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September  2008, 1(3): 387-404. doi: 10.3934/krm.2008.1.387

On the slowing down of charged particles in a binary stochastic mixture

Jean-François Clouet 1, , François Golse 2, , Marjolaine Puel 3, and  Rémi Sentis 1,

1. 

CEA/Bruyères, Bruyères-le-Chatel, 91297 Arpajon Cedex, France, France
2. 

Centre de Mathématiques, Ecole Polytechnique, 91128 Palaiseau Cedex, France
3. 

Laboratoire MIP, Université paul Sabatier, 31062 Toulouse, France

Received  January 2008 Revised  June 2008 Published  August 2008

A kinetic equation is addressed for the straight line slowing-down of charged particles, the geometrical domain consists of randomly distributed spherical grains of dense material imbedded in a light material. The dense material is assumed to be a Boolean medium (the sphere centers are sampled according to a Poisson random field). We focus on the fraction of particles $P$ which stop in the light medium. After setting some properties of the Boolean medium, we perform an asymptotic analysis in two extreme cases corresponding to grain radius very small and very large with respect to the stopping distance of the dense material. A fitted analytic formula is proposed for the quantity $P$ and results of numerical simulations are presented in order to validate the proposed formula.
Keywords: Particle slowing-down, Stochastic geometry., Poisson germ-grain random set, Boolean medium, Underwood theorem, Partial differential equation in random media, Mean chord length.
Mathematics Subject Classification: Primary: 35Q72, 60D05 . Secondary: 65C0.
Citation: Jean-François Clouet, François Golse, Marjolaine Puel, Rémi Sentis. On the slowing down of charged particles in a binary stochastic mixture. Kinetic and Related Models, 2008, 1 (3) : 387-404. doi: 10.3934/krm.2008.1.387
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