Kinetic equations for a plasma

Abstract

Starting with Liouville's equation, a set of equations is derived in the random-phase approximation for the evolution of the spatial Fourier components of the complete distribution function of a particle in a plasma. A procedure is used which takes account of all the contributions coming from many-body interactions in the random-phase approximation. The equations thus describe the collective part of the response of plasma to the particle. The equations which have the structure of the Fokker-Planck equation describe collisions of electrons carrying an envelope of plasma waves emitted by them. It is shown that in the Markoff approximation this envelope degenerates into a Debye shielding cloud, so that in this approximation the equations describe the collisions of electrons clothed in Debye shielding clouds.