Resistive tearing mode in weakly two-dimensional neutral sheets

Abstract

The resistive tearing mode is expected to be rather sensitive to a magnetic field component perpendicular to the singular layer (B⊥) that typically occurs in weakly two-dimensional sheets, and a stabilizing effect was suggested by previous authors. A normal mode analysis is performed by rigorous application of the singular perturbation technique, i.e., the scalings are determined from the significant degeneration of the differential operator and matching is accomplished by the overlap hypothesis. For B⊥/B0=O(ε2α), a tendency of the plasma flow to follow the (curved) field lines is demonstrated (ε is the width of the singular layer and α is the wavenumber of the perturbation, both are normalized to the thickness of the current sheet). The dispersion relation, however, derived in closed analytical form for S−2/5⩽α=O(1), shows no influence of the normal component on the growth rate (S is the magnetic Reynolds number). Thus, the classical results of Furth, Killen, and Rosenbluth are recovered and an analytical expression for their numerical results in the regime of the maximum growth rate is given.