Bunch coherence in parametric X-ray radiation

The amplitude of Parametric X-ray radiation emitted coherently by a bunch of electrons crossing a crystal (CPXR) is calculated. When the bunch density is modulated with a longitudinal period close to the X-ray wavelenght, constructive many-electron interferences enhance the intensity by Nb * |F(K)|^2, where Nb is the number of electrons in the bunch, F(K) the bunch form factor and K a specified wave vector. CPXR can be used to test the microbunching in a X-ray free-electron laser.