Nonlinear error field response in the presence of plasma rotation and real frequencies due to favorable curvature

Abstract

We present nonlinear resistive MHD simulations of the response of a rotating plasma to an error field when the plasma has weakly damped linear tearing modes (TM's), stabilized by pressure gradient and favorable curvature. Favorable curvature leads to the Glasser effect: the occurrence of real frequencies and stabilization with positive stability index $Δ'$. A cylinder with hollow pressure is used to model the toroidal favorable curvature. Linear simulations with rotation and an error field $\tildeψ_w$ show, in agreement with analytic results, that the peak reconnected flux occurs for a rotation rate near the TM phase velocity. Nonlinear simulations with small $\tildeψ_w$ show that the real frequency and stabilization by favorable average curvature are masked by a nonlinear effect that occurs for very thin islands: flattening of the pressure across the island, mainly due to sound wave propagation. This flattening causes the disappearance of real frequencies destabilization of the mode, allowing it to grow to large amplitude similar to a $β=0$ unstable TM. The flattening of the current for larger islands saturates the mode nonlinearly. In the post-saturation phase, the interaction of the error field with the destabilized spontaneous tearing mode, which rotates with the plasma, leads to oscillations in the Maxwell torque and therefore modulations in the plasma rotation. The islands also rotate with modulated phase velocity, undergoing small-amplitude oscillations due to these modulations. We also present a quasilinear model with an unstable spontaneous TM and error fields, showing that the superposition of these fields results in similar oscillations.