{"record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"b558c60fb625397b291ba06e9ce97bc1992ddda9f26c93898236768227a672c7","created":"2026-10-03T07:17:56Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["5475cf5dc5b1a72283d26dc95dc6e00d7ea4e00096a7c6492e409a1816eeb011"],"salt":"eaf8a9f4630b60a12352d1a836d5ad02eb13406f9222c233fd15015a4fbea6e0","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":"1","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 1e-4, chromaticity, and synchrotron motion with energy spread 1e-3, and compare with measurements of amplitude-dependent tune shift at IOTA.","problem_ref":null,"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":"7c02bc0932cd39db40c654c1af162e4d605ebff51574000fcd91aa1d4d9677ff"},"attested":{"attestation":{"batch":null,"client_id":null,"id_token_sha256":null,"kind":"platform"},"record_hash":"002d94c9a59e9fef5c9480977eb165e27842e86c9ce825a133376afb710f53b9","schema":"pubphys.attested/1"},"envelope":{"attested_hash":"323dbfc4d980b0a6154d346f91c0edd34f9efe8ca52123f64e1e07f37fb07ca5","platform_signature":{"key_id":"c6afc19b31429869751f06879c75cd64ea92654423d15b44be775bf1310a60da","sig":"MEB346uH_jt0bq_HjyPHw9wEPHbViaQnVzTMaDmkna8uANOA1MZnFnH-n4doLq-iylkZh54-qNJqlzfxiOA4Cg"},"schema":"pubphys.envelope/1"},"record_hash":"002d94c9a59e9fef5c9480977eb165e27842e86c9ce825a133376afb710f53b9","leaf_index":680}