Electron component of a plasma in a homogeneous electric field.

Abstract

We investigate spatially homogeneous stationary solutions of the Boltzmann equation describing the electron component of a gas plasma in a homogeneous electric field. We consider both elastic and weakly inelastic collisions of electrons with the neutral-particle plasma component as well as the Coulomb interaction between charged particles, described by Landau's collision integral. The Boltzmann equation for the electron swarm is linearized around a Maxwellian with some unknown temperature. For some important cases the problem reduces to a single-parameter system of two integrodifferential equations. Its solution allows us to treat plasmas under a variety of conditions in a rather simple way. We solve this system with the help of the spline-collocation method, and find the first two corrections to the Maxwellian corresponding to symmetrical and flow components of the velocity distribution function. The equation for the electron temperature then comes from the energy balance condition and from the requirement that the solution of the kinetic equation be unique. The electron temperature and energy absorption are described by curves with hysteresis as functions of the electric-field intensity. The conductivity versus electron temperature has a single maximum. Its rising slope corresponds to Spitzer's well-known formula, when the electron temperature is not very high and electron--neutral-particle collisions are unimportant. All numerical results are obtained under the assumption that the cross section for electron--neutral-particle collisions is independent of electron energy but generalizations are possible, since the analytical solution of the problem is far advanced.