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Title: Shortest wavelength at which a self-amplified FEL can saturate
Plain: Lasing at shorter wavelengths requires more energetic electrons, but these radiate randomly in the magnets, which spreads their energies and stops the lasing.
Precise: 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.
Settled by: An optimization over beam and undulator parameters including quantum diffusion and emittance growth, giving the minimal wavelength.
Kind: well-posed
Answer type: value
References: (empty)
Literature status: open
Status note: (empty)
Posed since: (empty)