Model Fokker-Planck Equation for a Plasma and Its Solution

Abstract

A model Fokker-Planck equation for a single species of particles in a plasma is discussed. This equation has several properties in common with the real equation, and ascribes an approximately correct behavior to most of the particles, though incorrect for the high-energy tail in the thermal distribution. It is shown that the equation can be solved completely, for the small perturbations of a uniform plasma by electric fields harmonic in space and time, in an external magnetic field. Applications to ionospheric radar scattering are briefly discussed; it is shown that in certain circumstances, ion-ion collisions can have a profound effect on the scattering even though the collision frequency is much smaller than the ion gyrofrequency, and this appears to agree with observation.