Stabilization of sawteeth in tokamaks by sheared poloidal flows

Abstract

The resistive internal kink mode in a current profile with a central safety factor q(0)<1 is shown to be stabilized by sheared poloidal flows. The internal kink mode is found to be stabilized when the local gradient in the poloidal rotation frequency ω at the q=1 resonant surface r1 is larger than the local gradient in the shear Alfvén frequency ωA=k∥(r)VA, where VA is the Alfvén velocity and the parallel wave number k∥(r)=R−1[1−1/q(r)] with R the major radius of the torus and q(r) the safety factor profile in the minor radial coordinate r; i.e., ‖dω/dr‖r1≥‖dωA/dr‖r1. The internal kink is stabilized by sub-Alfvénic flows in which the peak velocity is only a very small fraction of the Alfvén velocity. When the shear in the rotation frequency at the resonant surface is too weak to linearly stabilize the internal kink mode, then the kink mode can still be nonlinearly stabilized, resulting in incomplete reconnection, if the shear in the rotation increases just outside the resonant surface at larger radii.