Numerical solutions of resistive finite-pressure magnetohydrodynamic equilibria for non-axisymmetric toroidal plasmas

TL;DR

This paper introduces a hybrid spectral/finite-element numerical code that efficiently computes resistive finite-pressure MHD equilibria in complex, non-axisymmetric toroidal plasma configurations without assuming nested flux surfaces.

Contribution

It presents a novel computational approach combining hyperbolic pressure updating and resistive magnetic relaxation, applicable to diverse three-dimensional toroidal plasma systems.

Findings

Successfully applied to stellarators, tokamaks, and RFPs.

Accurately captures non-axisymmetric equilibria.

Demonstrates flexibility in complex geometries.

Abstract

A hybrid spectral/finite-element code is developed to numerically solve the resistive finite-pressure magnetohydrodynamic equilibria without the necessity of postulating nested magnetic flux surfaces in the non-axisymmetric toroidal systems. The adopted approach integrates a hyperbolic parallel damping equation for pressure updating, along with a dynamic resistive relaxation for magnetic field. To address the nonaxisymmetry in toroidal geometry, a pseudo flux mapping is employed to relate the axisymmetric computational domain to the physical domain. On the computational mesh, an isoparametric C1-continuous triangular element is utilized to discretize the poloidal plane, which is complemented with a Fourier decomposition in the toroidal direction. The versatility of the code is demonstrated through its application to several different non-axisymmetric toroidal systems, including the inherently three-dimensional equilibria in stellarators, the helical-core equilibrium states in tokamak plasmas, and the quasi-single-helicity states in a reversed-field pinch.