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Klaus Jungmann Kernfysisch Versneller Instituut University of Groningen Netherlands

Muon g-2 Collaboration Meeting Fermilab 18-19 March 2011. Systematics on  p. Precision Measurement of the Magnetic Field for a Muon g-2 Determination. Klaus Jungmann Kernfysisch Versneller Instituut University of Groningen Netherlands. Context Basics Fundamental Constants

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Klaus Jungmann Kernfysisch Versneller Instituut University of Groningen Netherlands

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  1. Muon g-2 Collaboration Meeting Fermilab 18-19 March 2011 Systematics on p Precision Measurement of the Magnetic Field for a Muon g-2 Determination Klaus Jungmann Kernfysisch Versneller Instituut University of Groningen Netherlands

  2. Context • Basics • Fundamental Constants • Field Measurement • Open Issues

  3. Context • Basics • Fundamental Constants • Field Measurement • Open Issues

  4. Open technical issues • Local magnetic environment • Shimming • Field monitoring • Field analysis • Quench protection • Requires very careful work • nothing less – nothing more K. Jungmann, mar 2011

  5. Context • Basics • Fundamental Constants • Field Measurement • Open Issues

  6. Spin Precession Frequency  electric field plays minor role

  7. Two quantities are measured: • magnetic field  proton NMR, wp • anomaly frequency decay electrons, wa • BOTH EQUALLY IMPORTANT

  8. Looks like a simple Experiment * One is inclined to believe a and Bare just other constants to be measured. * This were true, if spin could follow field changes adiabatically, i.e. field changes seen by the particle happen on a timescale >> 1 / a * However:

  9. correction = (0,0,Bz) dimension m }jz J • (2* jmax+ 1) possibilities for • mJ =jz • Allow for correction • m = gmB Magnetic Moment – in Quantum Mechanics • Magnetic Moment proportional • to angular Momentum • Energy in external Magnetic Field B • is scalar product of Field and • Magnetic Moment • Precession frequency in external • Magnetic Field

  10. Allows for non-trivial Corrections  Contains all interesting physics Magnetic Moment Angular Momentum Gives dimensions and scale for a particle

  11. B0=1.45T  n0=62 MHz e.g. Proton NMR to determine a field Lepton Spin Resonance / Nuclear Magnetic Resonance For tranverse polarized particles Precession with frequency n0 : Energy E0+ s mB B Somewhat more QM correct: <sz> =0 <sx(t)> = ssin(2pn0t) <sy(t)> = scos(2pn0t) n0 : Larmor frequency 2 s hn0 E0 S E0– s mB e.g. S =1/2 • measure m, if B is known • measure B, if m is known B0 Magnetic Field

  12. Note: • NMR measures: • Maxwells equations require: • 0th order • 2nd order Zeeman effect • measure • shimming watch out for timedependent correlated field variations

  13. Magnetic Moment Measurements Proton: best measurement from proton NMR in water (spherical water probe) Electron: e.g. from hydrogen maser also calculated from constants Best values: come from least square adjustment of Fundamental Constants. CODATA (NIST, B.Taylor & P. Mohr, ~every 2 years) Finds also way in particle data book Involves heavily theory : Check for intellectual Phase locking !

  14. Context • Basics • Fundamental Constants • Field Measurement • Open Issues

  15. Theory: * need a for muon ! * hadronic and weak corrections *various experimental sources of a<better 100ppb>need constants at very moderate *a no concern for (g-2)maccuracy wa wammc Experiment: wp = am = mm wa emB - wp mp * wa and B (wp) measured in (g-2)m experiment <better 0.35 and 0.1 ppm> * c is a defined quantity <“infinite” accuracy> *mm (mm) is measured in muonium spectroscopy (hfs) <better 120 ppb> NEW 1999 *em is measured in muonium spectroscopy (1s -2s) <better 1.2 ppb> NEW 1999 *mp in water known >> probe shape dependence<< <better 26 ppb> *m3He to mp in water >> gas has no shape effect << <better 4.5 ppb> being improved

  16. m g-2 hadronic contribution weak contribution New Physics QED QED h mm, a, gm mm m+e- DnHFS, n=1 m+e- Dn1S-2S QED mm mm a QED corrections weak contribution mm QED corrections

  17. Solenoid Sm m+ e- Gated Detector m+in MW-Resonator/Kr target Muonium Hyperfine Structure Yale - Heidelberg - Los Alamos

  18. Solenoid Sm m+ e- Gated Detector m+in MW-Resonator/Kr target Muonium Hyperfine Structure Yale - Heidelberg - Los Alamos Very same equipment to calibrate field than for g-2 Therefore:: Use these values, NOT adjusted values !!! unless you are prepared to redo that experiment

  19. History of Muonium Ground State Hyperfine Splitting Measurements NEVIS CHICAGO-SREL LAMPF LAMPF latest experiment Quoted Uncertainty [kHz] Year

