Quantum based overall frequency dependence of induced Bremsstrahlung amplification

Qunantum electrodynamic perturbation technique is used to derive the transition rates of emission and absorption of photons by passing an electron beam through a transverse wiggler magnetic field without any additional assumptions such as of virtual photons, of virtual Compton scattering, etc. In this simplified model we show that there exists a net gain over the broad range of photon energies from infrared through short wavelength of X-rays, which decreases as the inverse square root of photon frequency in a fixed period of a magnetic wiggler array arrangement.