The first measurement of the positive muon magnetic anomaly, a=(g-2)/2, from the Fermi National Accelerator Laboratory (Fermilab) Muon g-2 Experiment (E989) yielded an experimental relative uncertainty of 0.46 ppm, which combined with the previous measurement from the Brookhaven National Laboratory (BNL) Muon g-2 Experiment (E821) differs from the current Standard Model (SM) prediction by 4.2 standard deviations. In contrast to E821, the goal of the experiment at Fermilab is to deliver a measurement of the anomaly to a precision of 0.14 ppm or less in order to reach more than 5-sigma discrepancy with the SM and, therefore, strongly establish evidence for new physics. In view of this stringent determination, a thorough description of the delivery, storage, and dynamics of the detected muon beam sets the stage for constraining beam-dynamics driven effects to the muon magnetic anomaly at the ppb level. To that extent, this dissertation introduces the background, principles, and beam requirements of E989; elaborates data-driven numerical models of the Beam Delivery System and Muon g-2 Storage Ring at Fermilab; characterizes the linear and nonlinear dynamics of the muon beam in the storage ring; and describes the contributions to the quantification of the largest beam-dynamics systematic corrections and their uncertainties in the experiment derived from this work.
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