Master Equation for Plasmas

A straightforward derivation of the general kinetic equation describing the irreversible evolution of the N-momenta distribution function for a classical spatially homogeneous stable plasma (nrD3 ≫ 1) is given. Collective effects are included. This plasma master equation reduces to the weak-coupling master equation when collective effects are neglected. The results are given first in terms of a coupled pair of equations analogous to those obtained by Bogoliubov for the kinetic description of a plasma. The equation for the generalized correlations is then solved for stable plasma in terms of the N-momenta distribution function; the master equation then follows by substitution, and is shown to possess an H theorem. The conditions under which these results reduce to the kinetic equation of Balescu and Lenard, are discussed. The origins of irreversibility in plasmas are discussed in the light of this and other recent work, and the properties of the stationary solutions of the general kinetic equations are analyzed.