Approach to nonlinear magnetohydrodynamic simulations in stellarator geometry

TL;DR

This paper extends the M3D-$C^1$ code to perform nonlinear MHD simulations in stellarator geometries by introducing logical coordinates and coordinate mapping, enabling accurate modeling of stellarator plasma dynamics.

Contribution

The authors develop a novel approach to adapt existing axisymmetric MHD codes for non-axisymmetric stellarator geometries using logical coordinates and coordinate mapping.

Findings

Successful simulation of heating, destabilization, and equilibration of stellarator plasmas.

Verification of the approach through simulations of magnetic field relaxation.

Demonstration of the method's capability in realistic stellarator geometries.

Abstract

The capability to model the nonlinear magnetohydrodynamic (MHD) evolution of stellarator plasmas is developed by extending the M3D-$C^1$ code to allow non-axisymmetric domain geometry. We introduce a set of logical coordinates, in which the computational domain is axisymmetric, to utilize the existing finite-element framework of M3D-$C^1$. A $C^1$ coordinate mapping connects the logical domain to the non-axisymmetric physical domain, where we use the M3D-$C^1$ extended MHD models essentially without modifications. We present several numerical verifications on the implementation of this approach, including simulations of the heating, destabilization, and equilibration of stellarator plasmas with strongly anisotropic thermal conductivity, and of the relaxation of stellarator equilibria to integrable and non-integrable magnetic field configurations in realistic geometries.