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

In electron microbeam techniques, the particle beam is focused on the mater ial to be analysed. When the election beam enters the target, the electrons give rise to ionization processes producing secondary electrons and photon s, the latter being used to characterize the material. As a consequence, a detailed description of the photon diffusion requires the solution of two c oupled 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 ele ctron transport equation. In this article, an alternative approach is sugge sted which is based on the use of an approximate solution for the electron transport using the Fokker-Planck equation [5]. The resulting electron dist ribution, computed analytically as a solution of the above equation, is ver y similar to the ionization distribution and is used as the source term in the Boltzmann transport equation describing the photon diffusion in the mat erial. The 3D photon transport equation for unpolarised photons with this s ource term is solved to obtain a detailed description of the photon fluores cence from a homogeneous slab.