Coherent radiation characteristics of modulated electron bunch formed in stack of two plates

The present article is devoted to the radiation from the electron bunch with modulated density passes through the stack consisting of two plates with different thicknesses and electrodynamic properties. The new elegant expression for the frequency-angular distribution of transition radiation is obtained. Using the existence of resonant frequency at which the longitudinal form-factor of bunch not suppresses radiation coherence and choosing parameters for the stack of plates, one can also avoid suppression of the radiation coherence by transverse form-factor of bunch. The radiation from a bunch with modulated density in the process SASE (self-amplified spontaneous emission) FEL can be partially coherent at a resonant frequency. Then the intense sub monochromatic beam of X-ray photons is formed. On the other hand one can define an important parameter of the bunch density modulation depth which is unknown to this day.