Quantum Kinetic Equations for Unstable Plasmas

Abstract

A treatment of the transport equation for a classical unstable electron plasma by K. Nishikawa and Y. Osaka [Progr. Theoret. Phys. (Kyoto) 33, 402 (1965)] is extended to the quantum-mechanical multicomponent case. The quantum Bogoliubov-Born-Green-Kirkwood-Yvon hierarchy of equations is truncated at the second stage, and the technique due to Dupree is employed. In the limit of weak instability, the kinetic equation, that proves to be the direct extension of the classical case, can be rewritten in the form of a set of simultaneous equations, the form of which agrees completely with the equations proposed by Pines and Schrieffer.