Wavefront sensing at a high-repetition-rate X-ray free-electron laser.

Wavefront characterization is essential for diagnosing, interpreting and mitigating performance limitations at X-ray free-electron lasers (XFELs). However, the dramatic increase in thermal load and data throughput at high repetition rates makes established wavefront characterization methods difficult to implement effectively. Here, we demonstrate that X-ray speckle arising from beamline optics can enable fast, robust and sensor-free wavefront metrology at next-generation XFEL facilities. Combining this approach with a statistical formulation of X-ray speckle tracking, we quantify local wavefront fluctuations within pulse trains at the European XFEL. We find that shot-to-shot wavefront fluctuations are predominantly planar phase tilts with distinct statistical signatures across intra- and inter-train timescales. The dominant source of wavefront error is periodic at frequencies consistent with known mechanical oscillation modes of the photon transport optics, while intra-train fluctuations correlate with instabilities in the electron bunch trajectory. Our results establish a practical framework for high-repetition-rate wavefront characterization and diagnostics at next-generation XFELs.