Effect of rigid toroidal rotation on the stability of a high-beta tokamak to external kink modes

Abstract

The effect of rigid toroidal rotation on the stability of a tokamak to external kink modes is examined. For simplicity a surface current model is assumed. For a high-β tokamak it is shown that to leading order the equations governing stability in the presence of rotation are identical to those for a static plasma with β replaced by β+S, where β is the plasma beta and S is a parameter which provides a measure of the rotation rate. For a circular cross-section tokamak the critical beta for stability to external kink modes in the presence of rigid toroidal rotation is given, to leading order in the inverse aspect ratio ε, by β=0.21ε−S. For an elliptical cross-section tokamak the largest critical beta is obtained for a vertical elongation of 2.2 and is given, to leading order in ε, by β=0.37ε−S. The lower limit on the kink safety factor q* or the Mercier q increases with increase in S. Quantitative estimates of this increase can be obtained from the stability boundaries for the static problem.