V. Yu. Popov

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.

Splitting of thin current sheets in the Earth’s magnetosphere

An analytic model of a one-dimensional self-consistent anisotropic thin current sheet is proposed. This model describes the sheet with a split (or bifurcated) structure, where the current density is minimal at the center and maximal at the edges. The model is specified by the set of Vlasov-Maxwell equations that reduces to the Grad-Shafranov equation. Under the assumption that particles move quasi-adiabatically, i.e., that the approximate integral of motion Iz is conserved, the slow evolution of the system in the course of diffusion of the distribution function in Iz is analyzed. Scattering processes can give rise to the partial capture of flying ions near the current sheet. Since the current of such quasi-trapped particles is directed oppositely to the current of flying particles, the local current at the center of the sheet is fully or partially compensated. As a result, the ordinary single-peak shape of the current density profile changes to the bifurcated shape. Such a structure is characteristic of the thin current sheet before the total destruction, when the tension of the magnetic field is unbalanced. Numerical calculations are corroborated by the observations of split current sheets in the magnetotail by the Cluster and Geotail satellites. The obtained results indicate that a possible mechanism of the destruction of the thin current sheet is not necessarily associated with the development of plasma instabilities but can be evolutionary.

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 (Bz) in the sheet is almost constant, while the tangential (Bx) and shear (By) components depend on the transverse coordinate z. The current density in the sheet also has two self-consistent components (jx and jy, 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 By and, accordingly, two thin current sheet configurations can exist for the same input parameters. For the mode with an antisymmetric z profile of the By component, the magnetic field lines within the sheet are twisted, whereas the profiles of the plasma density, current density component jy, and magnetic field component Bx differ slightly from those in the case of a shearless magnetic field (By = 0). For the symmetric By 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.

Forced current sheets in the Earth's magnetotail: Their role and evolution due to nonadiabatic particle scattering

Abstract Current sheets in the Earths magnetosphere may be considered as the regions of the acceleration and heating of solar wind and ionospheric plasmas. We devote our attention to the formation of very thin current sheets (TCSs) in the magnetotail. Various models of TCS equilibrium are discussed. We extend our previous self-consistent analysis of TCS formation. We delineate the relative role of two types of ion populations: (1) current- carrying Speisers ions, impinging from the mantle, (2) nonadiabatic ions resulting from chaotic scattering of ions on transient Speiser-type orbits. To take into account the effect of population (2) we use the centrifugal impulse model, which treats the scattering of the particle magnetic moments as the result of perturbation of the gyromotion by an impulsive centrifugal force. Using several “snapshots” of the scattered distribution function, we obtain a series of quasi-stationary TCS equilibria. It is shown that nonadiabatic effects do not influence significantly the TCS thickness but generally alter the structure of the “young” Speiser-orbit based current sheet, “polluting” the sheet by particles with large magnetic moments, which suppress the positive current in the center of the sheet. In other words, TCS are “aging” due to scattering. When the quasi-trapped population becomes too abundant, the equilibrium solutions decay. The characteristic lifetime of such TCS due to intrinsic nonadiabaticity of the system is found to be about 10–60 minutes.

Influence of Trapped Plasma on the Structure of Collisionless Thin Current Sheets

Using both analytical and numerical models of the collisionless anisotropic current sheet generated by the impinging flows of transient ions, we have studied the self-consistent solutions taking the plasma trapped in the sheet into account. It is demonstrated that there exists a limited “window” in the space of system parameters where self-consistent solutions can exist. When the density of the quasi-trapped plasma is sufficiently large, a redistribution of the total current can be a cause of the sheet decay, when the local current of the trapped particles compensate (totally or in part) the main current in the center and at the edges of the sheet, while the total current generated by ions on the trapped trajectories vanishes.

