Low-frequency linear response of a cylindrical tokamak with arbitrary cross-section to ‘helical’ perturbations

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Abstract
Current driven, ‘helical’ (non-axisymmetric) modes of a tokamak with arbitrary cross-section are considered in the straight (cylindrical) geometry approximation. The plasma is considered surrounded by a resistive wall. The plasma may be unstable on a fast time-scale, namely the MHD or tearing mode time-scale, on a slow time-scale given by the wall properties or it may be stable. The formalism given in this paper allows determination of stability by relatively simple numerical means. In the case of instability on the slow time-scale, the formalism allows determination of growth rates and mode structures. Since the formalism is an eigenvalue formalism with orthogonal eigenfunctions, it is well suited for calculation of the effects on a stable plasma of slow error fields caused by externally driven error currents flowing predominantly in the direction of the ignorable co-ordinate.