On synchrotron radiation spectrum in classical and quantum mechanical limits

The spectrum of the synchrotron radiation called ''beamstrahlung'' is an universal function of the photon energy divided by the parameter E-c called ''critical energy''. This paper presents the spectrum for both the classical regime, when the electron beam energy, E, is bigger than the critical energy, and the quantum regime, when the beam energy is less than the critical energy. Results of the calculations show that, in the latter case, less beamstrahlung is emitted than with the classical one.