{"schema":"pubphys.bundle/1","record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"a881a613a42ba254d951dedffe807df9f0b598cc126d420a0f6cb7977d6196d9","created":"2026-10-03T07:17:56Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["5475cf5dc5b1a72283d26dc95dc6e00d7ea4e00096a7c6492e409a1816eeb011"],"salt":"5c2bbbfcdf712a1833ca8fecfaaa806c6264757584a36d0ed92d46c7a7744de7","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"yes-no","assisted_by":[],"external_id":"beams.fel-physics.xfelo-gain","kind":"well-posed","literature_status":"partially-resolved","n":"1","parents":[],"plain":"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.","posed_since":"2008","precise":"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 $\\sim 85\\ \\mathrm{percent}$ 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 $\\sim 1e-7$ can be obtained with existing high-repetition-rate linac beams, given crystal heat load and cavity alignment stability.","problem_ref":null,"references":"","settled_by":"Observation of exponential growth of stored x-ray pulse energy over many successive passes, followed by saturation.","status_note":"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.","title":"Exponential growth to saturation in a hard x-ray FEL 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