{"record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"9a880ab087d501b9114b689f8764a0b99a6ea58e4fb8086dbfef53f8e5c1b54a","created":"2026-10-15T23:43:22Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["002d94c9a59e9fef5c9480977eb165e27842e86c9ce825a133376afb710f53b9","ce59fb6cd812fc05906d0c60a71c75ea22bc686bcf38e7c3ef7010834d98ee7b"],"salt":"902b16e94a700ccb1e00164a69b4ce278339e81a4b2b64f063d0f140881fa56c","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"value","assisted_by":[],"external_id":"beams.nonlinear-dynamics.integrable-lattice-tolerance","kind":"well-posed","literature_status":"partially-resolved","n":"2","parents":[],"plain":"Specially designed nonlinear magnets make orbits regular in theory; how much of that survives real magnet errors and energy spread is open.","posed_since":"2010","precise":"Danilov-Nagaitsev nonlinear integrable optics keeps two invariants of transverse motion for a special elliptic potential inserted in a drift whose outside lattice acts as a phase-advance-pi lens. Determine the tune spread and dynamic aperture that survive relative magnet errors of $10^{-4}$, chromaticity, and synchrotron motion with energy spread $10^{-3}$, and compare with measurements of amplitude-dependent tune shift at IOTA.","problem_ref":"002d94c9a59e9fef5c9480977eb165e27842e86c9ce825a133376afb710f53b9","references":"","settled_by":"Tracking with measured error models reproducing IOTA tune-spread and invariant-conservation data, plus tolerances stated for a proton ring.","status_note":"Electron experiments at the Fermilab IOTA ring from about 2019 reported quasi-integrable motion with large tune spread; tolerances to chromatic and error effects remain to be quantified.","title":"Error tolerance of nonlinear integrable accelerator lattices","topic_ref":null},"attested":{"attestation":{"batch":null,"client_id":null,"id_token_sha256":null,"kind":"platform"},"record_hash":"fb80bbfb544ef1f6f928a5297e210df2ea4957e62b90500330623299137b6df8","schema":"pubphys.attested/1"},"envelope":{"attested_hash":"c147f4ecc1cfa5d28aa5495b92ac532b7fa3f107b81fe7439bfdfb0dc71b51f4","platform_signature":{"key_id":"c6afc19b31429869751f06879c75cd64ea92654423d15b44be775bf1310a60da","sig":"WnJpPC5l3kQFhPKjVKFJyJ_3T_-YBZTjWXfrYQjXRcv3AZOKuvoZy086uO-Z4NgZsYrj29mYkWdS0VG4qAlLAA"},"schema":"pubphys.envelope/1"},"record_hash":"fb80bbfb544ef1f6f928a5297e210df2ea4957e62b90500330623299137b6df8","leaf_index":2500}