Simulated annealing of reduced magnetohydrodynamics by mixed Hamiltonian and artificial dynamics*

Simulated annealing (SA)[1], a kind of relaxation method, has been applied to equilibrium calculations and stability analyses of reduced magnetohydrodynamics (RMHD) systems[2, 3].  The artificial dynamics of SA is derived utilizing Hamiltonian nature of the system so that the energy of the system monotonically changes while the Casimirs are preserved.  An energy minimum is an equilibrium of RMHD, which can be reached by SA.  Also, the stability of a given equilibrium can be analyzed by SA from the view point of energy.  Since SA solves an initial-value problem for the relaxation, the simulation time tends to be longer, especially near the equilibrium.  Therefore, accelerated relaxation is necessary.  We have developed such a method in [3].  In this presentation, we examine whether the relaxation can be accelerated if we include the original Hamiltonian dynamics in addition to the SA dynamics.  Numerical results show that the inclusion of the Hamiltonian dynamics rather slows down the relaxation to the equilibrium in the cases tested until now.

[1] G. R. Flierl, P. J. Morrison, Physica D 240, 212 (2011). 

[2] Y. Chikasue and M. Furukawa, Phys. Plasmas 22, 022511 (2015),  M. Furukawa and P. J. Morrison, Plasma Phys. Control. Fusion 59, 054001 (2017),  M. Furukawa, Takahiro Watanabe, P. J. Morrison, K. Ichiguchi, Phys. Plasmas 25, 082506 (2018).

[3] M. Furukawa and P. J. Morrison, Phys. Plasmas 29, 102504 (2022).