Outline. He Magnetometry for g 2. Babak Abi Oxford - 28April

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3He NMR Magnetometer Apparatus Design concept Probe

1 3 He Magnetometry for g Outline Muon G- experiment Proposed 3He for Absolute Calibration Probe General concept of MEOP 3He NMR Magnetometer Apparatus Design concept Probe schematics Main challenges Conclusion and Plan Babak Abi Oxford - 8April 1

Standard Model: a μ = 116 591 80 ± 49 10-11 (0.

2 Muon g experiment Muon anomalous magnetic dipole moment a g a 1 QED a a Hadronic a Weak New physics? Standard Model: a μ = ± (0.4 ppm) BNL measurement: Discrepancy ~3.6σ a μ = ± (0.54 ppm) a a s eb m c

3 Muon g (the Magic Momentum) Uchida s talk IOP-Manchester 015 3

Field Measurement Magnetic field must be shimmed to 1ppm uniformity

probes Measurement error with from water probe : a m eb a p a p a p μ μ

(FID) is used to measure ωp Send a RF pulse to excite the proton and

4 Field Measurement Magnetic field must be shimmed to 1ppm uniformity Measure field in terms of proton spin precession frequency ω p using NMR probes Measurement error with from water probe : a m eb a p a p a p μ μ /μ p measured from muonium hyperfine splitting Free Induction Decay (FID) is used to measure ωp Send a RF pulse to excite the proton and flip it 90 Read the signal generated due the spinning the proton Extract the frequency 4

5 G- and absolute calibration The g magnetic field measurement; We need to measure the magnitude of the 1.45T field very precisely up to 70ppb in terms of proton precession frequency. 378 fixed probes monitor field when beam is on 17 mobile trolley probes map field when beam is off All probes calibrated against standard spherical water probe Measurement error with from water probe : B p 1 B t t HO b p s σ HO diamagnetic shielding by atomic electrons δ b bulk diamagnetism of water δ p paramagnetic impurities in water δ s paramagnetic / diamagnetic materials in probe structure 5

Proposed 3 He Absolute Calibration Probe Cross-check calibration of standard spherical water probe Lower uncertainty on diamagnetic shielding Temperature coefficient 100 times smaller Negligible

6 Proposed 3 He Absolute Calibration Probe Cross-check calibration of standard spherical water probe 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 Further improvements may be possible by careful probe design and selection of materials Further systematic effects to be expected Longer term; Replacement for standard water probe? Need precision measurement of μ μ /μ 3He Water probe 3 He probe NMR detection and measurement 15 Field homogeneity Materials outside probe Sample holder shape 15 negligible Probe materials Diamagnetic shielding 14 negligible Temperature effect 10 negligible Total 34ppb 1ppb Aleksandrov, Physics ± Uspekhi 5 (6) 573 ± 601 (009) 6

7 MEOP 3 He NMR Magnetometer Plan is to the use Metastability exchange optical pumping (MEOP) of 3 He in Free Induction Decay mode. major steps to produce Hyperpolarized 3 He I. RF discharge of 3 He II. Optical pumping in 1083nm Previous works I. Paul Neumayer MSc thesis, Heidelberg (1999) II. M. Abboud PhD thesis, Paris IV Uni. (005) III. A. Nikiel, W. Heilet al., Mainz. Eur. Phys. J. D 68, 330 (014) Expect Long T* from several seconds to 100S. Theoretical achievable accuracy magnetic field measurement from NMR signal estimated by the Cramer-Rao Lower Bound (CRLB) is δb/b < (T* = 100s, SNR=1000, B z = 10 7 ) Recent Paper [A. Nikiel] reported achieving relative precision δb/b < 10 1 Expect less precision for absolute measurement due to instrumentation. we aim to reach δb/b < 10 9 M. Abboud thesis 005 7

Apparatus Design concept Discharge Plats RF

RF Power Amplifier 0W@15-80MHZ RF 1083nm Laser

9 R I L frequency synthesizer 10MHz IF VGA

8 Apparatus Design concept Discharge Plats RF receiver chain Low Noise Amplifier with 66dB and NF=.1 IF=50/10KHz, IF amplifier 60dB variable gain RF Power Amplifier RF 1083nm Laser RF PA 15-80W LNA 40dB / NF=0.9 R I L frequency synthesizer 10MHz IF VGA Rubidium reference Clock FE-5680A, Frequency stability in 100s period δf/f < 1.4x10 11 Pulse Generator Frequency Synthesizer Keithley 3390 Phase noise -115 dbc/hz DAQ / Control unit DAQ system 100MSPS/10MS buffer 8

Probe schematic/concept I Two alternative design (a) Whole Optical and RF circuitry in one (b) Separating optical Pumping section from NMR coil Field should be parallel to laser beam for optical

9 Probe schematic/concept I Two alternative design (a) Whole Optical and RF circuitry in one (b) Separating optical Pumping section from NMR coil Field should be parallel to laser beam for optical pumping. I. Spherical shape 1cm with 1/4/8mbar cell made from Pyrex glass II. III. Laser source tune-able Broadband@1083nm Must cover the C9/fm 3 He line Optical circuit Linear Polarizer Circular polarizer Collimator Absorption monitoring Laser λ=1083 nm Sealed collimator IV.Capacitive RF Discharge Electrodes V. NMR coil and tuning capacitor Beam Dumping RF Discharge Polarizer σ - σ + Sealed Probe Body >0cm B Photo diode Mirror 3 He Cell.8cm 1cm NMR Coil Mirror 9

10 3 He cell I Polarization vs Pressure ; Steady-state polarization obtained by MEOP at low magnetic field as a function of the 3 He pressure. Stars: results published in [Gen-93] from OP on C9 with a 4.5 W laser. Triangles: Abboud s results with a W laser tuned on C9. Circles : Abboud s results with a 0.5 W laser tuned on fm. Cell Shape; long cylinders with their axis parallel to the external field and spheres will create no additional field gradients inside their inner volume. 1/T R [ 4 B z p] Transverse relaxation time depends on Gas pressure p cell size R and field gradient B z. Considering 3 He cells Spherical cell 1cm with 1/4/8mbar From [A. Nikiel] Fig of Marie Abboud s thesis From [Gen-93] 10

3 He cell II Tim kindly helping us by making the

Thanks to Tim and his grad s Skyler and Midhat.

