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Calculations are presented for the femtosecond time-evolution of intensities of beams diffracted by perfect Bragg crystals illuminated with radiation expected from X-ray free-electron lasers (XFELs) operating through the self-amplified spontaneous emission (SASE) process. After examining the case of transient diffraction of an electromagnetic delta-function impulse through flat, single- and double-crystal monochromators, the propagation of a 280 fs-duration SASE XFEL pulse of 8 keV photons through the same optics is discussed. The alteration of the sub-femtosecond spiky microbunched temporal structure of the XFEL pulse after it passes through the system is shown for both low-order (broad bandwidth) and high-order (narrow bandwidth) crystal reflections. Finally, the shot-to-shot statistical fluctuations of the integrated diffracted intensity is simulated. Implications of these results for XFEL applications are addressed.

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