Effects of Pressure and Resistivity on the Ambipolar Diffusion Singularity: Too Little, Too Late

Ambipolar diffusion, or ion-neutral drift, can lead to steepening of the magnetic field profile and even to the formation of a singularity in the current density. These results are based on an approximate treatment of ambipolar drift in which the ion pressure is assumed vanishingly small and the frictional coupling is assumed to be very strong, so that the medium can be treated as a single fluid. This steepening, if it really occurs, must act to facilitate magnetic reconnection in the interstellar medium, and so could have important consequences for the structure and evolution of the galactic magnetic field on both global and local scales. In actuality, the formation of a singularity must be prevented by physical effects omitted by the strong coupling approximation. In this paper we solve the coupled equations for charged and neutral fluids in a simple slab geometry, which was previously shown to evolve to a singularity in the strong coupling approximation. We show that both ion pressure and resistivity play a role in removing the singularity, but that, for parameters characteristic of the interstellar medium, the peak current density is nearly independent of ion pressure and scales inversely with resistivity. The current gradient length scale, however, does depend on ion pressure. In the end, effects outside the fluid approximation, such as the finite ion gyroradius, impose the strictest limit on the evolution of the magnetic profile.