11 3 He cell II Tim kindly helping us by making the cells and a letting to letting us to use his lab. Thanks to Tim and his grad s Skyler and Midhat. Gas handling system in Michigan and cell filling 3He. Cleaning, degassing, baking. Long procedure before filling 3He. I. 1 3He cell.6mbar II. 10mm cell.6/5mbar First cell was filled and discharged He Obserption lines in 1mT

Main challenges Optical pumping circuitry Laser source specifications and cost. Minimum magnetics susceptibility 3He Cell making perfect sphere is very difficult.

12 Main challenges Optical pumping circuitry Laser source specifications and cost. Minimum magnetics susceptibility 3He Cell making perfect sphere is very difficult. Magnet Need a perpendicular magnet with very homogenous field at 1.45T Stat of art Electronics a. High resolution frequency extraction algorithm. b. Rubidium base DAQ system c. Custom design NMR spectrometer electronics d. Ultra low phase-noise and precise RF source 100um d Ø 1cm Field gradient due to container Shape [Nikiel] 1

13 Conclusion and Plan Status for prototype zero Green section; are almost ready. Blue section; design almost done. Red section (Probe); concept design is done but waiting for 3He and laser source. Planning to write an technical internal note 014 from September (done) I. Visit Mainz group to learn about NMR magnetometry optical pumping II. III. Literature review and requirements Design concept proof of concept and prototype P0 I. Electronics blocks and confirm functionality with water probe. II. Acquire 3 He cell and 1083nm laser system and Construct and test probe s optical pumping circuitry III. Construction of prototype 3 He magnetometer and performance test. 016 I. Measurements in test magnet at Fermilab, measure shifts due to II. III. IV. magnetic materials Re-design if needed and constructing the improved probe. Study systematics error and corrections. Cross calibration with water probe. 13

14 BackUp slides 14

15 Probe schematic/concept II Separating optical Pumping section from NMR coil I. Hyperpolarizing 3 He in a bench size in low B filed II. Insert the 3He cell into probe. III. Move probe to the field Advantage I. Minimum magnetic footprint II. Easy design Laser λ=1083 nm Polarizer σ - σ + 10cm 15cm B 3 He Cell RF Discharge Disadvantage NMR Coil I. Transition from low field to high field should be adiabatic II. Limited hyperpolarization time III. Slow prepration before each measurment B 1cm 1.3cm 15

16 Laser source specifications 100mW to W optical power. Manual/Electrical tuneable wavelength at 1083nm ±0.5nm with 0.001nm span resolution Broadband Linewidth 500MHz< FWHM < GHz (0.0075nm) (the average absorption line 4GHz in 1.5T) Wavelength stability < 0.5GHz ( ±0.00nm ) over several hours Optical fibre or small magnetics footprint M. Abboud et al., Laser Phys. 15, 475 (005) Michael Wolf Phd Thesis, Mainz Uni. 004 abserption efficiency vs laser line width16

Laser source, available form keopsys Keopsys laser module 0W

studied 9 other possible source of lasers One categories that are

power and very narrowband or do not have enough

17 Laser source, available form keopsys Keopsys laser module 0W CYFL-GIGA series 1083nm, the laser can overlap 3He transitions C3 to C9 and fm/f4m lines. Majority of groups are using this one but it is very EXPENSIVE We studied 9 other possible source of lasers One categories that are ready to use benchtop module like figure (b) are either very low power and very narrowband or do not have enough stability/resolution One categories are just bare bone diode laser that they need to make a very precise temperature and current controller. 17

18 Absolute Calibration Probe Uncertainties: NMR signal Nikiel et al. Eur. Phys. J. D 68, 330 (014) 1 T f B * 1 SNR 4 8R 175D 0, 3 1 SNR f C T, T He f BW B T z T BW * 3 T 73 3 p C T, T * Gas sample Higher diffusion coefficient Longer T in given field gradient allows longer measurement time T[s] SNR Fei et al Nikiel et al Measurements may be limited by stability of field with time 18

19 Principles of measuring a μ Consider μ + in a B field (storage ring) with...and a spin precession (Larmor) frequency..the difference in frequencies : eb s g 1 m c eb m eb m a s eb m c g 1 eb g m eb a m The μ + spin will precess about the direction of flight at a rate proportional to a μ Know B & measure spin (t) find a μ

20 Principles of measuring a μ Boils down to measuring muon spin orientation in time... How? Highest energy e + from μ + e + ν μ ν e align along μ + spin Need polarized μ + use π + μ + ν μ μ + are polarized Inject into a storage ring with uniform magnetic field μ + will need focussing : q-pole E field is used ω e 1 a B a a m 1 β E c Remedy: p μ =3.094 GeV magic γ=9.3 and set coefficient of β E = 0 (above)

21 Principles of measuring a μ Measure ω a from N(e+, t E e+ >1.9)

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