TEARING STABILITY OF THE 2-DIMENSIONAL MAGNETOTAIL

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 (B-n). In contrast to the Harris sheet with the equilibrium magnetic field [B=B-0 tanh(z/a)(x) over cap], the two-dimensional plasma sheet with the field [B=B-0 tanh(z/a)(x) over cap+B-n (z) over cap], in which the B-n field lies in the plane of the B-x field, has no neutral line if B-n not equal 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 B-n/B-0 similar to 0.1) compared with that in the Harris sheet model (B-n=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 B-n. For larger values of B-n, all modes behave diffusively, scaling as S-1. The collisionless electron tearing mode growth rate is found to be proportional to delta(e)(2) in the presence of significant B-n(>10(-2)B(0)) and large k(x)(similar to 0.1a(-1)-0.5a(-1)), and becomes completely stable (gamma<0) for B-n/B-0 greater than or equal to 0.2. Implications for magnetospheric substorms are discussed. (C) 1995 American Institute of Physics.