Simulated annealing of reduced magnetohydrodynamic systems

TL;DR

This paper reviews the theory of simulated annealing (SA) based on a double bracket Hamiltonian formulation, demonstrating its application to reduced magnetohydrodynamic systems and other models for equilibrium and stability analysis.

Contribution

It introduces a double bracket formulation of SA for Hamiltonian systems and applies it to reduced MHD models, showing its effectiveness in stability analysis.

Findings

Numerical results validate SA's usefulness for equilibrium analysis.

SA successfully applied to both finite and infinite degree-of-freedom systems.

The study discusses future challenges in applying SA to complex systems.

Abstract

Theory of simulated annealing (SA), a method for equilibrium and stability analyses for Hamiltonian systems, is reviewed. The SA explained in this review is based on a double bracket formulation that derives from Hamiltonian structure. In addition to general theoretical aspects, the explicit formulation as well as numerical applications are presented. Both finite and infinite degree-of-freedom systems are treated, in particular, the heavy top, a toy model mimicking low-beta reduced magnetohydrodynamics (MHD) and low- and high-beta reduced MHD. Numerical results successfully demonstrate the usefulness of SA for equilibrium and stability analyses. At the same time, the results raise some future issues that are discussed in the paper.