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

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 open-quotes effective shellclose quotes 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 open-quotes resonant shells,close quotes for which the eddy currents excited in the shell are able to flow in unidirectional continuous loops around the plasma, and open-quotes nonresonant shells,close quotes 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. copyright 1997 American Institute of Physics