{"schema":"pubphys.bundle/1","record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"a6af6290bf3e4c6a3d590b8194f5b9ff7b83156f591c5ca24aed533ac6a9bcd0","created":"2026-10-03T07:17:56Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["5475cf5dc5b1a72283d26dc95dc6e00d7ea4e00096a7c6492e409a1816eeb011"],"salt":"d318285e31e11fe767fac1fe1a9a11a59bcb203c3306467b714b32795d8476cd","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"value","assisted_by":[],"external_id":"beams.fel-physics.shortest-sase-wavelength","kind":"well-posed","literature_status":"open","n":"1","parents":[],"plain":"Lasing at shorter wavelengths requires more energetic electrons, but these radiate randomly in the magnets, which spreads their energies and stops the lasing.","posed_since":"","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.","problem_ref":null,"references":"","settled_by":"An optimization over beam and undulator parameters including quantum diffusion and emittance growth, giving the minimal wavelength.","status_note":"","title":"Shortest wavelength at which a self-amplified FEL can 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