An Analytical Model for the Current Structure of the Magnetosheath Boundary in a Collisionless Plasma

Analytical Model of a Magnetopause in a Multicomponent Collisionless Plasma with a Kappa Energy Distribution of Particles

“…Other calculations of the currents and magnetic field, carried out on the basis of the analytical model developed for various combinations of plasma components, in particular, those typical for magnetopauses of planets, also show that the cases of the kappa distribution considered and the previously investigated Maxwellian distribution [13] for similar parameters of fractions correspond to significantly different structures, which is important for interpretation of observations. The resulting profiles vary within a wide range…”

“…Difficulties arise both due to the observed complex current density profiles, for example, nonmonotonic and having two or three humps or several different scales, and due to the measured substantially anisotropic and non-Maxwellian distribution functions of electrons and ions, which can have a comparable energy content. Attempts at an accurate analytical description of current sheets also lead to very particular models given, for example, in review [10] or in [11,12], including the model of the authors of [13], which, like most other models, assumes a Maxwellian distribution of particles by energy.…”

“…Since everywhere , the dependence is monotonic and reversible, making it possible to find in a parametric form an unambiguous solution to the problem of the equilibrium magnetopause. To obtain an analytical answer, it is only necessary to calculate integral (5) explicitly, which was done previously for the Maxwellian distribution of particles (see [13] and the literature cited there).…”

Force balance in current sheets in collisionless plasma

“…In Earth's magnetosphere, TCS constantly exists at the magnetopause and also forms in the near magnetotail during the growth phase of a magnetospheric substorm. An important feature of the latter as well as of most observed TCS is the existence of a normal magnetic field component, which makes them considerably different from sheets without the normal com-ponent [Speiser, 1965;Ashour-Abdalla et al, 1994;Zelenyi et al, 2011Zelenyi et al, , 2016, with a given set of stationary analytical solutions -Harris's solution [Harris, 1962] and others [Kocharovsky et al, 2016[Kocharovsky et al, , 2019.…”

“…Note that the development of numerical and approximate analytical models of stationary TCS with the normal magnetic field component has a long history, which is described in the reviews [Zelenyi et al, 2011[Zelenyi et al, , 2016 and in [Mingalev et al, 2018]. Analytical models represent protons in the quasi-adiabatic approximation [Kropotkin et al, 1995], and the most advanced models describe electrons in the so-called semi-fluid approximation (see, e.g., [Sitnov et al, 2000;Zelenyi et al, 2011]). The most advanced numerical models for protons use the particle-in-cell method to solve the stationary Vlasov equation and, as do analytical models, take into account the contribution of electrons in the semifluid approximation [Bykov et al, 2008[Bykov et al, , 2016.…”