The evolution of a spatially homogeneous unstable plasma is investigated. A complete expression for the plasma wave contributions to the kinetic equation for f(v; t) (the velocity distribution) is derived under the usual plasma approximations (mode-coupling effects are ignored) and in the treatment of f(v; t) as slowly varying in time. The equation has a characteristic dependence on the initial correlation. It can alternatively be written in the form of simultaneous equations which in the limit of weak instability agree in form with the Pines-Schrieffer equations. Applicability of the various forms of the equation is discussed. In particular, it is shown that the stabilization process can be studied by the simultaneous equations derived in this paper, but not by any kinetic equation for f(v; t) obtainable within the ring approximation.
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Nishikawa et al. (1965) studied this question.