Variational methods for studying tokamak stability in the presence of a thin resistive wall

Abstract

External magnetohydrodynamic modes stabilized by the presence of a close-fitting perfectly conducting wall become destabilized when the wall is assumed to possess finite resistivity. A simple variational principle giving an estimate for the resulting growth rate and the threshold for stability is derived in terms of quantities relating to the ideal system with and without a perfectly conducting wall. This variational principle is valid for an arbitrary three-dimensional external mode in an arbitrarily shaped plasma possessing an arbitrarily shaped, but thin, resistive wall. As an example of the utility of the method, the variational principle is used to investigate the axisymmetric (n=0) stability of straight, zero pressure elliptical tokamaks with arbitrary current density profiles in the presence of a resistive wall.