Axisymmetric gravitational MHD equilibria in the presence of plasma rotation

TL;DR

This paper develops a kinetic description of axisymmetric gravitational Hall-MHD equilibria in accretion disk plasmas near compact objects, focusing on the formulation of equilibrium distribution functions and constraints on fluid fields.

Contribution

It introduces a kinetic framework for gravitational Hall-MHD equilibria, providing explicit distribution functions and conditions for their existence in accretion disk environments.

Findings

Explicit superpositions of Maxwellian distributions for species.

Constraints on fluid fields for equilibrium existence.

Functional forms of densities and pressures derived.

Abstract

In this paper, extending the investigation developed in an earlier paper (Cremaschini et al., 2008), we pose the problem of the kinetic description of gravitational Hall-MHD equilibria which may arise in accretion disks (AD) plasmas close to compact objects. When intense EM and gravitational fields, generated by the central object, are present, a convenient approach can be achieved in the context of the Vlasov-Maxwell description. In this paper the investigation is focused primarily on the following two aspects: 1) the formulation of the kinetic treatment of G-Hall-MHD equilibria. Based on the identification of the relevant first integrals of motion, we show that an explicit representation can be given for the equilibrium kinetic distribution function. For each species this is represented as a superposition of suitable generalized Maxwellian distributions; 2) the determination of the constraints to be placed on the fluid fields for the existence of the kinetic equilibria. In particular, this permits a unique determination of the functional form of the species number densities and of the fluid partial pressures, in terms of suitably prescribed flux functions.