Asymptotic theory of the linear transport equation in anisotropic media

作者：Sanchez Richard^*; Ragusa Jean; Masiello Emiliano

来源：Journal of Mathematical Physics, 2008, 49(8): 083504.

DOI：10.1063/1.2966094

We consider linear transport in an anisotropic medium with velocity dependent cross sections sigma(r, v, t) and scattering kernel P(r, v' --> v, t). We introduce a scaling in terms of a small parameter epsilon, where the leading-order term describes an equilibrium in velocity space between collisions with a cross section that is an even function of v and scattering modes even-even and odd-odd in v and v'. We show that the asymptotic solution of the transport equation leads to a diffusion equation with a drift term with an error in epsilon(2) and derive consistent initial and boundary conditions from the analysis of the initial and boundary layers. The analysis of the drift terms shows that they result from anisotropic interactions with the medium and also from streaming between neighboring but different equilibria. The restriction of our results to isotropic media yields back the Larsen-Keller diffusion equation, while the one-speed form reduces to the result obtained by Pomraning and Prinja [Ann. Nucl. Energy 22, 159 (1995)] for the particular case of isotropic cross sections with an "output" scattering kernel P(r, Omega, t).

• 出版日期2008-8
• 单位中国地震局