Simulated annealing for three-dimensional low-beta reduced MHD equilibria in cylindrical geometry

TL;DR

This paper applies simulated annealing, based on Hamiltonian mechanics, to compute three-dimensional low-beta reduced MHD equilibria in cylindrical geometry, successfully finding equilibria including magnetic islands.

Contribution

It extends the application of simulated annealing to 3D MHD equilibria in cylindrical geometry, introducing new artificial dynamics for smoothing.

Findings

Successfully computed 3D MHD equilibria with magnetic islands.

Demonstrated the effectiveness of artificial dynamics for smoothing.

Extended previous 2D methods to 3D cylindrical geometry.

Abstract

Simulated annealing (SA) is applied for three-dimensional (3D) equilibrium calculation of ideal, low-beta reduced MHD in cylindrical geometry. The SA is based on the theory of Hamiltonian mechanics. The dynamical equation of the original system, low-beta reduced MHD in this study, is modified so that the energy changes monotonically while preserving the Casimir invariants in the artificial dynamics. An equilibrium of the system is given by an extremum of the energy, therefore SA can be used as a method for calculating ideal MHD equilibrium. Previous studies demonstrated that the SA succeeds to lead to various MHD equilibria in two dimensional rectangular domain. In this paper, the theory is applied to 3D equilibrium of ideal, low-beta reduced MHD. An example of equilibrium with magnetic islands, obtained as a lower energy state, is shown. Several versions of the artificial dynamics are developed that can effect smoothing.