Stochastics of Multiple Electron-Photon Head-on Collisions

The problem of stochastis in multiple electron-photon head-on collisions has been considered in this paper. The kinetic equations for the distributions over the electron energy and collisions number along with the equations for these distributions moments have been obtained. The equations for the first moments have been solved by the iteration method. It has been shown that the variance of the energy distribution as a function of the mean number of collisions has a maximum at some value of $\bar n$. It is seen from this analysis that multiple scattering of electrons influences on the spectra both electrons and photons even for the photon target of small thickness. The data of approximate analytical calculations agree with the results of the Monte Carlo simulation.