Design and Performance of the Precision Water Magnetometer for the Fermilab Muon $g-2$ Experiment

We present the design and performance of a high-accuracy pulsed nuclear magnetic resonance (NMR) magnetometer that operates in a magnetic field $\vert \vec{B} \vert = 1.45$ T. The magnetometer determines the magnitude of the local $B$-field from measurements of the precession frequency of the free-induction decay of protons in a sample of water. This is accomplished using the well-known magnetic moment of protons shielded in water and after correcting for perturbations to the field from materials used in the probe construction. These perturbations and other corrections have been studied and quantified. The device is used in the Muon $g-2$ Experiment at Fermi National Accelerator Laboratory to determine relative $B$-field magnitudes to an accuracy of 15 parts-per-billion (ppb), and absolute magnetic fields in terms of Tesla to 19 ppb.