The linearized incompressible magnetohydrodynamic equations that include a generalized Ohm's law are solved for tearing eigenmodes of a plasma sheet with a normal magnetic field (Bn). In contrast to the Harris sheet with the equilibrium magnetic field [B=B0 tanh(z/a)x̂], the two-dimensional plasma sheet with the field [B=B0 tanh(z/a)x̂+Bnẑ], in which the Bn field lies in the plane of the Bx field, has no neutral line if B n≠0. Such a geometry is intrinsically resilient to tearing because it cannot change topology by means of linear perturbations. This qualitative geometrical idea is supported by calculations of growth rates using a generalized Ohm's law that includes collisional resistivity and finite electron inertia as the mechanisms for breaking field lines. The presence of B n reduces the resistive tearing mode growth rate by several orders of magnitude (assuming Bn/B0∼0.1) compared with that in the Harris sheet model (Bn=0). The growth rate scaling with Lundquist number (S) has the typical S-3/5 (S-1/3) dependence for large (small) wave numbers and very small values of Bn. For larger values of Bn, all modes behave diffusively, scaling as S -1. The collisionless electron tearing mode growth rate is found to be proportional to δe2 in the presence of significant Bn(> 10-2B0) and large k x(∼0.1a-1-0.5a-1), and becomes completely stable (γ<0) for Bn/B0≥0.2. Implications for magnetospheric substorms are discussed.
All Science Journal Classification (ASJC) codes
- Condensed Matter Physics