Mathematical modelling of 3D electron-photon transport in microbeam analysis

In electron microbeam techniques, the particle beam is focused on the material to be analysed. When the electron beam enters the target, the electrons give rise to ionization processes producing secondary electrons and photons, the latter being used to characterize the material. As a consequence, a detailed description of the photon diffusion requires the solution of two coupled equations describing respectively electron and photon diffusion. The approach considering two transport equations, even if formally correct, is almost unaffordable because of the high mathematical complexity of the electron transport equation. In this article, an alternative approach is suggested which is based on the use of an approximate solution for the electron transport using the Fokker-Planck equation [5]. The resulting electron distribution, computed analytically as a solution of the above equation, is very similar to the ionization distribution and is used as the source term in the Boltzmann transport equation describing the photon diffusion in the material. The 3D photon transport equation for unpolarised photons with this source term is solved to obtain a detailed description of the photon fluorescence from a homogeneous slab. © Springer-Verlag 2000.