Calculation of large-aspect-ratio tokamak and toroidally-averaged stellarator equilibria of high-beta reduced magnetohydrodynamics via simulated annealing

TL;DR

This paper introduces a simulated annealing method for calculating high-beta MHD equilibria in toroidal devices, successfully applying it to tokamaks and stellarators, revealing effects of poloidal rotation and confirming previous results.

Contribution

The paper presents the first successful application of simulated annealing to compute toroidal MHD equilibria in high-beta plasmas.

Findings

Poloidal rotation increases the Shafranov shift quadratically.

The SA method accurately reproduces stellarator equilibria.

A mapping explains the quadratic dependence of equilibrium shifts on rotation.

Abstract

A simulated annealing (SA) relaxation method is used for calculation of high-beta reduced magnetohydrodynamics (MHD) equilibria in toroidal geometry. The SA method, based on artificial dynamics derived from the MHD Hamiltonian structure, is used to calculate equilibria of large-aspect-ratio and circular-cross-section tokamaks as well as toroidally averaged stellarators. Tokamak equilibria including incompressible poloidal rotations are obtained and the Shafranov shift is seen to increase nearly quadratically in the rotation speed. A mapping procedure between non-rotating and poloidally rotating equilibria is shown to explain a quadratic dependence of equilibria shift on rotation. Calculated stellarator equilibria are seen to agree reasonably with previous results. The numerical results demonstrate the first successful application of the SA method to obtain toroidal equilibria.