Can XFELs produce stable transform-limited hard X-ray pulses?
In plain words
The best possible laser pulse has the narrowest color range allowed by its duration. Whether hard X-ray lasers can reach that limit shot after shot is open.
Precise statement
Determine whether a seeded or cavity-based XFEL at photon energy $> 5\ \mathrm{keV}$ can deliver pulses with time-bandwidth product within 1.5 times the transform limit and pulse-to-pulse energy fluctuation below a few percent, given shot noise and microbunching in the electron beam.
What would settle it
Single-shot spectral and temporal measurements of a hard X-ray FEL meeting the stated criteria over many shots.
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