Adaptive Grids in Simulations of Toroidal Plasma Starting from Magneto-Hydrodynamic Equilibrium

This paper introduces the notion of Tokamak Magneto-Hydrodynamics (TMHD), which explicitly reflects the anisotropy of a high temperature tokamak plasma. The set of TMHD equations is formulated for simulation of macroscopic plasma dynamics and disruptions in toka- maks. Free from the Courant restriction on the time step, this set of equations is adequate to plasma dynamics with realistic parameters of high performance plasmas and does not require any extension of the MHD plasma model. At the same time, TMHD requires the use of magnetic field aligned numerical grids. Examples of their use in 2-dimensional cases of tokamak equilibria and dynamics of the wall touching kink mode are presented. For the 3-dimensional case of an ergodic magnetic field, this paper introduces the reference magnetic coordinates as a practical algorithm for generating adaptive grids for TMHD.