Shortest wavelength at which a self-amplified FEL can saturate
In plain words
Lasing at shorter wavelengths requires more energetic electrons, but these radiate randomly in the magnets, which spreads their energies and stops the lasing.
Precise statement
For a SASE FEL with electron energy $\gamma m c^2$, normalized emittance eps_n, slice energy spread $\sigma_E$, undulator period $\lambda_u$ and parameter $K$, quantum diffusion from incoherent undulator radiation grows $\sigma_E^2$ at a rate $\sim \gamma^4 K^2 F(K)/\lambda_u^3$. Find the minimal resonant wavelength at which saturation is reachable for eps_n >= 1e-5 cm and realistic undulator technology, and whether lasing at photon energies above $100\,\mathrm{keV}$ is possible.
What would settle it
An optimization over beam and undulator parameters including quantum diffusion and emittance growth, giving the minimal wavelength.