Fokker-Planck modeling for particle slowing down and Maxwellian distribution

In this paper the Fokker-Planck equation, which takes into account the medium absorbtion and the Maxwellian behavior of the field particles at low energy for Coulomb interactions is obtained. The analytical solution of the stationary distribution function is obtained in angle and velocity variables. In particular the electron distribution for electron-ion collisions has been obtained using this diffusion approximation for beam and isotropic sources. If the absorption is neglected the solution recovers the classical stationary Maxwellian distribution. For low absorption rates the solution shows a typical slowing down spectrum for high energy and a Maxwellian-like distribution at thermal energy. For moderate and high absorption rates the test particles do not reach the thermal equilibrium and the Maxwellian distribution does not appear.