Nonlinear tearing modes in the presence of resistive wall and rotation

Abstract

Nonlinear simulations of tearing modes with a resistive wall and plasma rotation in a two-dimensional (2-D) incompressible slab are presented. The regimes of interest include cases (1) in which a tearing mode is unstable even for a perfectly conducting wall; (2) in which a resistive wall tearing mode is unstable but may be stabilized by rotation. In (1), the mode can lead to a wall locking process, in which both the flow and the mode’s phase velocity are slowed, allowing flux diffusion through the wall and a wider island. There is a bifurcation with hysteresis between locked and unlocked states. If the decay of total momentum is large, the range with multiple states is smaller. In (2) resistive wall modes grow and lock for all parameters with linear instability. And even if rotation gives linear stability, there is nonlinear instability. The bifurcation diagram is similar to that for case (1), but in which the zero island width state takes the place of the unlocked state. Results are shown for case (2) giving the critical field error to drive nonlinear instability and begin locking.