Magnetometry standard for the muon g2 experiment g2 p measurement - - PowerPoint PPT Presentation

Magnetometry standard for the muon g−2 experiment

• g−2 ωp measurement
• NMR magnetometers
• Absolute calibration problem
• 3He magnetometry
• How to polarize 3He – state of the art

Sam Henry, University of Oxford

1

The g−2 magnetic field measurement

2

eB m a

a



  

We need to measure the magnitude of the 1.45T field to 0.07ppm…

p a p p a

a      

 

 



Measure magnetic field in terms of proton precession frequency

(Measured by E1054 muonium experiment)

Measure with proton NMR magnetometer probes …averaged over muon distribution (7m radius ring)

• 378 fixed probes – monitor

field when beam is on

• 17 mobile trolley probes –

map field when beam is off

3

Pulsed Nuclear Magnetic Resonance Magnetometry

Free Induction Decay NMR of proton in water sample

• Apply 61.74MHz pulse to Ls coil to rotate polarization of

protons by π/2 to magnetic field

• Spins precess at ωp – rotating dipoles produce magnetic signal

– measure emf in Lp coil

• Digitize – analyse signal to determine frequency  61.79MHz

4

Absolute Calibration Problem

• ωp 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

 B

1 B

t p

  

 

6 p p O H

10 15 689 , 25 1

2



               

Protons in spherical water sample Free protons

Philips et al. Metrologia 1977, 13, 179-195

• 50ppb accuracy

for Brookhaven experiment

• Target 35ppb for

Fermilab

s p b O H t

2

        

Measurement of λ=μμ/μp (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‒)

 

37 18334524 3.

p

  

120ppb

• QED theory, using mμ/me set by hyperfine interval measurement

 

84 183345107 3.

p

  

26ppb

5

Limited by 14ppb measurement by Philips et al to take proton in water to free proton

6

Proposed 3He Absolute Calibration Probe

     

 

6 O H

10 C 7 . 34 T 30 01036 . 14 792 . 25

2



      

 

6 He

10 10 43 967 . 59

3



  

• 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 3He to get useful NMR signal

Polarisation of 3He for NMR

7

• Cryogenic techniques
• ‘Brute force’ approach
• Gas at 4.2K in static field
• Optical pumping
• Spin Exchange (SEOP) – mixture of 3He 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

3He magnetometry – work at NPL

• Development of optical

pumping techniques at NPL in 1990s to measure fields of 0.6T With spherical water sample measured to 4.3×10-9 Compare to ESR frequency of atomic hydrogen

• Use as reference NMR

frequency in physical chemistry research

 

p h

He  

3

 

B h

He  

3

8

9

Polarized 3He work for medical applications

• Recent development

allow larger polarizations for larger pressures

10

3He 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 3He in plunging probes
• Replace free proton with helion as magnetic field reference?
• Need precision measurement of μμ/μ3He

11

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

• 3He probe: potential to significantly improve accuracy and will

provide independent check

• Challenge: polarise large number of 3He nuclei in 1.45T field