Model of a Thin Current Sheet in the Earth’s Magnetotail with a Kinetic Description of Magnetized Electrons

Steady-state two-dimensional thin current sheets (TCSs) in collisionless space plasma, similar to the current sheet of the near-Earth magnetotail, are considered. The magnetic field of the sheet is orthogonal to the current and has a nonzero normal component, the electrons are magnetized, and the ions are unmagnetized. To solve the problem of kinetic description of electrons in such current sheets in a general form, they are described by the Vlasov equation in the drift approximation, the general solution to which is found in the form of a function of three independent integrals of the system of drift motion equations. An important case is considered in which the electron guiding centers obey a Maxwell–Boltzmann distribution in a stationary electromagnetic field. The obtained results make it possible to create one- and two-dimensional numerical− analytical models of current sheets in which unmagnetized ions are described by the Vlasov equation, which should be solved numerically, whereas the contribution of magnetized electrons is taken into account analytically. To numerically solve the time-independent Vlasov equation, a new method is proposed that allows one to perform the bulk of computations by using graphic processors. On the basis of the new theory, a one-dimensional numerical−analytical model of a steady-state TCS in the near-Earth magnetotail is presented, TCS configurations are calculated, and the role of electrostatic effects and electron pressure anisotropy is analyzed.