Kinetic axi-symmetric gravitational equilibria in collisionless accretion disc plasmas

TL;DR

This paper develops a theoretical framework for collisionless, axi-symmetric plasma equilibria in accretion disks, revealing a potential kinetic dynamo effect that can generate magnetic fields without radial accretion flows.

Contribution

It introduces a new class of kinetic equilibria with temperature anisotropy and differential rotation, and proposes the kinetic dynamo effect as a mechanism for magnetic field generation.

Findings

Existence of generalized bi-Maxwellian equilibria with toroidal rotation.

Potential for self-sustaining magnetic fields via kinetic effects.

Conditions and properties of these equilibria are detailed.

Abstract

A theoretical treatment is presented of kinetic equilibria in accretion discs around compact objects, for cases where the plasma can be considered as collisionless. The plasma is assumed to be axi-symmetric and to be acted on by gravitational and electromagnetic fields; in this paper, the particular case is considered where the magnetic field admits a family of toroidal magnetic surfaces, which are locally mutually-nested and closed. It is pointed out that there exist asymptotic kinetic equilibria represented by generalized bi-Maxwellian distribution functions and characterized by primarily toroidal differential rotation and temperature anisotropy. It is conjectured that kinetic equilibria of this type can exist which are able to sustain both toroidal and poloidal electric current densities, the latter being produced via finite Larmor-radius effects associated with the temperature anisotropy. This leads to the possibility of existence of a new kinetic effect - referred to here as a \textquotedblleft kinetic dynamo effect\textquotedblright\ - resulting in the self-generation of toroidal magnetic field even by a stationary plasma, without any net radial accretion flow being required. The conditions for these equilibria to occur, their basic theoretical features and their physical properties are all discussed in detail.