Influence of the phase distribution on the coherent radiation of a relativistic beam in synchrotron and ondulator

The article presents a derivation of a formula for the intensity of radiation due interference in a synchrotron and undulator. It is shown that the radiation intensity is a function of the parameters of the coordinate and velocity distribution of particles. Exponential damping of radiation at high frequencies is controlled by the ratio of the minimum spatial parameter of the beam to the emitted wavelength.