Analytical theory of self-consistent current structures in a collisionless plasma

Abstract

The most-studied classes of exact solutions to Vlasov–Maxwell equations for stationary neutral current structures in a collisionless relativistic plasma, which allow the particle distribution functions (PDFs) to be chosen at will, are reviewed. A general classification is presented of the current sheets and filaments described by the method of invariants of motion of particles whose PDF is symmetric in a certain way in coordinate and momentum spaces. The possibility is discussed of using these explicit solutions to model the observed and/or expected features of current structures in cosmic and laboratory plasmas. Also addressed are how the magnetic field forms and the analytical description of the so-called Weibel instability in a plasma with an arbitrary PDF.

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

“…Until recently, an analysis of the general picture of the observed phenomena was absent, since it was carried out mainly by narrowly specialized numerical or approximate analytical methods (references to them can be found in [7,9,10]). 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.…”

“…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.…”

Collisionless current sheet equilibria

“…We will only discuss non-relativistic cases (for examples of relativistic treatments see e.g. [4]). We shall also assume that the plasma systems we discuss are quasi-neutral (i.e.…”

“…VM equilibrium theory has a long history (see the discussion and references in, for example [2][3][4]) and is, of course, not restricted to Cartesian geometry (see e.g. [3] for some references, but also e.g.…”

“…[5,6]), to spatial variations in just one direction (see e.g. [2,4,[7][8][9][10][11][12][13]) or to systems that are not charge-neutral (e.g. [14]).…”