Computation of Magnetohydrodynamic Equilibria with Voigt Regularization

TL;DR

This paper introduces Voigt regularization as a novel numerical method for computing magnetohydrodynamic equilibria, enabling magnetic reconnection and island formation without assuming nested flux surfaces, and demonstrating improved convergence in resistive MHD problems.

Contribution

It is the first to apply Voigt regularization to MHD equilibrium computation, allowing for magnetic reconnection and chaos, and improving convergence in resistive MHD simulations.

Findings

Voigt regularization accelerates convergence in resistive MHD problems.

The method allows magnetic reconnection and island formation.

Challenges remain in applying to ideal MHD systems.

Abstract

This work presents the first numerical investigation of using Voigt regularization as a method for obtaining magnetohydrodynamic (MHD) equilibria without the assumption of nested magnetic flux surfaces. Voigt regularization modifies the MHD dynamics by introducing additional terms that vanish in the infinite-time limit, allowing for magnetic reconnection and the formation of magnetic islands, which can overlap and produce field-line chaos. The utility of this approach is demonstrated through numerical solutions of two-dimensional ideal and resistive test problems. Our results show that Voigt regularization can significantly accelerate the convergence to solutions in resistive MHD problems, while also highlighting challenges in applying the method to ideal MHD systems. This research opens up new possibilities for developing more efficient and robust MHD equilibrium solvers, which could contribute to the design and optimization of future fusion devices.