Multiphoton stimulated Compton laser

When Compton backscattering (head to head collisions) arises between a relativistic electron beam and one of two intense counterpropagating laser beams, electrons are mainly scattered by the laser beam from the reverse direction and can hardly interact with the other laser beam propagating in the same direction. Thus, the interaction of electrons with the latter laser beam, which induces stimulated Compton scattering, can be treated as a perturbation. With perturbation theory, we calculate the probability of stimulated emission and absorption of the photons by electrons in two intense counterpropagating laser beams. The results demonstrate that stimulated emission or absorption is significant only if the momenta of photons and the energy of the electron satisfy certain condition. We also formulate the gain coefficient of the multiphoton stimulated Compton laser, which is sensitive to the intensity of the pumping laser and the energy spread of the electron beam.