Nonlinear dynamics of feedback modulated magnetic islands in toroidal plasmas

Abstract

An analysis is presented of the dynamics of a helical magnetic island chain embedded in a toroidal plasma, in the presence of an externally imposed, rotating, magnetic perturbation of the same helicity. Calculations are carried out in the large aspect-ratio, zero-β, resistive magnetohydrodynamical limit, and incorporate a realistic treatment of plasma viscosity. There are three regimes of operation, depending on the modulation frequency (i.e., the difference in rotation frequency between the island chain and the external perturbation). For slowly modulated islands, the perturbed velocity profile extends across the whole plasma. For strongly modulated islands, the perturbed velocity profile is localized around the island chain, but remains much wider than the chain. Finally, for very strongly modulated islands, the perturbed velocity profile collapses to a boundary layer on the island separatrix, plus a residual profile which extends a few island widths beyond the separatrix. Analytic expressions are obtained for the perturbed velocity profile, the island equation of motion, and the island width evolution equation in each of these three regimes. The ion polarization correction to the island width evolution equation, which has previously been reported to be stabilizing, is found to be destabilizing in all three regimes.