Method of the equivalent photons for modulated electron beam

Abstract

It is shown in this work that electromagnetic self-field of the periodically density modulated electron bunch can be considered as the beam of the equivalent photons (pseudo-photons), collimated along the electron velocity. Pseudo-photon spectrum includes both the incoherent contribution being proportional to number of electrons in the bunch and the coherent part with the sharp maximum corresponding the modulation frequency. Method of the equivalent photons can be applied for description of the interaction between the electron bunch and a crystal that leads to generation of the coherent parametric X-ray radiation by the modulated bunches exited from the undulator of the X-ray free electron laser. It provides the possibility to obtain the X-ray pulses directed at the large angle to the electron velocity where intensity of the background radiation essentially decreased. It is defined the conditions when the spectral and angular distributions of the coherent pseudo-photons can be compared with the analogous values for the pulses of the X-ray laser.