Design and performance of an in-vacuum, magnetic field mapping system for the Muon g-2 experiment

The E989 Muon $g-2$ experiment at Fermilab aims to measure the anomalous magnetic moment, $a^{}_\mu$, of the muon with a precision of 140 parts-per-billion. This requires a precise measurement of both the anomalous spin precession frequency, $\omega^{}_a$, and the average magnetic field in terms of the shielded proton Larmor frequency, $\omega'^{}_p$. The measurement of $\omega'^{}_p$ with a total systematic uncertainty of 70 parts-per-billion involves a combination of various NMR probes. There are 378 probes in fixed locations constantly monitoring field drifts. A water-based probe provides the calibration. A crucial element for the multi-step measurement of $\omega'^{}_p$ is the regular mapping of the magnetic field over the muon storage region. The former E821 experiment at Brookhaven employed an in-vacuum field mapping system equipped with 17 NMR probes, which was developed by the University of Heidelberg. We have refurbished and upgraded this system with new probes and electronics. The upgrades include a new communication scheme incorporating time-division multiplexing to separate the important NMR reference clock from the data communication. The addition digitization of the NMR signals replaced the hardware-implemented zero-crossing counting of the E821 system. The digitized signals offer new capabilities in the NMR frequency analysis and its related systematic uncertainties. While the mechanical systems that move the field mapper around the ring have been mostly refurbished, the motion control system was completely replaced with a custom-built electronics centered around a commercial Galil motion controller. Both the field mapping NMR system and its motion control were successfully commissioned at Fermilab and have been in reliable operation during the first data taking periods. This article provides details of the upgrades of the field mapper and its performance.