Nonlinear stability of magnetic islands in a rotating helical plasma

Coexistence of the forced magnetic reconnection by a resonant magnetic perturbation (RMP) and the curvature-driven tearing mode is investigated in a helical (stellarator) plasma rotated by helical trapped particle-induced neoclassical flows. A set of Rutherford-type equations of rotating magnetic islands and a poloidal flow evolution equation is revisited. Using the model, analytical expressions of criteria of spontaneous shrinkage (self-healing) of magnetic islands and sudden growth of locked magnetic islands (penetration of RMP) are obtained, where nonlinear saturation states of islands show bifurcation structures and hysteresis characteristics. Considering radial profile of poloidal flows across magnetic islands, it is found that the self-healing is driven by neoclassical viscosity even in the absence of micro-turbulence-induced anomalous viscosity. Effects of unfavorable curvature in stellarators are found to modify the critical values. The scalings of criteria are consistent with low-β experiments in the large helical device.