Kinetic theory of a weakly unstable plasma

Abstract

The evolution of a weakly unstable spatially uniform classical plasma is studied. Two methods are used. In the first method the nonlinear Vlasov equation is solved by a rigorous expansion technique with two small parameters γ k ω k and E k 2 nκT , where γ k and ω k are the growth rate and frequency of the unstable modes with wave vector k, and E k is a typical amplitude of the electric field in the unstable modes. This leads to a quasi-linear theory in which mode coupling effects are important and these are fully discussed. In the second method the problem is considered on the basis of a kinetic theory developed from the B-B-G-K-Y hierarchy of equations. In this case a further expansion parameter is 1 nλ d 3 , where n is the number density and λ d the Debye length. It is shown that the Balescu-Lenard kinetic theory may be modified to include instabilities provided the field fluctuations in the unstable modes are correctly treated by a nonlinear theory which again includes mode-coupling effects. The two methods are compared and discussed.