On a Plasma sheath with a Small Normal Magnetic Field Separating Regions of Oppositely Directed Magnetic Field

Current sheets form intermittently during plasma turbulence and are a fundamental signature of the turbulence's non-linear character. An understanding of the simple current sheet configurations therefore become an important building block for turbulence theory. The Harris-sheet model [1] provides an exact solution to the kinetic plasma equations 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. In contrast to the magnetic moment, the action variable associated with the oscillatory orbit motion perpendicular to the current sheet, is well conserved. This facilitates the development of a new “action kinetic” model, providing a new kinetic solution for 1D current sheets including a normal magnetic field. Considering the case of isotropic ion pressure, the current sheets are supported by electron pressure anisotropy, and the total current across a particular sheet is set by the fire-hose condition based on the electron pressures normalized by the pressure of the asymptotic magnetic field. Analytical approximations are obtained for the numerical solutions expressed in terms of the asymptotic electron temperature anisotropy and the ion temperature.

[1] E. Harris, On a plasma sheath separating regions of oppositely directed magnetic field, Nuovi Cimento 23, 115+ (1962).