Computation of multi-region relaxed magnetohydrodynamic equilibria

TL;DR

This paper introduces a new computational approach for multi-region relaxed MHD equilibria, combining ideal MHD and Taylor relaxation, enabling well-posed 3D equilibrium calculations compatible with chaos theory.

Contribution

It develops the MRXMHD model and implements it in the SPEC code, providing a novel method for computing complex 3D MHD equilibria with convergence validation.

Findings

Successful discretization using mixed finite-element and Fourier methods

Convergence demonstrated with respect to resolution

Compatible with Hamiltonian chaos theory

Abstract

We describe the construction of stepped-pressure equilibria as extrema of a multi-region, relaxed magnetohydrodynamic (MHD) energy functional that combines elements of ideal MHD and Taylor relaxation, and which we call MRXMHD. The model is compatible with Hamiltonian chaos theory and allows the three-dimensional MHD equilibrium problem to be formulated in a well-posed manner suitable for computation. The energy-functional is discretized using a mixed finite-element, Fourier representation for the magnetic vector potential and the equilibrium geometry; and numerical solutions are constructed using the stepped-pressure equilibrium code, SPEC. Convergence studies with respect to radial and Fourier resolution are presented.