Kinetic construction of the high-beta anisotropic-pressure equilibrium in the magnetosphere

TL;DR

This paper develops a theoretical model for high-beta anisotropic-pressure equilibrium in the magnetosphere by linking the Grad-Shafranov and Vlasov equations, and validates it with numerical solutions matching laboratory data.

Contribution

It introduces a novel kinetic construction method for magnetospheric equilibrium considering anisotropic pressure and entropy-maximizing distribution functions.

Findings

Numerical solutions align with RT-1 laboratory magnetosphere data.

The pressure tensor depends on magnetic field and flux function.

The model provides a consistent framework for high-beta plasma equilibrium.

Abstract

A theoretical model of the high-beta equilibrium of magnetospheric plasma was constructed by consistently connecting the (anisotropic pressure) Grad-Shafranov equation and the Vlasov equation. The Grad-Shafranov equation was used to determine the axisymmetric magnetic field for a given magnetization current corresponding to a pressure tensor. Given a magnetic field, we determine the distribution function as a specific equilibrium solution of the Vlasov equation, using which we obtain the pressure tensor. We need to find an appropriate class of distribution function for these two equations to be satisfied simultaneously. Here, we consider the distribution function that maximizes the entropy on the submanifold specified by the magnetic moment. This is equivalent to the reduction of the canonical Poisson bracket to the noncanonical one having the Casimir corresponding to the magnetic moment. The pressure tensor then becomes a function of the magnetic field (through the cyclotron frequency) and flux function, satisfying the requirement of the Grad-Shafranov equation. Numerical solutions have been obtained to interpret the experimental data of the RT-1 laboratory magnetosphere.