Integral Boltzmann equation in the study of diffusion of test particles

• DOI: 10.1007/bf02728613
• Publication Date: 2007-12-18T09:13:53Z
• Authors: V. C. Boffi; V. G. Molinari
• Keywords: 0103 physical sciences; 01 natural sciences

The problem of test particles which, in the presence of an external conservative force, diffuse through a random distribution of field particles, is extensively studied by resorting to an appropriate integral form of the linearized Boltzmann equation. In particular, under the hypothesis of isotropic scattering and of a constant external force, a set of two linear integral equations governing the distributions of the total density and of the total flux vector, respectively, is formulated, and it is then shown how the relevant scattering kernels—in which the contribution of the scattering is separated from the one due to the creation by collision—can be evaluated in general. For a simple physical situation exact solutions are at last presented for both stationary total density and total flux vector as well as for the electrical conductivity. Numerical results are also reported.