Optimization of Muon Injection and Storage in the Fermilab g-2 Experiment: From Simulation to Reality

Abstract

The anomaly of the muon magnetic dipole moment, $a_\mu \equiv (g_\mu - 2)/2$, is a sensitive probe into the Standard Model~(SM) of particle physics because it can be calculated with high precision and also measured with high precision. Comparison of the experimental and theoretical values of $a_\mu$ therefore provides a stringent test of the completeness of the Standard Model, with any deviation suggesting the existence of new physics as a possible explanation. The most recent experimental determination of $a_\mu$ was performed by the E821 collaboration at Brookhaven National Laboratory~(BNL) from 1997--2001, where a final precision of $\delta a_\mu / a_\mu = \pm 540\;\text{parts per billion}$~(ppb) was achieved. The value of $a_\mu$ obtained by E821 presently differs from the SM prediction by 3.5--4.0 standard deviations, hinting strongly---albeit inconclusively---of the existence of new physics. The BNL experiment was limited by statistics. A next-generation experiment at Fermi National Accelerator Laboratory (Fermilab), which utilizes the same BNL storage-ring magnet with many significant upgrades, aims to measure $a_\mu$ to a final precision of 140\,ppb, thus helping to resolve the discrepancy between experiment and theory once and for all. The new Fermilab measurement of $a_\mu$ requires approximately $\sim$20X the entire BNL dataset to be recorded and analyzed, a difficult task. Therefore, optimization of the muon injection efficiency, capture fraction, and stored-muon beam properties are critical requirements for completing the new measurement in a timely manner with the required precision. These topics are the subject of this thesis.