Precision Magnetic Field Measurement with NMR Probes at Fermilab Muon g-2 Experiment

The Fermilab Muon g-2 Experiment measured the muon magnetic moment anomaly to a precision of 200 parts per billion (ppb). This requires a high-precision measurement of the muon spin precession frequency, as well as the magnetic field experienced by the muons. In the experiment, the magnetic field is measured using Nuclear Magnetic Resonance (NMR) probes and is related to the Larmor frequency of protons shielded in a spherical water sample at a specific reference temperature. Absolutely calibrated NMR probes mounted on a survey trolley measure the magnetic field inside the muon storage ring, and fixed NMR probes located at various locations around the ring track the field over time. The measurements are synchronized and interpolated, then averaged over space and time, and weighted by the muon density. Additional transient corrections reduce the magnetic field uncertainty to below 60 ppb. The probe used for absolute calibration in the Fermilab Muon g-2 Experiment is cross-calibrated with NMR probes designed for the Muon g-2/EDM Experiment (E34) and the Muonium Spectroscopy Experiment Using Microwave (MuSEUM) at Japan Proton Accelerator Research Complex (J-PARC), using the Argonne National Laboratory (ANL) 4T Magnet Facility. While Fermilab Muon g-2 probes use pulsed NMR and the others use the continuous wave (CW) technique, the cross-calibration efforts aim to cross-check the probes with an uncertainty at a 35-ppb level.