Symmetry transformations for magnetohydrodynamics and Chew-Goldberger-Low equilibria revisited

TL;DR

This paper revisits symmetry transformations in magnetohydrodynamics and Chew-Goldberger-Low equilibria, revealing conditions under which geometrical symmetries can be broken or preserved, especially in purely poloidal magnetic fields.

Contribution

It generalizes existing symmetry transformations to anisotropic pressure CGL equilibria and clarifies when these transformations can alter geometrical symmetries.

Findings

Symmetry transformations can break geometrical symmetry only with purely poloidal magnetic fields.

Derived 3D CGL equilibria from axisymmetric ones under certain conditions.

Generic symmetry transformations do not break symmetries unless velocity and magnetic fields are collinear and purely poloidal.

Abstract

Being motivated by the paper [O. I. Bogoyavlenskij, Phys. Rev. 66, 056410 (2002)] we generalise the symmetry transformations for MHD equilibria with isotropic pressure and incompressible flow parallel to the magnetic field introduced therein in the case of respective CGL equilibria with anisotropic pressure. We find that the geometrical symmetry of the field-aligned equilibria can break by those transformations only when the magnetic field is purely poloidal. In this situation we derive three-dimensional CGL equilibria from given axisymmetric ones. Also, we examine the generic symmetry transformations for MHD and CGL equilibria with incompressible flow of arbitrary direction, introduced in a number of papers, and find that they cannot break the geometrical symmetries of the original equilibria, unless the velocity and magnetic field are collinear and purely poloidal.