Stabilization of sawteeth in tokamaks by sheared poloidal flows

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 Alfven frequency ωA = kparallel(r)VA, where VA is the Alfven velocity and the parallel wavenumber kparallel(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 gradient in the shear Alfven frequency is determined by the shear in the magnetic field at the resonant surface. This criterion for stabilization does not depend at all on the plasma resistivity or on the global details of the poloidal velocity profile and the current profile. The internal kink is stabilized by sub-Alfvenic flows in which the peak velocity is only a very small fraction of the Alfven velocity. For the high β plasmas of tokamaks like TFTR and JET (β ∼ 10-2), sawteeth are stabilized by sub-sonic flows in which the poloidal velocity is less than the sound speed. The application of perpendicular neutral beam injection in an annulus around the resonant surface can generate the sheared poloidal flow necessary for the stabilization of sawteeth