2000/07/10 by L. L. Bonilla, J. Soler
Physics and Astronomy · #cond-mat.stat-mech
published as Math. Mod. Meth. Appl. Sci. 11 (8), 1457-1468 (2001) · 6 pages, 2 column Revtex
arxiv created 2000/07/10 · arxiv updated 2009/11/30
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.