{"record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"097f36aa7941ef38536ba48278c5efe29c0e39a80f4e4917de14f85afb45dc82","created":"2026-10-03T07:17:56Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["5475cf5dc5b1a72283d26dc95dc6e00d7ea4e00096a7c6492e409a1816eeb011"],"salt":"517d8c48abf7e061cfac34ce5ba67b95074ac6090a6ae0f25e82c48261349edc","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"value","assisted_by":[],"external_id":"beams.nonlinear-dynamics.long-term-da-scaling","kind":"well-posed","literature_status":"partially-resolved","n":"1","parents":[],"plain":"Computers can track particles for about a million turns, but colliders store beams for billions; the rule used to extrapolate the stable region is a conjecture.","posed_since":"1996","precise":"The dynamic aperture $D(N)$, the largest initial amplitude stable for $N$ turns of the 4D or 6D symplectic one-turn map of a hadron collider, is fitted by Nekhoroshev-type laws D(N) = D_inf + b/(log N)^kappa. Determine whether such a law fitted for $N \\le 1e6$ predicts $D(N)$ and the resulting intensity decay at $N \\sim 1e9$ (about 1e5 s of LHC operation) to within 10 percent, and derive $\\kappa$ from the resonance structure of the map.","problem_ref":null,"references":"","settled_by":"Direct tracking to 1e9 turns of a realistic lattice compared with the extrapolation, plus a derivation of $\\kappa$ from normal-form or resonance analysis.","status_note":"Fitted scaling laws described LHC intensity and luminosity evolution in several fills (2018-2019 papers); a derivation of the exponent and a test at 1e9 turns are missing.","title":"Extrapolating dynamic aperture from a million to a billion turns","topic_ref":"7c02bc0932cd39db40c654c1af162e4d605ebff51574000fcd91aa1d4d9677ff"},"attested":{"attestation":{"batch":null,"client_id":null,"id_token_sha256":null,"kind":"platform"},"record_hash":"7c76a666c47331c2654443388577edd6af3e7ba9731421380c24cf9ee050572a","schema":"pubphys.attested/1"},"envelope":{"attested_hash":"aa1554a8a9afec1995ee16e6298f66d88b06df9947784c2d40dfce0b6aed2054","platform_signature":{"key_id":"c6afc19b31429869751f06879c75cd64ea92654423d15b44be775bf1310a60da","sig":"r78F3-OaBwCLo91y68iV_SLw62UCa1UIrhoARxnZVCzDAqLWlq3oDqIqBgPpkgg53CqB3maUnyKvyDkp3NgKCw"},"schema":"pubphys.envelope/1"},"record_hash":"7c76a666c47331c2654443388577edd6af3e7ba9731421380c24cf9ee050572a","leaf_index":681}