A new formulation of the resistive tearing mode stability criterion

Abstract

A new formulation of the toroidal, finite beta, resistive tearing stability problem is presented. As in standard tearing mode theory, the mode structure throughout most of the configuration is determined by an ideal, inertia-free model. Thus, it is very closely related to that obtained from standard ideal magnetohydrodynamic (MHD) numerical stability programs that depend on an energy principle. The effects of inertia, resistivity, and any other plasma properties are important only in thin layers enclosing resonant surfaces. These surfaces are distinguished by the fact that they are composed of closed field lines. Instability growth rates are obtained from the condition of matching between the inner and outer regions. The data needed from the outer region for matching are conventionally reduced to a quantity Δ′, but in toroidally coupled axisymmetric systems the relevant quantity is a matrix. A previous paper [Pletzer and Dewar, J. Plasma Phys. 45, 427 (1991)] presented a relation between an extension of the ideal energy and the information from the outer region that is needed in matching to the inner layers. Here, this is used to construct a relation for the tearing mode growth rates directly in terms of an extension of the ideal energy matrix. This demonstrates a convenient way to extend the numerical programs for ideal stability to include stability against tearing modes. Show more