Beam Dynamics Corrections to the Run-1 Measurement of the Muon Anomalous Magnetic Moment at Fermilab
AbstractThis 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
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
is 0.50 ± 0.09 ppm; the uncertainty is small
compared to the 0.43 ppm statistical precision of
Muon g-2 Collaboration,
Physical Review Accelerators and Beams, 24 (2021) 044002.
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