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A broadband energy-chirped hard X-ray pulse has been demonstrated at the SwissFEL (free electron laser) with up to 4% bandwidth. We consider the characteristic parameters for analyzing the time dependence of stationary protein diffraction with energy-chirped pulses. Depending on crystal mosaic spread, convergence, and recordable resolution, individual reflections are expected to spend at least ≈ 50 attoseconds and up to ≈ 8 femtoseconds in reflecting condition. Using parameters for a chirped XFEL pulse obtained from simulations of 4% bandwidth conditions, ray-tracing simulations have been carried out to demonstrate the temporal streaking across individual reflections and resolution ranges for protein crystal diffraction. Simulations performed at a higher chirp (10%) emphasize the importance of chirp magnitude that would allow increased observation statistics for the temporal separation of individual reflections for merging and structure determination. Finally, we consider the fundamental limitation for obtaining time-dependent observations using chirped pulse diffraction. We consider the maximum theoretical time resolution achievable to be on the order of 50–200 as from the instantaneous bandwidth of the chirped SASE pulse. We then assess the ability to propagate ultrafast optical pulses for pump-probe cross-correlation under characteristic conditions of material dispersion; in this regard, the limiting factors for time resolution scale with crystal thickness. Crystals that are below a few microns in size will be necessary for subfemtosecond time resolution.

Applications and Limits of Time-to-Energy Mapping of Protein Crystal Diffraction Using Energy-Chirped Polychromatic XFEL Pulses