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This paper describes how to efficiently solve time-dependent x-ray dynamic diffraction problems in distorted crystals with an FFT-based beam propagation method (FFT BPM). We show examples of using the technique to simulate the propagation of x-ray beams in deformed crystals in space and time domains relevant to the cavity-based x-ray Free Electron Lasers (CBXFELs) and XFEL self-seeding systems.

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