Convergent Kinetic Equation for a Classical Plasma

Abstract

A general quantum-mechanical transport equation is used to derive a kinetic equation for an electron gas which in the classical limit is not subject to the usual short-range divergence and is exact to first order in the plasma parameter. The method is based on a direct analogy with the well-known equilibrium theory of the electron gas. No arbitrary separations or cutoffs are necessary. The resulting collision integral is similar to that of Weinstock and of Frieman and Book, but the Boltzmann and Fokker-Planck terms are evaluated for the static screened Coulomb potential instead of the bare Coulomb potential. It is shown that the equation of Guernsey, although convergent, does not contain all first-order contributions in the plasma parameter, and that the equations of Weinstock and of Frieman and Book must be carefully interpreted to achieve correct results. Numerical results, given in the classical limit for the dc electrical conductivity, explicitly exhibit the dominant and nondominant terms.