Necessary and Sufficient Condition for Hydromagnetic Stability of the Bennett Pinch. III. Reverse B_z Pinch

Abstract

Newcomb’s method for obtaining the necessary and sufficient condition for hydromagnetic stability is applied to the linear Bennett pinch of length 2πR. The longitudinal magnetic fields B_z inside and outside of the pinch are assumed to be opposite directions. The stability condition for the kink mode, some disturbances are stabilized and others are destabilized by reversing B_z field. However, the stability condition for all kink disturbances does not change from that of the parallel-B_z pinch. The necessary and sufficient condition for the stability of the Bennett pinch with reverse B_z is same as the one for the parallel-B_z pinch.