Applied Physics and Mathematics Annotation << Back Cascade degradation processes Part 3. Cascade degradation processes: spatial problem Nikerov V.A. The analytical model of the generalized diffusion of fast particles is formulated for a wide range of cascade degradation processes. The generalized diffusion model provides the possibility of calculation with precision 10–30% of the mean free path along the coordinate of the accelerated electrons and photons in a wide range of particle energies and media parameters, as well as the estimation of distribution of the mean free paths, of the energy input, and the fast particle relaxation time. This model is based on an analysis of the practical applicability of the limiting cases of diffusion and straightforward propagation of fast particles, as well as the creation of a generalized model that includes the linking of limiting cases. The main attention is paid to the integral characteristics that are most important for the transport of fast particles. As a basic example the nonrelativistic and relativistic electron beams transport in a various characteristic gas, plasma and solid media is considered in details. The principle difference of fast particles beams transport in thin and thick layers of media, as well as features of the beams reflection from the scattering media are shown. The reflection coefficients of the accelerated electrons and photons from various media are calculated using the diagrams method, with the straightforward approximation used as the zero approximation. The maximum thickness of the thin layer is calculated. It is shown that the use of thin layers formulas for transport in thick layers can produce five times higher values. The typical error of electrons mean free path along the coordinate calculations, which is caused by incorrect use of the average atomic number of the substances and mixtures consisting of atoms with substantially different charge number is analyzed. It is shown that this can lead to overstating electrons mean free path along the coordinate up to 10...23 %. Keywords: accelerated electrons, photons, generalized diffusion, straightforward approximation, volume reflection coefficient. Contacts: E-mail: Vnikerov@hse.ru Pp. 23-38.