Time evolution analysis of the electron distribution in Thomson/Compton back-scattering

We present the time evolution of the energy distribution of a relativistic electron beam after the Compton back-scattering with a counter-propagating laser field, performed in the framework of the Quantum Electrodynamics, by means of the code CAIN. As the correct angular distribution of the spontaneous emission is accounted, the main effect is the formation of few stripes, followed by the diffusion of the more energetic particles toward lower values in the longitudinal phase space. The Chapman-Kolmogorov master equation gives results in striking agreement with the numerical ones. An experiment on the Thomson source at SPARC-LAB is proposed.