Evolution of the energy and momentum distribution of electron beam in the gamma-ray laser synchrotron sources

Evolution of the relativistic electron beam in the laser-beam Compton scattering was investigated. The quantum kinetic equation for the electron beam distribution function is derived in the frame of the Klein–Gordon field theory. When the beam energy spread exceeds the energy of scattered photons, this equation is reduced to the diffusion-like kinetic equation which describes the laser cooling of electron beam and includes quantum fluctuations limiting the cooling process. In the opposite limit of high beam energies, we describe the evolution of transverse beam emittance in the laser-beam Compton scattering.