Comments on the asymptotic treatment of tokamak MHD-stability at large aspect ratio

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Abstract
In the asymptotic treatment of tokamak MHD stability at small inverse aspect ratio , the special case of poloidal wave number m = 0 has been treated improperly in the literature for both axisymmetric and non-axisymmetric modes. In axisymmetric stability, a contribution to the perturbational vacuum field is either omitted or cancelled. In a variational stability analysis this field contribution provides δ2W with a correction term proportional to (ln )−1, which may change the asymptotic range of stability and improve agreement with numerical finite-aspect-ratio results. In non-axisymmetric stability, for the perturbational vacuum field of the m = 0 modes, usually the wrong of two possible solutions is chosen. It is shown why in many cases this wrong choice has no consequences on the correctness of the stability results, and circumstances are pointed out under which consequences may arise.