Imprints of Quasi‐Adiabatic Ion Dynamics on the Current Sheet Structures Observed in the Martian Magnetotail by MAVEN

Numerous studies of the Current Sheets (CS) in the Earth magnetotail showed that quasi-adiabatic ion dynamics plays an important role in formation of complicated multilayered current structures. In order to check whether the similar mechanisms operate in the Martian magnetotail we analyzed 80 CS crossings using MAVEN measurements on the nightside of Mars at radial distances ~1.0–2.8RM. We found that CS structures experience the similar dependence on the value of the normal component of the magnetic field at the neutral plane (BN) and on the ratio of the ion drift velocity outside the CS to the thermal velocity (VT/VD) as it was observed for the CSs in the Earth’s magnetotail. For the small values of BN a thin and intense CS embedded in a thicker one is observed. The half-thickness of this layer is L~30–100km ≤ ρH+ (ρH+ is a gyroradius of thermal protons outside the CS). With the increase of BN the L also increases up to several hundred km (~ρO+, ρO2+), the current density decreases and the embedding feature disappears. Our statistical analysis showed a good agreement between L values observed by MAVEN and the CS scaling obtained from the quasi-adiabatic model, if the plasma characteristics in Martian CSs are used as input parameters. Thus, we may conclude that, in spite of the differences in magnetic topology, ion composition and plasma thermal characteristics observed in the Earth’s and Martian magnetotails, similar quasi-adiabatic mechanisms contribute to the formation of the CSs in the magnetotails of both planets.

Current Sheet in a non-Maxwellian collisionless plasma: Self-consistent theory, simulation, and comparison with spacecraft observations

A self-consistent theory is constructed of anisotropic current equilibria maintained in a non-Maxwellian plasma consisting of cold electrons and two hot ion components of different temperatures. The ion plasma components are described in the quasi-adiabatic approximation, and the plasma electrons, in the MHD approximation. Approximate steady solutions to the set of Vlasov-Maxwell equations are obtained and investigated parametrically. It is shown that the solutions can describe various current sheet profiles: from thin current structures with a maximum current density in the neutral sheet to comparatively “thick” current sheets with two to three maxima of the current density. It is also shown that the electron plasma component predominates at the current sheet center and can maintain a narrow central peak in the current density. The ion plasma component predominates at the edge of the current sheet, thereby determining the characteristic sheet thickness. The results of numerical simulations of a two-temperature plasma by the macroparticle method are compared with the experimental data from the Cluster spacecraft. Good agreement between the theoretical, numerical, and experimental results leads to the conclusion that the theory developed here provides a fairly adequate description of collisionless current sheets in space plasmas.

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.

Evolution of ion distribution functions during the “aging” process of thin current sheets

Abstract This paper is devoted to the analysis of ion distributions in the velocity space {vx, vy} of the self-consistent thin current sheets (TCSs) due to the influence of nonadiabatic effects. In the frame of 1D-model it is shown that nonadiabatic jumps of the approximate integral of motion Iz may lead to the trapping of the particle in the vicinity of the sheet and influence significantly the structure of newly formed current sheets supported by ions at Speiser orbits. The part of the Speiser population is diffusing into the quasi-trapped domain, where ions have so called “cucumber” orbits. The scattering process results in the appearance of ions with large magnetic moments, which may reduce the current in the center of the sheet. We consider this process as deterioration, or “aging”, that might finally lead to TCS disruption. In the course of TCS “aging”, ion distribution functions experience characteristic evolution, which we are analyzing in this paper. The plots of velocity distribution functions corresponding to three characteristic moments of TCS “aging” are presented: 1) “young” sheet with only Speiser ions; 2) “deteriorated” TCS with the scattered quasi-trapped population; 3) “old” TCS before the very moment of destruction when the population of quasi-trapped plasma is very abundant. It is shown that quasi-trapped population occupies the well-defined domains in the phase space which could be identified by the in situ measurements of ion distribution function in the vicinity of the field reversal and may indicate the stage of the temporal TCS dynamical evolution.

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.