Kinetic Equations of Dilute Electron Plasmas in the Coherent Region

On the basis of the scale covariance of the correlation functions under a space-time coarse graining, kinetic equations are studied in the coherent region where the space-time cutoff (b, t,) satisfies l..n;pb;;,r,, 1/wp;;,t,;;,r, with 1-n being the Debye length, Wp the plasma frequency, ro the Landau cutoff and ro the corresponding time scale. A generalized Vlasov equation with a collision term is derived from the BBGKY hierarchy equations by using Mori's scaling method in an extended form. This collision term consists of three terms; the Boltzmann term, the Landau term and a new collision term which differs from the Balescu-Lenard term. An evolution equation for the two-particle correlation function is also derived. The kinetic equations in the kinetic region where l..n«:_b«:_lr, 1/wp«:_t,«:_rr with lr and rr being the mean free path and time, respec-tively, are derived from these equations by introducing a further space-time coarse graining. Thus it is shown that the generalized Vlasov equation derived here reproduces the Balescu-Lenard-Boltzmann-Landau equation in the kinetic region correctly