Stability of coupled tearing and twisting modes in tokamaks

Abstract

A dispersion relation is derived for resistive modes of arbitrary parity in a tokamak plasma. At low mode amplitude, tearing and twisting modes which have nonideal magnetohydrodynamical (MHD) behavior at only one rational surface at a time in the plasma are decoupled via sheared rotation and diamagnetic flows. At higher amplitude, more unstable ‘‘compound’’ modes develop which have nonideal behavior simultaneously at many surfaces. Such modes possess tearing parity layers at some of the nonideal surfaces, and twisting parity layers at others, but mixed parity layers are generally disallowed. At low mode number, ‘‘compound’’ modes are likely to have tearing parity layers at all of the nonideal surfaces in a very low-β plasma, but twisting parity layers become more probable as the plasma β is increased. At high mode number, unstable twisting modes which exceed a critical amplitude drive conventional magnetic island chains on alternate rational surfaces, to form an interlocking structure in which the O points and X points of neighboring chains line up.