  20. Muonium 1s-2s At RAL 1987 -2000

  21. m++ e-+ Ekin 0 -.25 Rm 2S 244 nm Energy 244 nm mm n1s2s= ¾ R -Rm 1S me + mm m+ Detection m+ Laser Mirror m+e- Target Diagnostics m+in Muonium 1S-2S Experiment Heidelberg - Oxford - Rutherford - Sussex - Siberia - Yale

  22. exp Dn 1s-2s = 2455 528 941.0(9.1)(3.7) MHz Dn 1s-2s = 2455 528 935.4(1.4) MHz mm+= 206.768 38 (17) me (0.8ppm) qm+= [ -1 -1.1 (2.1) 10-9 ] qe-(2.2 ppb) theo Results:

  23. CODATA CODATA Fine Structure Constant a a-1= 137.035 999 710 (96) a-1= 137.035 999 084 (51) Test of Internalconsistency of QED Test of Internal consistency of QED

  24. Context • Basics • Fundamental Constants • Field Measurement • Open Issues

  25. B0=1.45T  n0=62 MHz e.g. Proton NMR to determine a field Lepton Spin Resonance / Nuclear Magnetic Resonance For tranverse polarized particles Precession with frequency n0 : Energy E0+ s mB B 2 s hn0 E0 S E0– s mB e.g. S =1/2 • measure m, if B is known • measure B, if m is known B0 Magnetic Field

  26. Electronics, Computer& Communication Position of NMR Probes Key Elements of the Field Measurement System Absolute Calibration Probe: a Spherical Water Sample Fixed Probes in the walls of the vacuum tank Trolley with matrix of 17 NMR Probes

  27. all probes MUST be checked individually, refurbished and possibly filled with petroleum jelly  manpower !(student assistants)

  28. The fixed probes 4 ppm Proton NMR

  29. counting zero crossings • FFT of full 360 signals every second? • (check advantage)

  30. NMR trolley > 15 man years

  31. Magnetic Field vs Azimuth (1999) Before 1999 Inflector fringe field

  32. shimming shimming At this level, one hardly needs to know the muon distribution Improvement of Field 2000 1999 2001

  33. Systematic Uncertainties, Results (m-) • Magnetic Field • wp,0 spherical probe 0.05 ppm • wp(R,ti) 17 trolley probes 0.09 ppm • wp(R,t) 150 fixed probes 0.07 ppm • wp(R) trolley measurement 0.05 ppm • < wp> muon distribution 0.03 ppm • wp (RI) inflector fringe field - - • others 0.10 ppm • total systematic uncertainty • dwp=0.17ppm • Spin Precession • Pileup 0.08 ppm • Lost muons 0.09 ppm • Coherent Betatron oscillations 0.07 ppm • Gain Instability 0.12 ppm • others 0.11 ppm • total systematic uncertainty • dwa,sy = 0.21 ppm • total statistical uncertainty • dwa,st = 0.6 ppm wa/2p = 229 073.59(15)(5) Hz wp/2p = 61 791 400 (11) Hz

  34. What needs to be done: • survey magnetic environment • shimming – radial and azimuthal • frequent full field maps (trolley) at random time of day • frequent absolute calibrations (every 5th trolley run) • rigorous susceptibility police • of course, refurbishing of equipment

  35. Open technical issues (I) • Local magnetic environment near the ring • monitor environment : • close ring storage ring AND transients caused far away (accelerator) • on its way ( T. Chupp) • susceptibility ‘Sherif’ : materials, lamps, screwdrivers, … • ( local respected authority !!!!!) • training of technicians AND scientists • we have all necessary tools available – manpower important • people to do the job •  everybody needs to know the real issues K. Jungmann, mar 2011

  36. Open technical issues (II) • Shimming • nothing too spectacular (like detectors per se) BUT very important • no showstoppers expected to <.2 ppm integral (aver.) homogeneity • HOWEVER: Time needed! • several rounds: allow for time to do – analyze- learn – do – analyze … • wedges, o.k. just do it • surface coils : most urgent issue - power supplies • shorter cables or new supplies • activate dipole extra shimming coils ? •  define TEAM NOW K. Jungmann, mar 2011

  37. Ring relocation • Heavy-lift helicopters bring coils to a barge • Rest of magnet is a “kit” that can be trucked to and from the barge • What’s the effect on the coils?

  38. Electronics, Computer& Communication Position of NMR Probes Don’t even Think about Touching Absolute Calibration Probe: a Spherical Water Sample Trolley with matrix of 17 NMR Probes unless you are prepared to spend >20 man years

  39. Usefull Modifications: Fixed Probes in Orbital Plane Some Fixed Probes relocated

  40. Useful Modification : Trolley Drive Motors it turns out: We could use Stepping Motors advantage: Possible Speed

  41. He3 probes are shape independent nice additional independent absolute field measurement

  42. Evolution uncertainties in muon g-2 Improvements for future Field: temperature stability, absolute calibration, trolley position, more probes Precession: new scraping scheme, thresholds, energy calibration, new calorimeters, more complete digitization Statistics: more muons, backward decaying pions, new inflector

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