Exponential growth to saturation in a hard x-ray FEL oscillator
In plain words
An x-ray FEL oscillator traps x-rays between diamond crystal mirrors and amplifies them on every pass, which would give a fully coherent, very narrow-band beam; amplification over a few passes has been seen, but steady growth to a stable, saturated output has not.
Precise statement
In an x-ray FEL oscillator, hard x-ray pulses of photon energy $\sim 5\text{-}15\ \mathrm{keV}$ circulate in a Bragg-crystal cavity with round-trip reflectivity above $\sim 85\%$ and are amplified by successive electron bunches synchronized with the round trip. Determine experimentally whether round-trip gain exceeding total cavity loss, sustained exponential growth over many passes, and saturation with relative bandwidth $\sim 10^{-7}$ can be obtained with existing high-repetition-rate linac beams, given crystal heat load and cavity alignment stability.
What would settle it
Observation of exponential growth of stored x-ray pulse energy over many successive passes, followed by saturation.
Status in the literature
Unverified note: it names recent work and was partly written without a live literature search; it awaits a check by an editor.
Spectral narrowing and proof-of-concept multi-pass amplification were reported at the European XFEL demonstrator (Li, Rauer, Huang, Deng, review arXiv:2608.15244, https://arxiv.org/abs/2608.15244, 2026); sustained growth to saturation is not reported.
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