We study a simplified model of the Fokker-Planck equation of plasma physics. This model only involves a linear angular diffusion for a monoenergetic beam. We discuss the problem of existence and uniqueness of solutions in both the evolution and the stationary cases; Then we justify the diffusion approximation, with either the Dirichlet, or the Robin boundary conditions. For that purpose, we are led to give some results on the Milne problem and to compute the extrapolation length.
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Degond et al. (1987) studied this question.
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