\section{\label{sec:intro} Introduction}
\textcolor{orange}{Jason}
\medskip

The muon magnetic moment is a property that can be calculated in the context of the standard model of particle physics. A comparison of the measured and predicted anomaly is a grand test of the model. The goal of the experiment is to measure the anomaly with 140~part-per-billion~(ppb) precision.

The experimental method is to circulate a beam of polarized muons in a storage ring and to measure the precession frequency, or rather the difference between
the precession frequency and the revolution frequency, $\omega_a$,  the spin tune. The \SI[per-mode=symbol]{3.094}{\giga\eV\per\clight} momentum
muons decay with lifetime of about \SI{64}{\micro\second} in the lab frame to a positron and a pair of neutrinos. The energy of the positron in the lab frame is correlated with the polarization of the parent muon. The variation in the number of high energy positrons with time is the measure of $\omega_a$. 

The frequency with which the muons precess depends on the details of the magnetic and electric guide field of the storage ring. Magnetic focusing is evidently precluded as it would introduce an unacceptable variation in the magnetic field across the storage volume. Instead vertical focusing is provided by electrostatic quadrupoles. The muon momentum is chosen to minimize the effect of the electric field on the precession frequency. Indeed, at the muon magic momentum, \SI[per-mode=symbol]{3.094}{\giga\eV\per\clight}, the contribution of the electric field to the difference frequency vanishes.

We describe the electric and magnetic guide field of the \SI{44.69}{m} circumference storage ring, the lattice functions and the process for injecting and storing polarized muons. The detector systems that inform the beam distributions are introduced. The contributions to $\omega_a$ that arise from finite beam width and length,  momentum spread,  and coherent oscillation of the centroid are described, as are the measurements of the distributions that are essential to accounting for the effects. 
