Magnetometry standard for the muon g−2 experiment • g−2 ω p measurement • NMR magnetometers • Absolute calibration problem • 3 He magnetometry • How to polarize 3 He – state of the art Sam Henry, University of Oxford 1
The g−2 magnetic field measurement m We need to measure the magnitude of a a the 1.45T field to 0.07ppm… eB a p Measure magnetic field in a terms of proton precession p a p frequency (Measured by E1054 muonium experiment) Measure with proton NMR magnetometer probes …averaged over muon distribution • 378 fixed probes – monitor (7m radius ring) field when beam is on • 17 mobile trolley probes – map field when beam is off 2
Pulsed Nuclear Magnetic Resonance Magnetometry Free Induction Decay NMR of proton in water sample • Apply 61.74MHz pulse to L s coil to rotate polarization of protons by π /2 to magnetic field • Spins precess at ω p – rotating dipoles produce magnetic signal – measure emf in L p coil • Digitize – analyse signal to determine frequency 61.79MHz 3
Absolute Calibration Problem • ω p is a measure of the absolute magnitude of the magnetic field • But some absolutes are more absolute than others • Every probe will introduce shift ~0.1ppm due to paramagnetic properties of probe material • All probes calibrated against standard probe with spherical water sample • 50ppb accuracy for Brookhaven experiment • Target 35ppb for Fermilab B B 1 t H O b p s p t 2 Protons in spherical water sample p 6 1 25 , 689 15 10 H O 2 p 4 Free protons Philips et al. Metrologia 1977, 13, 179-195
Measurement of λ = μ μ / μ p (E1054 experiment) • Used same standard magnetometer probe • W. Liu et al., PRL 82 711 (1999) • High precision measurements of Zeeman hyperfine transitions in muonium ( μ + e ‒ ) 3 . 18334524 37 120ppb p • QED theory, using m μ /m e set by hyperfine interval measurement 3 . 183345107 84 26ppb p Limited by 14ppb measurement by Philips et al to take proton in water to free proton 5
Proposed 3 He Absolute Calibration Probe 6 25 . 792 14 0 . 01036 30 T 34 . 7 C 10 H O 2 6 59 . 967 43 10 10 3 He • Lower uncertainty on diamagnetic shielding • Temperature coefficient 100 times smaller • Negligible magnetic susceptibility – no sample shape dependence • NMR signal per atom larger – potential to use smaller probe Challenge: • Polarise sufficient amount of 3 He to get useful NMR signal 6
Polarisation of 3 He for NMR • Cryogenic techniques • ‘Brute force’ approach • Gas at 4.2K in static field • Optical pumping • Spin Exchange (SEOP) – mixture of 3 He and other atoms (e.g. K) • High pressure, long time needed • Metastability Exchange (MEOP) • Low pressure gas (~1mbar) • 1083nm semiconductor laser diode • Significant improvements in recent years to allow use in large fields at higher pressures 7
3 He magnetometry – work at NPL • Development of optical pumping techniques at NPL in 1990s to measure fields of 0.6T With spherical water sample 3 He h p measured to 4.3 × 10 -9 Compare to ESR frequency of atomic hydrogen 3 He h B • Use as reference NMR frequency in physical chemistry research 8
Polarized 3 He work for medical applications • Recent development allow larger polarizations for larger pressures 9
3 He magnetometry for g−2 This project: • Cross-check calibration of standard spherical water probe • Probes should agree to within 4.2ppb Longer term? • Replacement for standard water probe? • Could reduce uncertainty on calibration to 14ppb (proton in water – free proton) • Use 3 He in plunging probes • Replace free proton with helion as magnetic field reference? • Need precision measurement of μ μ / μ 3He 10
Conclusions • g−2 experiment requires monitoring of magnetic field in muon ring to 0.07ppm • Proton NMR magnetometers • 378 fixed + 17 trolley probes calibrated against standard probe • Spherical water probe: limited by shape and temperature dependent shifts • 3 He probe: potential to significantly improve accuracy and will provide independent check • Challenge: polarise large number of 3 He nuclei in 1.45T field 11
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