Beam Dynamics Challenges in the Muon g-2 Experiment

Thesis (Ph.D.)--University of Washington, 2023The muon's anomalous magnetic moment $a_{\mu}$ has hinted at physics beyond the standard model for nearly 20 years. The Muon $g-2$ experiment at Fermilab aims to measure $a_{\mu}$ to 140 parts per billion (ppb) precision. The 460 ppb result from its first data run (Run-1), released in 2021, agreed with the previous 2006 Brookhaven Muon $g-2$ result. The experimental average stands in tension with the standard model theory $a_{\mu}$ prediction by $4.2 \sigma$. The result of Run-2/3 data analysis is set be released in summer 2023, and will improve on the Run-1 precision by a factor of two. With the data collected in all six runs, the experiment is on track to produce a 140 ppb measurement of $a_{\mu}$. If the experiment and theory central values are both unchanged, the tension would exceed $5 \sigma$. The measurement is accomplished by injecting muons into a magnetic storage ring and precisely measuring two observable frequencies: $\omega_a$, the muons' anomalous precession frequency, and $\tilde{\omega}'_p$, the precession frequency of protons which determines the magnetic field strength experienced by the muons. This thesis presents a selection of muon beam dynamics effects which are critical for reaching the experiment precision goal. A system of detectors assists with the challenging beam injection into the storage ring, and a measurement of the injected beam provides input for simulating the stored beam dynamics. A new method is introduced to reduce a critical systemic caused by time dependence in the stored beam momentum, enabled by a detector which directly profiles the stored beam. Finally the analysis of $\tilde{\omega}'_p$, the muon-weighted magnetic field, for the Run-2/3 result is presented. Systematics of $\tilde{\omega}'_p$ due to beam effects are evaluated in detail, and shown to be sub-dominant