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Using the methods of statistical optics the formation of delayed X-ray pulses in the diffraction reflection of an incident pulse with an arbitrary degree of temporal coherence from a system of parallel crystals with different lattice periods is considered. The results are of interest for constructing delay lines in experiments with a time resolution of the pump-and-probe type and realizing of the self-seeding mode to increase the degree of temporal coherence of the X-ray free-electron laser radiation.
A rigorous theory of dynamic diffraction in Bragg geometry is applied to the diffraction reflection of short X-ray pulses from a system of two parallel crystals with arbitrary thicknesses, and also, for a system of two pairs of parallel crystals. The dependence of the delay time and the intensity of the delayed pulses on the thickness of the crystals and the distances between them are analyzed. Since the pulses from the X-ray free electron laser have high spatial coherence, i.e. a small angular divergence, but very poor temporal coherence, special attention is paid to the effect of the degree of temporal coherence on the width of the energy spectrum of the incident pulses and on the influence of this width on the intensity of the delayed pulses.
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