Quantum self-amplified spontaneous emission regime of the x-ray Compton laser

In this work we consider in general the high-gain SASE x-ray Compton FEL in the quantum regime of amplification arising from the self-consistent set of the Maxwell and relativistic quantum kinetic equations. The analytical solutions are obtained which are valid before the saturation. The quantum seed-shot noise and subsequent SASE power are calculated. A considerable increase in start-up and narrowing of the spectrum of the SASE power for amplifying x-ray frequencies is shown compared with the classical SASE regime.