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

The Muon g−2 experiment at Fermilab (E989) aims to measure the anomalous magnetic moment, aμ, of the muon with a precision of 140 parts-per-billion. This requires a precise measurement of both the anomalous spin precession frequency, ωa, of muons stored in a magnetic field of 1.45 T, and a precise measurement of that magnetic field in terms of the shielded proton Larmor frequency, ω′p. The measurement of ω′p with a total systematic uncertainty of 70 parts-per-billion involves a combination of various nuclear magnetic resonance (NMR) probes. There are 378 probes mounted in fixed locations that constantly monitor field drifts. A water-based, cylindrical calibration probe provides the calibration in terms of the shielded proton Larmor frequency. A crucial element for the multi-step measurement of ω′p is the regular mapping of the magnetic field over the muon storage region. The former experiment at Brookhaven National Laboratory (BNL) 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 the addition of 16-bit, 1 MSPS digitization of the NMR signals, which replaced the hardware-implemented zero-crossing counting of the system at Brookhaven. The digitized signals offer new capabilities in the NMR frequency analysis and its related systematic uncertainties. To sustain the higher data rates, a new communication scheme with time-division multiplexing was implemented to separate the important NMR reference clock from the data communication in order to reach the specifications for the accuracy and stability of the reference clock. A new barcode reader provides more precise azimuthal position determination during the measurement and calibration. While the mechanical systems that move the field mapper inside the storage ring have been mostly refurbished from BNL, 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 three data taking periods of the experiment at Fermilab. This article will provide the details of the upgrades of the field mapper and its performance.