Analytical theory of energy relaxation upon propagation of a high-energy electron beam in gas

This study is devoted to the development of an analytical theory for calculating the spatial distribution of the energy release upon propagation of a high-energy ($1$–$100$ keV) electron beam in a gas (based on the example of air). Based on the analysis of data on the cross sections of elastic and inelastic interactions between electrons and molecules of gases that are in the air composition, it was suggested that inelastic interaction causes energy relaxation, whereas elastic interaction leads to momentum relaxation. The model cross section of inelastic collisions of electrons with molecules is used for solving the Boltzmann kinetic equation for electrons; this cross section provides adequate description of the experimentally found energy dependence of the mass stopping power of electrons. The results for the dependence of the mean electron energy on the number of inelastic collisions are in good agreement with the results of calculation based on expansion of the distribution function in the number of collisions and solution by the Monte Carlo method. The calculations we performed show that the consideration of elastic collisions increases the spatial density of the energy release due to narrowing of the region where the main part of the energy of fast electrons is released, in comparison with calculations where only inelastic deceleration is taken into account.