Abstract
The problem of the electron beam energy spread damping using the linear back Compton scattering process is considered in the paper. The adjoint kinetic equation for the electron energy distribution is used to get the equations for the mean energy and for the energy distribution variance. The equations for the distribution moments are obtained and solved by an iteration method. It is shown that the variance of the energy distribution has a maximum at some value of light target thickness for the electron beams with small incident energy spread. The problem of radiation cooling in the laser-electron storage ring is discussed. The data of approximate analytical calculations agree with the results of the Monte Carlo simulation.
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