We use numerical modeling to study the features of parametric (quasi-Cherenkov) cooperative radiation arising when an electron bunch passes through a crystal (natural or artificial) under the conditions of dynamical diffraction of electromagnetic wav
es in the presence of shot noise. It is shown that in both Laue and Bragg diffraction cases, parametric radiation consists of two strong pulses: one emitted at small angles with respect to the particle velocity direction and the other emitted at large angles to it. Under Bragg diffraction conditions, the intensity of parametric radiation emitted at small angles to the particle velocity direction reaches saturation at sufficiently smaller number of particles than the intensity of parametric radiation emitted at large angles. Under Laue diffraction conditions, every pulse contains two strong peaks, which are associated with the emission of electromagnetic waves at the front and back ends of the bunch. The presence of noise causes a chaotic signal in the interval between the two peaks.
Time evolution of the parametric X-Ray radiation, produced by a relativistic charged particle passing through a crystal, is studied. The most attention is given to the cases when the radiation lasts much longer (t_{PXR} ~0.1 ns) than the the time t_p
of the particle flight through the crystal (t_p ~ 1 ps). It is shown that such long duration of the radiation makes possible the detailed experimental investigation of the complicated time structure of the parametric X-ray pulses, generated by electron bunches, which are available with modern acceleration facilities.
