Localized resistive instabilities in general toroidal configurations, with applications to INTOR equilibria

Abstract

A useful method for studying localized resistive instabilities in toroidal equilibria at and near the ideal stability limit is presented. In particular, a valuable relation is given explicitly which allows direct calculation of the resistive growth rate at the ideal ballooning limit in terms of line-averaged equilibrium quantities. The method, which is valid not only for axisymmetric equilibria but also for toroidal, nonsymmetric 3-D configurations, is derived without making any of the usual restricting assumptions such as small inverse aspect ratio, low pressure etc. The actual evaluation of stability criteria and dispersion relations is illustrated by studying the stability of typical INTOR equilibria with respect to localized ideal and resistive modes. Configurations which are stable with respect to ideal ballooning modes (and are therefore also Mercier stable) are shown to be unstable with respect to resistive ballooning instabilities, and the corresponding growth rates are calculated. Considerable growth rates ( gamma -1 approximately 1 ms) are found at values of ( beta ) that are 80-90% of the critical value. Below these values of ( beta ), the growth rates decrease very rapidly. A subject of more general interest is also treated, namely the situation which appears when the Mercier exponent sM exceeds the value 1/2, and a new dispersion relation for a model equation is derived.