On a plasma sheath with a small normal magnetic field separating regions of oppositely directed magnetic field

Abstract

The Harris-sheet model provides an elegant solution to the kinetic plasma equation for a steady state 1D current sheet geometry separating regions with oppositely directed magnetic field. However, adding just a small normal magnetic field to the Harris configuration yields thermal streaming of particles into and out of the current sheet, fundamentally changing the form of its kinetic description. The action variable, J z, associated with the oscillatory orbit motion perpendicular to the current sheet is well conserved and can be applied for solving the kinetic equation in the 1D sheet geometry that includes a small normal magnetic field. Revisiting this problem, we develop a new formalism that permits numerical solutions to be readily obtained for general upstream/asymptotic electron and ion distributions. In particular, we consider the case of isotropic ion pressure and anisotropic bi-Maxwellian electrons. The current sheets are then supported by electron pressure anisotropy. Furthermore, the total current across a particular sheet is set by the fire-hose condition based on the electron pressures normalized by the asymptotic magnetic field pressure. Analytical approximations are obtained for the numerical solutions expressed in terms of the asymptotic electron temperature anisotropy and the ion temperature. We discuss a preliminary application of the framework to the electron diffusion region of anti-parallel magnetic reconnection.