On the energy spectrum evolution of electrons undergoing radiation cooling

Radiative cooling of electron beams interacting with counter-propagating electromagnetic waves is analyzed, taking into account the quantum modification of the radiation friction force. Central attention is paid to the evolution of the energy spectrum of electrons accelerated by the laser wake field acceleration mechanism. As an electron beam loses energy to radiation, the mean energy decreases and the form of the energy distribution also changes due to quantum-mechanical spectral broadening.