Simulated annealing for MHD equilibria with flow and/or magnetic island

As a new method of MHD equilibrium calculation, the authors propose simulated annealing. By solving the artificial evolution equation derived based on the fact that the ideal MHD equation is written using Hamiltonian and Poisson brackets, it is possible to lead energy to the extremum while maintaining the invariant underlying in the MHD equation. This energy extremum is MHD equilibrium. This paper firstly describes the general theory on the formularization with symmetrical brackets used when applying simulated annealing to MHD. Then as a specific example, it shows the motion of an incompressible neutral fluid on a two-dimensional plane and low-beta simplified MHD that are considered as the simplest specific example as a partial differential equation system. Next this paper introduces, in the cylindrical plasma, the simulation results where the steady solution containing magnetic island has been obtained as the energy minimum state using the low-beta simplified MHD. Finally, it describes future tasks. (A.O.)