Kinetic Equations for Turbulent Plasmas. I. Quasilinear Theory

The Vlasov equation is not applicable for those turbulent plasmas in which certain higher-order correlation functions may play just as important a part as the single-particle distribution function. We construct the many-particle distribution functions by summing certain selected products of the single-particle distribution functions and the pair correlation functions, and show that, in the Rostoker-Rosenbluth fluid limit, those distribution functions satisfy the Bogoliubov-Born-Green-Kirkwood-Yvon (BBGKY) hierarchy and enable us to truncate it at the second equation. The resulting equations contain an asymmetric feature in that the single-particle distribution function develops in time with inclusion of the correlation effects in the collision term, while the time evolution of the pair correlation function is governed by a solution of the linearized Vlasov equation. It is shown explicitly that those kinetic equations become identical to the quasilinear equations without mode coupling if the contribution of the growing plasma oscillation is singled out in the pair correlation function.