Near-ideal relaxed MHD in slab geometry

TL;DR

This paper presents the first numerical solutions of the relaxed MHD model (RxMHD) in slab geometry, demonstrating its mathematical well-definedness, computational feasibility, and the natural emergence of cross-field flows and self-organized relaxed regions.

Contribution

It introduces the first numerical implementation of the RxMHD model, extending the understanding of MHD equilibria with ideal constraints in slab geometry.

Findings

RxMHD solutions are mathematically well-defined.

Cross-field flows can exist without angular momentum constraints.

Self-organization of relaxed regions is observed during optimization.

Abstract

We investigate the solutions of the relaxed MHD model (RxMHD) of Dewar \& Qu [J. Plasma Phys. {\bf 88}, 835880101 (2022)]. This model generalizes Taylor relaxation by including the ideal Ohm's law constraint using an augmented Lagrangian method, providing a pathway to extend the multi-region relaxed MHD (MRxMHD) model. We present the first numerical solution of the RxMHD model by Dewar \& Qu, demonstrating that it is mathematically well-defined and computationally feasible for constructing MHD equilibria in slab geometry. We also show that a cross-field flow can exist without enforcing an arbitrary constraint on the angular momentum, as is done in the case of MRxMHD with flow. Our results also demonstrate the self-organization of fully relaxed regions during the optimization, which was an important motivation behind developing this model.