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A natural co-ordinate system in which the current and magnetic field lines are straight is utilized to study localized hydromagnetic interchange instabilities in general toroidal configurations. This provides a clarification of the nature of the energy sources which are available to drive the instability and of the constraints which the perturbation must satisfy. An analysis in which the electrical resistivity is small but non-zero is made. This provides a reasonable generalization of the V" criterion for average-mimimum-B systems and shows that if the condition is satisfied then purely growing instabilities cannot grow as fast as η1/3 in the limit of small resistivity.
Johnson et al. (1967) studied this question.