Stationary distribution function for non-adiabatic particle motion in a one dimensional current sheet

The problem of pitch angle scattering in field configurations similar to those found in the geomagnetic tail has been studied previously by Tsyganenko (1982). Tsyganenko used a scattering matrix to map pitch angle distributions through the current sheet. By using numerical solutions of the resulting integral equations he showed for weakly non-adiabatic particles the Stationary Distribution Function (SDF) was isotropic. Using his procedure the SDF was found to develop anisotropies with increasing non-adiabaticity. The work presented here shows analytically that for any degree of scattering the SDF must be isotropic for a general planar field reversal. Computations of particle trajectories have been used to verify some aspects of the analytic work.