Electron Energy Spread in Laser Cooling Process

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.