Extension of Doughterty's model Fokker–Planck equation for a plasma

Abstract

A generalization of the Appleton–Hartree equation is made to include the effects of energy-dependent electron-neutron collisions, Coulomb encounters and spatial dispersion. The frequency of electromagnetic waves propagating in a magneto-plasma is sufficiently high that the ion motion may be neglected compared with the electron motion. The present analysis extends Dougherty (1963, 1964) to include the simultaneous effect on wave propagation of Coulomb forces, spatial dispersion and energy-dependent electron-neutral collisions, where one or more of these effects can have a significant influence on circularly polarized waves propagating at frequencies near electron cyclotron resonance. The electrical conductivity tensor is expressible in terms of appropriate velocity moments of the electron distribution function. The electron velocity distribution function is determined by expanding the inverse of the differential operator of the linearized kinetic equation in a small parameter ε2', where in one case ε2 is the ratio of Coulomb collision frequency to signal frequency, and in the second case ε2 is the ratio of electron-neutral collision frequency to signal frequency. For wave propagation along the magnetic field, the dispersion relations for right-hand and left-hand circularly polarized waves, and also the dispersion relation for longitudinal waves, are solved numerically, and graphs are presented to show the effects of collisionless damping, velocity dependent electron-neutral collisions and Coulomb collisions.