Kinetic axisymmetric gravitational equilibria in collisionless accretion disk plasmas

Abstract

A theoretical treatment is presented of kinetic equilibria in accretion disks ͑AD͒ around compact objects, for cases where the plasma can be considered as collisionless. The plasma is assumed to be axisymmetric 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 "kinetic dynamo effect"-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.

Kinetic description of quasi-stationary axisymmetric collisionless accretion disk plasmas with arbitrary magnetic field configurations

“…Requirements 1) -7) clearly imply that the solution cannot generally be a Maxwellian. However, in analogy with Paper I, it is possible to show that they can be fulfilled by a suitable modified bi-Maxwellian expressed solely in terms of first integrals of motion and adiabatic invariants [6,10,39]. It follows that this is necessarily a QSA-KDF.…”

“…(6). In terms of the hybrid variables z ≡ (x,v) (with x and v denoting respectively the particle position and velocity vectors), this is expressed as…”

“…[6], hereafter referred to as Paper I), we presented preliminary results in this direction, concerning formulation of kinetic theory for investigating stationary solutions for collisionless AD plasmas, focusing on configurations with locally-closed magnetic flux surfaces. The present paper is intended as a continuation of the previous one, with the aim of generalizing the previous solution to arbitrary magnetic field configurations, which are no longer restricted to localized spatial domains in the disk.…”

“…Kinetic theory is essential for studying both stationary configurations and dynamical evolution of plasmas when kinetic effects are relevant, such as ones associated with conservation of particle adiabatic invariants, temperature anisotropy, finite Larmor-radius (FLR) effects (as pointed out in Ref. [6]) and kinetic trapping phenomena. These properties are relevant for magnetized plasmas and in particular for those arising in ADs [7][8][9] whenever the plasma is regarded as collisionless or weakly collisional [6,10].…”

“…[6]) and kinetic trapping phenomena. These properties are relevant for magnetized plasmas and in particular for those arising in ADs [7][8][9] whenever the plasma is regarded as collisionless or weakly collisional [6,10].…”