Precision Magnetic Field Calibration for the Muon $g-2$ Experiment at Fermilab

The Muon g-2 Experiment at Fermilab (E989) has been designed to determine the muon anomalous magnetic moment to a precision of 140 parts per billion (ppb), a four-fold improvement over the Brookhaven E821 measurement. Key to this precision goal is the absolute determination of the magnetic field of the experiment's muon storage ring to better than 70 ppb. The magnetic field will be measured and monitored by nuclear magnetic resonance (NMR) probes, which are mounted on a trolley and pulled through the muon storage region when muons are not being stored. These trolley probes will be calibrated in terms of the free-proton Larmor precession frequency $\omega_{p}$ by a specially-constructed NMR absolute calibration probe. In E821, the uncertainty in the field measurement was 170 ppb, of which 50 ppb was due to the absolute probe. In E989, these uncertainties will be reduced to 70 ppb and 35 ppb, respectively. To meet these stringent requirements, a new calibration probe has been designed and is currently under construction, along with a so-called plunging probe. This plunging probe will be used to transfer the calibration to the trolley probes. This poster will present the design, fabrication, and testing of the absolute and plunging probes, along with the calibration procedure.