The resistive tearing instability for generalized resistivity models: Theory

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Abstract
In collision‐dominated plasmas, as well as in plasma systems with anomalous dissipation, the resistivity, in general, depends on the local plasma parameters. Except for some special applications, this dependence is usually not taken into account for the resistive tearing mode. In this paper, a dispersion relation for the resistive tearing mode is derived in a closed analytical form, where generalized models for the resistivity are considered. Because of the dependence on electron temperature, e.g., for the Spitzer resistivity, a further transport equation for the electron temperature is assumed in the presented theory. For applications to more realistic systems, the equilibrium configuration is assumed to be weakly two dimensional. Thus the obtained dispersion relation represents a generalization, which includes a number of results of previous authors. In order to determine this dispersion relation, a constant Ψ approximation is not applied such that the parameter regime of maximum growth rate is covered by the presented theory.

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