The Possible Maximum Gain in Laser Electron Scattering

Following Madey’s calculations on the possible gain induced by stimulated radiation in Free Electron Laser(FEL), we derive the possible maximum gain in laser electron scattering basing on Quantum Electrodynamic(QED) in laser field via introducing the initial state density of laser electron system and the transition rate into a definite final photon state in laser electron scattering. The parameters of laser electron scattering experiments where X-ray or \gamma -ray photons were succesfully obtained are used to calculate the possible maximum gain in laser electron scattering, and the results are compared with that in the first lasing X-ray FEL(XFEL). The calculations show that if laser undulator FEL were built according to the existing experimental conditions in those laser electrons scattering experiments, the possible maximum gain would be much lower than that in the first lasing XFEL. While we have found appropriate parameters to achieve a relatively high gain when the wavelength of incident light is in radio frequency range.