Landau collision operators and general moment equations for an electron-ion plasma

Abstract

The general moment equations for an electron-ion plasma are established. The distribution functions for electrons and ions are expanded in terms of orthogonal polynomials of random velocity variables in contrast to the total velocity variables [J.-Y. Ji and E. D. Held, Phys. Plasmas 13, 102103 (2006)]. The moments of the streaming part of the kinetic equation are explicitly written with simple formulas. A simple version of the exact linearized Coulomb collision integrals is presented for like species. The electron-ion and ion-electron operators that conserve momentum and energy are also calculated with a small mass-ratio approximation. It is shown in the relaxation theory that the Lorentz operator, as a replacement of the like-species operator, is acceptable only for the high-order harmonic moments.