{"record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"1d888087a4c52636738160392f528ad1589ccab8eafdb3be78975c2282def958","created":"2026-10-15T23:43:22Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["cb0bad839d0d7d62952477778f20b1c7de116db2f973e1eb77266a8bca992ca0","ce59fb6cd812fc05906d0c60a71c75ea22bc686bcf38e7c3ef7010834d98ee7b"],"salt":"e06bf9e84d66ee65c724b66f2158e5ec2807ede547ea2c0d8f01559767793334","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":"2","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 >= $10^{-5}$ cm and realistic undulator technology, and whether lasing at photon energies above $100\\,\\mathrm{keV}$ is possible.","problem_ref":"cb0bad839d0d7d62952477778f20b1c7de116db2f973e1eb77266a8bca992ca0","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 saturate","topic_ref":null},"attested":{"attestation":{"batch":null,"client_id":null,"id_token_sha256":null,"kind":"platform"},"record_hash":"3cfe626170f5f103df16871a9a1e81d6edd4170ca3abf50a9074c7af035df4d3","schema":"pubphys.attested/1"},"envelope":{"attested_hash":"967d540c864ca41d662e659a9866bf05662d3c859f417476500dbff5707089be","platform_signature":{"key_id":"c6afc19b31429869751f06879c75cd64ea92654423d15b44be775bf1310a60da","sig":"MRViiUvkcX41w86eu63mY9WGDQiB7hXz2kYhB-GVLs1gGaRkajWmOpvXzl80QLyCtdn0cFjndkjZPzZLfx-nDA"},"schema":"pubphys.envelope/1"},"record_hash":"3cfe626170f5f103df16871a9a1e81d6edd4170ca3abf50a9074c7af035df4d3","leaf_index":2478}