Masaru Furukawa, Tottori University, Japan

"Stability analysis of MHD equilibria via simulated annealing"

Abstract: Simulated annealing (SA) is a kind of relaxation method, where we solve an initial-value problem derived for a Hamiltonian system so that the energy of the system changes monotonically while the Casimir invariants are preserved. We have applied SA for reduced MHD systems, where the energy is decreased by SA. Recently, it was shown that SA can be used for stability analyses since it tries to find a lower energy state. We found that spectral analysis of linearized SA equation shows instability for a cylindrically symmetric equilibrium with sheared poloidal rotation, where spectral analysis of linearized low-beta reduced MHD itself does not show instability. This indicates that a perturbed state has a lower energy, and that a negative energy mode exists. In the talk, the linear spectral analysis as well as the SA results including recent progress will be presented. Another analysis of a system with magneto-rotational instability (MRI) will also be included.