The resistive wall instability and critical flow velocity

Abstract

A cylindrical model with an equilibrium surface current and a uniform equilibrium plasma flow velocity parallel to the axis of the cylinder is used to investigate resistive wall instability. This system can be unstable to the ideal, external kink mode, which can be stabilized by the presence of a perfectly conducting wall. This is the classic condition for the resistive wall instability and the effect of a plasma flow velocity on this mode is explored. It is noted that a stable kink mode, Doppler shifted by the flow velocity, can pass through zero frequency for a velocity which depends on the marginal condition for the external kink instability. The passage through zero frequency is the condition for the kink mode to carry negative energy. It is shown how this mode implies a critical flow speed at which the resistive wall mode is further destabilized, with a growth rate inversely proportional to the square root of the wall time. Under these circumstances, the resistive wall mode behaves more like an ideal instability. All flow velocities are shown to be potentially destabilizing and the flow velocity can produce a resistive wall instability even when the plasma is stable to the external kink mode in the absence of a wall. At velocities well above the critical flow speed, the resistive wall growth rate is much reduced (inversely proportional to the wall time and to the flow speed).