Potential Vorticity Formulation of Compressible Magnetohydrodynamics

TL;DR

This paper reformulates compressible ideal magnetohydrodynamics using potential vorticity and magnetic flux per unit mass, simplifying analytic solutions and aiding modeling of laboratory and astrophysical plasmas.

Contribution

It introduces a potential vorticity formulation of compressible MHD using Lie brackets, offering a new approach to simplify analysis and modeling.

Findings

Simplifies analytic solutions in key MHD scenarios

Highlights implications for plasma modeling

Provides a new formulation framework

Abstract

Compressible ideal magnetohydrodynamics (MHD) is formulated in terms of the time evolution of potential vorticity and magnetic flux per unit mass using a compact Lie bracket notation. It is demonstrated that this simplifies analytic solution in at least one very important situation relevant to magnetic fusion experiments. Potentially important implications for analytic and numerical modelling of both laboratory and astrophysical plasmas are also discussed.