Diffusion and guiding center approximation for particle transport in strong magnetic fields

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September 2008, 1(3): 331-354. doi: 10.3934/krm.2008.1.331

Diffusion and guiding center approximation for particle transport in strong magnetic fields

Naoufel Ben Abdallah ^1, and Raymond El Hajj ^1,

1.	Institut de Mathématiques de Toulouse, Université de Toulouse and CNRS, Université Paul Sabatier, 31062 Toulouse Cedex 9, France, France

Received April 2008 Revised June 2008 Published August 2008

Abstract
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The diffusion limit of the linear Boltzmann equation with a strong magnetic field is performed. The giration period of particles around the magnetic field is assumed to be much smaller that the collision relaxation time which is supposed to be much smaller than the macroscopic time. The limiting equation is shown to be a diffusion equation in the parallel direction while in the orthogonal direction, the guiding center motion is obtained. The diffusion constant in the parallel direction is obtained through the study of a new collision operator obtained by averaging the original one. Moreover, a correction to the guiding center motion is derived.

Keywords: Diffusion limit, high magnetic field., guiding-center approximation.

Mathematics Subject Classification: Primary: 35B25, 35B40, 82C40, 82C70, Secondary: 82D1.

Citation: Naoufel Ben Abdallah, Raymond El Hajj. Diffusion and guiding center approximation for particle transport in strong magnetic fields. Kinetic & Related Models, 2008, 1 (3) : 331-354. doi: 10.3934/krm.2008.1.331

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