Stabilization of ideal modes by resistive walls in tokamaks with plasma rotation and its effect on the beta limit

It is shown that pressure-driven, ideal external modes in tokamaks can be fully stabilized by resistive walls with plasma rotation. For wall stabilized plasmas, there are two types of potentially unstable external modes: (i) the ‘‘resistive wall modes’’ that penetrate, and are nearly locked to the wall, and (ii) modes that rotate with the plasma and for which the wall acts as a good conductor. For the quickly rotating modes, the stabilizing effect of the wall increases when the wall is brought closer to the plasma, while for the resistive wall modes, the stabilization improves with increasing wall distance. When the plasma rotates at some fraction of the sound speed, there is a window of stability to both the wall-locked and the rotating mode. The stabilization depends principally on the toroidal coupling to sound waves and is affected by ion Landau damping. Two-dimensional stability calculations are presented to evaluate the gains in beta limit resulting from this wall stabilization for different equilibria and rotation speeds. Results are shown for advanced tokamak configurations with bootstrap fractions of ≊100%.