Early nonlinear regime of MHD internal modes: The resistive case

Abstract

It is shown that the critical layer analysis, involved in the linear theory of internal modes, can be extended continuously into the early nonlinear regime. For the m = 1 resistive mode, the dynamical analysis involves two small parameters: the magnetic Reynolds number S and the m = 1 mode amplitude A, that measures the amount of nonlinearities in the system. The location of the instantaneous critical layer and the dominant dynamical equations inside it are evaluated self-consistently, as A increases and crosses some S-dependent thresholds. A special emphasis is put on the influence of the initial q-profile on the early nonlinear behavior. Predictions are given for a family of q-profiles, including the important low shear case, and shown to be consistent with recent experimental observations.