High-field limit of the Vlasov-Poisson-Fokker-Planck system: A comparison of different perturbation methods

Details High-field limit of the Vlasov-Poisson-Fokker-Planck system: A comparison of different perturbation methods High-field limit of the Vlasov-Poisson-Fokker-Planck system: A comparison of different perturbation methods

2000-07-10

arxiv.org/abs/cond-mat/0007164v1

Math. Mod. Meth. Appl. Sci. 11 (8), 1457-1468 (2001)

Physics

Condensed Matter

Statistical Mechanics

6 pages, 2 column Revtex

Scientific paper

A reduced drift-diffusion (Smoluchowski-Poisson) equation is found for the electric charge in the high-field limit of the Vlasov-Poisson-Fokker-Planck system, both in one and three dimensions. The corresponding electric field satisfies a Burgers equation. Three methods are compared in the one-dimensional case: Hilbert expansion, Chapman-Enskog procedure and closure of the hierarchy of equations for the moments of the probability density. Of these methods, only the Chapman-Enskog method is able to systematically yield reduced equations containing terms of different order.

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