Asymptotic and Numerical Analysis of Charged Particle Beams.

Paper in proceeding, 2003

We study a model for a single particle moving through a homogeneous background medium. Starting with a transport process for the electron particles we derive ($i$) the Fokker-Planck equation using asymptotic expansions, (assuming small mean free path), then ($ii$) the Fermi equation by yet another asymptotic expansion assuming (in addition to small mean free path) small angular deviations. Finally ($iii$) we discuss some numerical solutions of a simplified 2-dimensional Fermi equation.