interferometry

The spatiotemporal dynamics of plasma sheets formed in argon plasma in two- and three-dimensional magnetic configurations with an X-type singular line was studied using holographic interferometry. An analogy is revealed between the development of plasma sheets and the time evolution of the current sheet structure, which was previously studied using magnetic measurements. In the late stage of the sheet evolution, a change in the rotation direction of plasma sheets formed in 3D magnetic configurations was observed. Apparently, this is caused by a change in the direction of the Hall currents at the side edges of the current sheet.     

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.     

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.     

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.     

Structure of Longitudinal and Transverse Currents in Current Sheets

The structure of magnetic fields and currents in current sheets formed in 2D and 3D magnetic configurations with an X line is analyzed using experimental data. It is found that, in addition to the main (longitudinal) current, transverse currents comparable in magnitude with the main current are also generated in current sheets. Relations between the longitudinal and transverse currents in current sheets formed in different magnetic configurations are obtained. The vectors of the total currents and their deviations from the direction of the main current in different regions of the sheet are determined. It is shown that the total magnetic fields and currents in current sheets have a 3D structure.     

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.     

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.     

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.     

Effect of the global topology of the interplanetary magnetic field on the properties of impulsive acceleration processes in distant regions of the Earth’s magnetospheric tail

The paper is devoted to a statistical study of high-speed ion beams (beamlets) observed by the Interball-1 and Interball-2 satellites in the boundary region of the plasma sheet of the geomagnetic tail and in the high-latitude auroral regions of the Earth’s magnetosphere. Beamlets result from nonlinear acceleration processes occurring in the current sheet in the distant regions of the geomagnetic tail. They propagate toward the Earth along the magnetic field lines and are detected in the boundary region of the plasma sheet and near the high-latitude boundary of the plasma sheet in the auroral region in the form of short (with a duration of 1–2 min) bursts of high-energy (with energies of about several tens of keV) ions. The sizes of the latitudinal zones where the beamlets are localized in the tail and in the auroral region are determined using the epoch superposition method. The relationship between the frequency of beamlet generation in the boundary region of the plasma sheet and the prehistory of the direction of the interplanetary magnetic field (the magnitude of a clock angle) is investigated. It was established that this direction exerts a global effect on the beamlet generation frequency; moreover, it was found that the beamlet generation frequency in the midnight local time sector of the tail and at the flanks depends differently on the direction of the interplanetary magnetic field. In the midnight sector, the beamlets are observed at almost all directions of the interplanetary field, whereas the frequency of their generation at the flanks is maximal only when the interplanetary magnetic field has a large y component.     

Spectroscopic measurements of the electron and ion temperatures and effective ion charge in current sheets formed in two- and three-dimensional magnetic configurations

The spatial distributions of the electron temperature and density, the effective and average ion charges, and the thermal and directed ion velocities in current sheets formed in two-dimensional magnetic fields and three-dimensional magnetic configurations with an X line were studied using spectroscopic and interference holographic methods. The main attention was paid to studying the time evolution of the intensities of spectral lines of the working-gas (argon) and impurity ions under different conditions. Using these data, the electron temperature was calculated with the help of an original mathematical code based on a collisional-radiative plasma model incorporating the processes of ionization and excitation, as well as MHD plasma flows generated in the stage of the current-sheet formation. It is shown that the electron temperature depends on the longitudinal magnetic field, whereas the ion temperature is independent of it. The effective ion charge of the current-sheet plasma was determined for the first time.     

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.     

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.     

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.     

Oscillations, shocks, and fine wave structures arising during the coalescence of two force-free current loops

Two-dimensional numerical simulations of the magnetic reconnection of two parallel force-free current loops are carried out using a high-resolution MHD code in which an artificial wind scheme is employed. Two typical cases (namely, co-helicity and counter-helicity reconnection) are investigated. The simulation results show that co-helicity reconnection involves only the reconnection of the poloidal component of the magnetic field, while counter-helicity reconnection involves the reconnection of both the poloidal and axial components of the magnetic field. Therefore, counter-helicity reconnection is much more complicated and violent as compared to co-helicity reconnection. In both cases, jetlike flows are generated. Counter-helicity reconnection is accompanied by oscillations of both the axial magnetic field and the axial component of the velocity. Due to these oscillations, quasi-steady models of a current sheet appear to be inapplicable, because the current sheet structure also changes. The complicated and unsteady structure of the current distribution shows that magnetic reconnection occurs not only in the central sheet between two loops in the earlier stage of the process, but also inside each loop in later stages. Rather complicated flows and waves with fine structures are also generated during reconnection. Some of the waves appear to be shock waves.     

Geometric properties of plasma equilibrium near a given magnetic surface

In order to describe plasma equilibrium near a given magnetic surface, it is sufficient to specify the shape of the surface, the distribution of the magnetic field strength on it, and two profile coefficients (the derivatives of the plasma pressure and current). Geometrically, this means that all the basis vectors of the flux coordinate system should be determined on the magnetic surface. Expressions for these vectors in an invariant basis are obtained. The maximum possible value of the pressure profile coefficient consistent with equilibrium is described by a universal geometric relationship that expresses the limiting value of the torsion of the magnetic field line on the magnetic surface as a function of the curvature of the surface. The relationships obtained are used to show that the stability of a system with closed magnetic field lines is governed by perturbations of the anti-Mercier type.     

Numerical integration of the equations of motion describing the acceleration of plasma particles in Syrovatski $$\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{l} $$ 's model of the dynamic current sheet

The acceleration of solar-wind protons in a current sheet in the Earth's magnetotail, in which the geomagnetic field lines reconnect, is investigated numerically using the dynamic current sheet model proposed by S.I. Syrovatski $\overset{\lower0.5em\hbox{$\overset{\lower0.5em\hbox{ . The dynamics of current sheets in the Earth's magnetotail is analyzed. In addition to the known solutions, the solution describing a contracting current sheet is derived. The time evolution of the magnetic field structure in Syrovatski $\overset{\lower0.5em\hbox{$\overset{\lower0.5em\hbox{ 's model is calculated numerically. The energy spectrum of the protons that are accelerated in the sheet by induction electric fields during rapid changes in the sheet topology is calculated and analyzed. A study is made of proton acceleration up to the time when the current sheet ruptures in the course of its evolution.