The effect of a partial resistive shell on the magnetohydrodynamical stability of tokamak plasmas

Abstract

A comprehensive theory is developed to determine the effect of a partial resistive shell on the growth rate of the external kink mode in a low-β, large aspect-ratio, circular flux-surface tokamak. In most cases, it is possible to replace a partial shell by a complete “effective shell” of somewhat larger radius. In fact, the radius of the effective shell can be used to parametrize the ability of a partial shell to moderate the growth of the external kink mode. It is necessary to draw a distinction between “resonant shells,” for which the eddy currents excited in the shell are able to flow in unidirectional continuous loops around the plasma, and “nonresonant shells,” for which this is not possible. As a general rule, resonant shells perform better than similar nonresonant shells. The theory is used to derive some general rules regarding the design of incomplete passive stabilizing shells. The theory is also employed to determine the effectiveness of two realistic feedback stabilization schemes for the resistive shell mode, both of which only require a relatively small number of independent feedback controlled conductors external to the plasma.