An analytic study of the magnetohydrodynamic stability of inverse shear profiles

This paper reports on the ideal magnetohydrodynamic (MHD) stability of tokamak field profiles that have a non-monotonic safety factor q(r). An analytic criterion is obtained for these ‘‘inverse shear’’ profiles by expanding in inverse aspect ratio and assuming that the minimum in q is slightly less than the m/n value of the mode under examination (m and n being the principal poloidal and toroidal mode numbers of the instability). Three terms are identified as controlling the stability of this ‘‘double kink’’; two of them are stabilizing and due, respectively, to field line bending and the interaction of average favorable curvature with the pressure gradient. The possibility of instability comes from the third term which is due to toroidal coupling and is ballooning in character. The analytic results are compared with those from a fully toroidal stability code.