Beam dynamics corrections to the Run-1 measurement of the muon anomalous magnetic moment at Fermilab

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23 Scopus citations


This paper presents the beam dynamics systematic corrections and their uncertainties for the Run-1 dataset of the Fermilab Muon g-2 Experiment. Two corrections to the measured muon precession frequency ωam are associated with well-known effects owing to the use of electrostatic quadrupole (ESQ) vertical focusing in the storage ring. An average vertically oriented motional magnetic field is felt by relativistic muons passing transversely through the radial electric field components created by the ESQ system. The correction depends on the stored momentum distribution and the tunes of the ring, which has relatively weak vertical focusing. Vertical betatron motions imply that the muons do not orbit the ring in a plane exactly orthogonal to the vertical magnetic field direction. A correction is necessary to account for an average pitch angle associated with their trajectories. A third small correction is necessary, because muons that escape the ring during the storage time are slightly biased in initial spin phase compared to the parent distribution. Finally, because two high-voltage resistors in the ESQ network had longer than designed RC time constants, the vertical and horizontal centroids and envelopes of the stored muon beam drifted slightly, but coherently, during each storage ring fill. This led to the discovery of an important phase-acceptance relationship that requires a correction. The sum of the corrections to ωam is 0.50±0.09 ppm; the uncertainty is small compared to the 0.43 ppm statistical precision of ωam.

Original languageEnglish
Article number044002
JournalPhysical Review Accelerators and Beams
Issue number4
StatePublished - Apr 2021

Bibliographical note

Funding Information:
We thank the Fermilab management and staff for their strong support of this experiment, as well as the tremendous support from our university and national laboratory engineers, technicians, and workshops. The Muon Experiment was performed at the Fermi National Accelerator Laboratory, a U.S. Department of Energy, Office of Science, HEP User Facility. Fermilab is managed by Fermi Research Alliance, LLC (FRA), acting under Contract No. DE-AC02-07CH11359. Additional support for the experiment was provided by the Department of Energy offices of High Energy Physics and Nuclear Physics (USA), the National Science Foundation (USA), the Istituto Nazionale di Fisica Nucleare (Italy), the Science and Technology Facilities Council (UK), the Royal Society (UK), the European Union’s Horizon 2020 research and innovation program under the Marie Skłodowska-Curie Grant Agreements No. 690835 and No. 734303, the National Natural Science Foundation of China (Grants No. 11975153 and No. 12075151), MSIP, NRF, and IBS-R017-D1 (Republic of Korea), and the German Research Foundation (DFG) through the Cluster of Excellence (EXC 2118/1, Project ID No. 39083149).

Publisher Copyright:
© 2021 authors.

ASJC Scopus subject areas

  • Nuclear and High Energy Physics
  • Physics and Astronomy (miscellaneous)
  • Surfaces and Interfaces


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