Asymptotic solutions and convergence studies of the resistive inner region equations

Abstract

A recent publication presents a detailed prescription for constructing global eigenfunctions and complex growth rates for resistive instabilities in axisymmetric toroidal systems, using the method of matched asymptotic expansions. At each singular surface in the plasma, the small-x asymptotic solutions of the ideal MHD outer-region equations are matched to the large-x asymptotic solutions of the resistive inner-region equations, with x being the distance from the singular surface. The success of this method depends upon accurate asymptotic solutions of the resistive inner region equations. Extensive studies have shown that there are not only regimes of excellent agreement with straight-through methods, without asymptotic matching, but also regimes of strong disagreement. In an effort to find the cause of this discrepancy, we present here a different method of constructing asymptotic solutions of the inner region equations and we study the convergence properties of the new and old solutions.