Kinetic Equations of Dilute Electron Plasmas in the Coherent Region

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Abstract
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, tc) satisfies λD≫b≫r0, 1/ωp≫tc≫τo with λD being the Debye length, ωp the plasma frequency, r0 the Landau cutoff and τ0 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 λD≪b≪lf, 1/ωp≪tc≪τf with lt and τt being the mean free path and time, respectively, 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.

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