Eur. Phys. J. D 60, 301-307 (2010)
https://doi.org/10.1140/epjd/e2010-00190-8

Angular moment model for the Fokker-Planck equation

¹ Centre Lasers Intenses et Applications, Université Bordeaux 1 - CNRS - CEA, 351, Cours de la Libération, 33405 Talence Cedex, France
² MMATHCCES, Department of Mathematics RWTH, Aachen University, Schinkelstr. 2, 52062 Aachen, Germany

Corresponding author: ^a feugeas@celia.u-bordeaux1.fr

Received: 24 April 2010
Revised: 11 June 2010
Published online: 27 July 2010

Abstract

An accurate and rapid kinetic model describing the collisional transport of particles is presented. It is derived from the Fokker-Planck equation and involves an angular closure in the phase space leading to a set of hyperbolic equations for the moments of the distribution function evolving in time, space and energy. This method provides an alternative to the prohibitive cost of a direct solution to the full kinetic equation. Moreover, it is exact for the cases of collimated beams and the quasi-isotropic distributions. It can be approximated with the usual numerical schemes of the non-linear hyperbolic analysis. This model has features that are required to simulate the electron or ion transport for the inertial confinement fusion and the dose deposition for radiation therapy of cancers.