  The problem of electrons energy spread in the linear back Compton scattering
process has been considered in the paper. The adjoint kinetic equation for the
electrons passing through a laser flash has been obtained and used to get the
equations for the mean energy and the variance of the energy distribution. The
equations for the distribution moments have been obtained and solved by the
iteration method in the continuous slowing down approximation with approximate
description of the energy loss fluctuation. It has been shown that the variance
of the energy distribution as a function of the electron - photon collisions
number in laser flash has a maximum for the electron beam with small incident
energy spread. The beam energy spread damping in the laser-electron storage
ring has been studied. The data of approximate analytical calculations are
compared with the results of the Monte Carlo simulation.
