Symmetries, conservation laws and exact solutions of static plasma equilibrium systems in three dimensions

TL;DR

This paper classifies symmetries and conservation laws of static plasma equilibrium models in three dimensions, revealing differences between isotropic and anisotropic cases and providing methods to generate new solutions.

Contribution

It offers a complete symmetry and conservation law classification for static plasma models, and introduces a transformation linking isotropic and anisotropic equations to construct solutions.

Findings

Isotropic equations have finite-dimensional symmetry algebra.

Anisotropic equations admit infinite symmetries depending on free functions.

New exact anisotropic solutions are constructed from classical equations.

Abstract

For static reductions of isotropic and anisotropic Magnetohydrodynamics plasma equilibrium models, a complete classification of admitted point symmetries and conservation laws up to first order is presented. It is shown that the symmetry algebra for the isotropic equations is finite-dimensional, whereas anisotropic equations admit infinite symmetries depending on a free function defined on the set of magnetic surfaces. A direct transformation is established between isotropic and anisotropic equations, which provides an efficient way of constructing new exact anisotropic solutions. In particular, axially and helically symmetric anisotropic plasma equilibria arise from classical Grad-Shafranov and JFKO equations.