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.

The attractiveness of future commercial tokamak reactors is sensitive to the attainable plasma performance, notably plasma energy confinement and allowable beta. The impact of varying levels of confinement and beta on the size and cost of the resulting tokamak reactor is systematically quantified. Several different classes of tokamak reactors are considered, and designs are optimized in terms of cost of electricity (COE) via a coupled physics/engineering/costing systems code. Surprisingly narrow ranges of plasma confinement and beta are found to be simultaneously useful in minimizing the reactor COE, i.e. improvement in only one of these quantities is not useful beyond some point without accompanying improvements in the other. For steady state, current driven reactors characterized by H mode confinement (where τE=HτE,L; τE,L being the confinement time predicted by the ITER.89 L mode scaling, and H ~ 2), the maximum useful Troyon β coefficient (βN) is only ~ 4.3%.mT/MA. These confinement levels are similar to those observed in present day experiments. If slightly better confinement is achievable (i.e. an enhancement factor over L mode of H ~ 2.5), the maximum useful Troyon coefficient increases to βN ~ 6 and the reactor COE decreases by 20%. Inductively driven, pulsed reactors have somewhat increased useful ranges of confinement relative to the steady state cases. In general, increasing the allowable beta over presently accepted limits offers the single biggest improvement in reactor attractiveness of the tokamak concept

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