Stability of resistive MHD tearing and ballooning modes in the tail current sheet

Abstract

We have analytically investigated the evolution of resistive MHD tearing and ballooning modes by assuming that the dissipation is anomalous in the current sheet region. A generalized technique is diplayed for obtaining the solutions for both these modes near the singular layer, where the Bx(z) field reverses sign. When the perturbation is limited to two dimensions, we have found that the stability of tearing modes is controlled by compressibility and the Lundquist number S, where S is the ratio of anomalous diffusion time to Alfvén time. For S ≪ 5 × 103, the fluid compressibility plays a significant destabilizing role while the normal component Bz contributes to a weak stabilization of tearing modes. In the three‐dimensional case with ky ≠ 0 (ky being the wavenumber), it is demonstrated that a linear coupling of the pressure gradient and the magnetic field curvature causes the excitation of a new class of unstable tearing and ballooning modes with their growth rates significantly dependent on anomalous resistivity and the Alfvénic frequency. The resistive ballooning modes, excited in the field reversal layer, are shown to enhance the current and the magnetic field gradients in the center of the plasma sheet and thereby provide the source for the excitation of tearing modes with a typical growth time of 5 s. Finally, the relevance of the newly excited modes to recent AMPTE/IRM, GEOS 2, and Geotail results is discussed.