H. V. Malova

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.

Flattened current sheet and its evolution in substorms

In this research, the properties of a tail current sheet, which has a flattened geometry, and its evolution during substorm activity have been investigated. The geometrical configuration of the magnetic field and the spatial distribution of the current density in a flattened current sheet have been revealed with certainty for the first time. It is found that such a flattened current sheet has sufficiently strong B-y (GSM) within its neutral sheet that the magnetic field lines (MFLs) in the neutral sheet are lie almost in the GSM equatorial plane and that the normal directions are generally northward. Detailed analyses show that, the magnetic field lines are spiral-like, not plane curves, which are left-handed or right-handed spirals for B-y > 0 or B-y < 0. This magnetic rotation occurs predominantly in the neutral sheet. The flattened current sheet may be very thin, and the thickness of the neutral sheet is much less than the minimum radius of the curvature of the MFLs in the current sheet. The analysis also suggests that the neutral sheet current is field-aligned and lies mainly duskward. The curvature current makes little contribution to the total current in the flattened current sheet. The main current carriers in the neutral sheet of the flattened current sheet are electrons. A statistical survey shows that there is one positive correlation between B-y in the flattened current sheet and IMF B-y and penetration efficiency is 0.67. Flattened current sheets may occur in both quiet and disturbed periods and may appear at all phases of the substorms. During the growth phase of a substorm event, the neutral sheet of the flattened current sheet is shown to become progressively thinner, while the associated current density is increasing gradually. It is found that the northern turning of the IMF has triggered the explosive growth phase at the end of the growth phase, which lasts several minutes. At the explosive growth phase, the flattened current sheet becomes much thinner and the current density in the neutral sheet then increases considerably and reaches a value larger than 0.017 mu Am-2. Just after the onset of the substorm, the current density in the neutral sheet drops abruptly and varies turbulently.

Self-consistent structure of a thin anisotropic current sheet

An approximate solution of the system of Vlasov-Maxwell equations for a collisionless current sheet with strongly anisotropic ion species (the bulk velocity outside the sheet is much greater than the thermal one) and sharply curved magnetic field lines (the curvature radius is much less than the ion gyroradius) is obtained in the form of a universal function with two asymptotics and an iterative procedure in between. The magnetic field spatial scaling suggested by Francfort and Pellat [1976] is confirmed analytically.

Quasi-neutral sheet tearing instability induced by electron preferential acceleration from stochasticity

The role of tearing instability in substorm expansion onset is examined. From a consideration of observational constraints on the onset mechanism we conclude that this instability must have a considerable initial stage when the equilibrium magnetic field topology (without neutral lines) is still conserved. Moreover, this instability is shown to have no linear stage. Instead, either explicitly nonlinear or pseudolinear instability of negative energy eigenmodes can develop. The latter possibility may arise from electron preferential acceleration. This acceleration occurs for the electrons near the equilibrium chaos/adiabatic boundary that interact with the perturbation electric field and provide a means of dissipation to restore positive feedback for the instability development. We compute a set of single-particle orbits with realistic pitch angle distributions in a given tearing field model and evaluate statistical averages over the ensemble of particles and wave phases to verify the preferential acceleration of electrons. The resulting instability is analyzed by using a quasi-hydrodynamical multifluid model. Its amplitude can be less than that required for neutral line formation. It has a fast growth rate well within the timescales for substorm expansion onset. Its excitation leads to earthward acceleration of electrons and ions as well as local current amplification in the near-Earth region for excitation of cross-field current instability. In the theme of substorm as a low-dimension catastrophe for the current sheet, this nonlinear tearing instability approximates a fold catastrophe near the upper energy state of the system, while the unstable whistler waves from the cross-field current instability correspond to positive energy oscillations near a new lower-energy state of the current sheet achieved in the catastrophe. The nonlinear saturation of these whistler waves provides the irreversible relaxation of this state.

Kinetic models of two-dimensional plane and axially symmetric current sheets: Group theory approach

In this paper, we present new class of solutions of Grad-Shafranov-like (GS-like) equations, describing kinetic plane and axially symmetric 2D current sheets. We show that these equations admit symmetry groups only for Maxwellian and κ-distributions of charged particles. The admissible symmetry groups are used to reduce GS-like equations to ordinary differential equations for invariant solutions. We derive asymptotes of invariant solutions, while invariant solutions are found analytically for the κ-distribution with κ=7/2. We discuss the difference of obtained solutions from equilibria widely used in other studies. We show that κ regulates the decrease rate of plasma characteristics along the current sheet and determines the spatial distribution of magnetic field components. The presented class of plane and axially symmetric (disk-like) current sheets includes solutions with the inclined neutral plane.

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.

Role of Electrostatic Effects in Thin Current Sheets

Thin current sheets (TCSs) are sites of energy storage and release in the Earth’s magnetosphere. A self-consistent analytical model of 1D TCS is presented in which the tension of the magnetic field lines is balanced by ion inertia rather than plasma pressure. The influence of the electron population and the corresponding electrostatic electric fields required to maintain quasineutrality are taken into account under the realistic assumption that electron motion is fast enough to support quasi-equilibrium Boltzmann distribution along field lines. Electrostatic effects can lead to specific features of local current density profiles inside TCS, for example, to their partial splitting. The dependence of electrostatic effects on the electron temperature, the form of electron distribution function, and the curvature of magnetic field lines are analyzed. Possible implications of these effects on the fine structure of current sheets and some dynamic phenomena in the Earth’s magnetotail 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.

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.

A possible mechanism of the enhancement and maintenance of the shear magnetic field component in the current sheet of the Earth’s magnetotail

The influence of the shear magnetic field component, which is directed along the electric current in the current sheet (CS) of the Earth’s magnetotail and enhanced near the neutral plane of the CS, on the nonadiabatic dynamics of ions interacting with the CS is studied. The results of simulation of the nonadiabatic ion motion in the prescribed magnetic configuration similar to that observed in the magnetotail CS by the CLUSTER spacecraft demonstrated that, in the presence of some initial shear magnetic field, the north-south asymmetry in the ion reflection/refraction in the CS is observed. This asymmetry leads to the formation of an additional current system formed by the oppositely directed electric currents flowing in the northern and southern parts of the plasma sheet in the planes tangential to the CS plane and in the direction perpendicular to the direction of the electric current in the CS. The formation of this current system perhaps is responsible for the enhancement and further maintenance of the shear magnetic field near the neutral plane of the CS. The CS structure and ion dynamics observed in 17 intervals of the CS crossings by the CLUSTER spacecraft is analyzed. In these intervals, the shear magnetic field was increased near the neutral plane of the CS, so that the bell-shaped spatial distribution of this field across the CS plane was observed. The results of the present analysis confirm the suggested scenario of the enhancement of the shear magnetic field near the neutral plane of the CS due to the peculiarities of the nonadiabatic ion dynamics.