{"paper":{"title":"Analytic Derivation of Vertical Chromaticity in the Fermilab Muon $g{-}2$ Storage Ring","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"physics.acc-ph","authors_text":"Eremey Valetov, Kyoko Makino, Martin Berz","submitted_at":"2026-06-05T20:50:55Z","abstract_excerpt":"We derive the vertical chromaticity $\\xi_y$ of the Fermilab Muon g-2 storage ring in closed analytic form. Expanding the Hamiltonian as a Taylor polynomial in the dynamical variables and integrating the equations of motion order by order, we obtain the vertical second-order aberrations of the homogeneous magnetic dipole ($\\mathtt{DI}$) and the combined-function dipole-and-electrostatic-quadrupole element ($\\mathtt{DIQ}$) used in the muon $g{-}2$ ring. Composing the per-element maps over the periodic dispersion orbit yields a closed-form expression for the vertical chromaticity $\\xichromy$ of t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.09903","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.09903/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}