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

Naoufel Ben Abdallah; Raymond El Hajj

doi:10.3934/krm.2008.1.331

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2008, Volume 1, Issue 3: 331-354. Doi: 10.3934/krm.2008.1.331

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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

Received: March 31, 2008

Revised: May 31, 2008

Published: August 2008

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Abstract

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.

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Mathematics Subject Classification: Primary: 35B25, 35B40, 82C40, 82C70, Secondary: 82D10.

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