Multiscale semi-ideal magnetohydrodynamics of a tokamak plasma

摘要

An analytical model of fast spatial flattening of toroidal current density and q profile in the non-linear stage of the m=1=1 kink instability of a cylindrical tokamak plasma is presented. The flattening is shown to be an essentially multiscale phenomenon characterized by, at least, two magnetic Reynolds numbers. The ordinary number, Rm, is related to a characteristic radial scale-length while the other one, R*m, corresponds to a characteristic scale-length of plasma inhomogeneity along the magnetic field line. In a highly conducting plasma inside the q=1 magnetic surface, where q does not differ much from unity, the plasma evolution is governed by multiscale non-ideal dynamics characterized by two well separated magnetic Reynolds numbers, Rm and R*m identical to (1-q)Rm. This dynamics consistently explains two seemingly contradictory features that were recently observed in a numerical simulation (Watanabe et al., 1995): (i) the current profile (q profile) is flattened on the magnetohydrodynamic time-scale within the q=1 rational surface; and (ii) the magnetic surface keeps its initial circular shape during this evolution. A theoretical consideration of multiscale semi-ideal magnetohydrodynamics with two magnetic Reynolds numbers, Rm and R*m, is presented; it reconciles the two above mentioned, seemingly contradictory features that were observed in the simulation.