A NEW FORMULATION OF THE RESISTIVE TEARING MODE-STABILITY CRITERION

A new formulation of the toroidal, finite beta, resistive tearing stab ility problem is presented. As in standard tearing mode theory, the mo de structure throughout most of the configuration is deter-mined by an ideal, inertia-free model. Thus, it is very closely related to that o btained from standard ideal magnetohydrodynamic (MHD) numerical stabil ity programs that depend on an energy principle. The effects of inerti a, resistivity, and any other plasma properties are important only in thin layers enclosing resonant surfaces. These surfaces are distinguis hed by the fact that they are composed of closed field lines. Instabil ity growth rates are obtained from the condition of matching between t he inner and outer regions. The data needed from the outer region for matching are conventionally reduced to a quantity DELTA', but in toroi dally coupled axisymmetric systems the relevant quantity is a matrix. A previous paper [Pletzer and Dewar, J. Plasma Phys. 45, 427 (1991)] p resented a relation between an extension of the ideal energy and the i nformation from the outer region that is needed in matching to the inn er layers. Here, this is used to construct a relation for the tearing mode growth rates directly in terms of an extension of the ideal energ y matrix. This demonstrates a convenient way to extend the numerical p rograms for ideal stability to include stability against tearing modes .