The Beam Dynamics and Beam Related Uncertainties in Fermilab Muon $g-2$ Experiment
The anomaly of the muon magnetic moment, $a_{\mu}\equiv (g-2)/2$, has played an important role in constraining physics beyond the Standard Model for many years. Currently, the Standard Model prediction for $a_{\mu}$ is accurate to 0.42 parts per million (ppm). The most recent muon $g-2$ experiment was done at Brookhaven National Laboratory (BNL) and determined $a_{\mu}$ to 0.54 ppm, with a central value that differs from the Standard Model prediction by 3.3-3.6 standard deviations and provides a strong hint of new physics. The Fermilab Muon $g-2$ Experiment has a goal to measure $a_{\mu}$ to unprecedented precision: 0.14 ppm, which could provide an unambiguous answer to the question whether there are new particles and forces that exist in nature. To achieve this goal, several items have been identified to lower the systematic uncertainties. In this work, we focus on the beam dynamics and beam associated uncertainties, which are important and must be better understood. We will discuss the electrostatic quadrupole system, particularly the hardware-related quad plate alignment and the quad extension and readout system. We will review the beam dynamics in the muon storage ring, present discussions on the beam related systematic errors, simulate the 3D electric fields of the electrostatic quadrupoles and examine the beam resonances. We will use a fast rotation analysis to study the muon radial momentum distribution, which provides the key input for evaluating the electric field correction to the measured $a_{\mu}$.