The Infinite Interface Limit of Multiple-Region Relaxed MHD

TL;DR

This paper demonstrates that as the number of regions in multi-region relaxed MHD approaches infinity, the model converges to ideal MHD, bridging the gap between relaxed and ideal plasma equilibrium theories.

Contribution

It proves the theoretical limit of multi-region relaxed MHD converging to ideal MHD and provides numerical evidence for this transition.

Findings

MRXMHD reduces to ideal MHD as regions become infinite

Numerical convergence confirms the theoretical limit

Generalizes the connection between relaxed and ideal MHD

Abstract

We show the stepped-pressure equilibria that are obtained from a generalization of Taylor relaxation known as multi-region, relaxed MHD (MRXMHD) are also generalizations of ideal MHD. We show this by proving that as the number of plasma regions becomes infinite, MRXMHD reduces to ideal MHD. Numerical convergence studies demonstrating this limit are presented.