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


T. Albahri, University of Liverpool
A. Anastasi, Istituto Nazionale di Fisica Nucleare, Sezione di Pisa
K. Badgley, Fermi National Accelerator Laboratory
S. Baeßler, University of Virginia
I. Bailey, Lancaster University
V. A. Baranov, Joint Institute for Nuclear Research, Dubna
E. Barlas-Yucel, University of Illinois Urbana-Champaign
T. Barrett, Cornell University
F. Bedeschi, Istituto Nazionale di Fisica Nucleare, Sezione di Pisa
M. Berz, Michigan State University
M. Bhattacharya, University of Mississippi
H. P. Binney, University of Washington
P. Bloom, North Central College
J. Bono, Fermi National Accelerator Laboratory
E. Bottalico, Istituto Nazionale di Fisica Nucleare, Sezione di Pisa
T. Bowcock, University of Liverpool
G. Cantatore, Istituto Nazionale di Fisica Nucleare, Sezione di Trieste
R. M. Carey, Boston University
B. C.K. Casey, Fermi National Accelerator Laboratory
D. Cauz, Istituto Nazionale di Fisica Nucleare - INFN
R. Chakraborty, University of Kentucky
S. P. Chang, Institute for Basic Science, Daejeon
A. Chapelain, Cornell University
S. Charity, Fermi National Accelerator Laboratory
R. Chislett, University College London
J. Choi, Institute for Basic Science, Daejeon
Z. Chu, Shanghai Jiao Tong University
T. E. Chupp, University of Michigan, Ann Arbor
S. Corrodi, Argonne National Laboratory
L. Cotrozzi, Istituto Nazionale di Fisica Nucleare, Sezione di Pisa
J. D. Crnkovic, Brookhaven National Laboratory
S. Dabagov, INFN, Laboratori Nazionali Di Frascati
P. T. Debevec, University of Illinois Urbana-Champaign
S. Di Falco, Istituto Nazionale di Fisica Nucleare, Sezione di Pisa

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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.

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