The g-2 Experimental Essentials David Hertzog University of Illinois  University of Washington

1. e Momentum Spin The g-2 Experimental EssentialsDavid HertzogUniversity of Illinois  University of Washington • Beam / Ring • Magnetic Field • Detectors / Electronics / DAQ • A word on Systematics DOE Intensity Frontier Review

2. n p+ m+ The key ingredients to measure am to high precision (1) Polarized muons ~97% polarized for forward decays (2) Precession proportional to (g-2) (3) Pm magic momentum = 3.094 GeV/c E field doesn’t affect muon spin when g = 29.3 (4) Parity violation in the decay gives average spin direction µ

3. The 900-m long decay beam: reduced flash; more store m/p See also, M. Syphers Flash compared to BNL Stored muons / POT BNL FNAL Gain FNAL/BNL Parameter

4. Benefits of a longer beamline • Reduced pion fraction that survive to ring • Permits “forward” decays (BNL was “off forward”) • Collects “all” forward muons • Eliminates “lost muon” systematic from muons born at the end of the channel having a different phase

5. The anomaly is obtained from three well-measured quantities

6. The Storage Ring exists. It will be moved to FNAL Talk by C. Polly

7. The Storage Ring components affect muon storage Fast Kickers Superconducting inflector magnet incoming muons Electrostatic Quadrupoles

8. Muons enter the ring in short bunch and spread out in predictable manner yielding key storage parameters: e+ at 1 Detector “Later” “Early” g-2 g-2 6 9 12 ms 36 39 42 ms Distribution of equilibrium radii

9. The present inflector magnet has closed ends which scatter away ~half the incoming muon beam As-used Closed-ended m Prototype Open-ended Length = 1.7 m; Central field = 1.45 T Open end prototype, built and tested  x2 increase in stored muons

10. Improvements in the kicker are planned because present one underkicks and pulse lasts too long. 149 ns cyclotron period Kicker waveform This kick affects the storage efficiency IDEAL kick  8% REAL kick  <3 % ?? Kicker Amplitude

11. We have developed a new simulation tool to guide our improvements. It includes all major subsystems • Vacuum vessel • Inflector • Kickers • Quadrupoles • Collimators

12. Example: Collective beam motion for stored muons is reproduced The predicted horizontal and vertical betatron oscillation frequencies match measured values from E821 at the percent level.

13. Ideal Square Kick We can simulate modified kicker pulse shapes to predict storage improvements % stored 10 8 6 4 2 0 Real LCR Kick

14. The wp(field) Measurement

15. The ± 1 ppm uniformity in the average field is obtained with special shimming tools. The dipole, quadrupole sextupole are shimmed independently 6 – 9 months required with cryogenics and ring on / off and in stable operating mode

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

17. The magnetic field is measured and controlled using pulsed NMR and the free-induction decay Electronics, Computer & Communication Position of NMR Probes Fixed Probes in the walls of the vacuum tank Absolute Calibration Probe: a Spherical Water Sample Trolley with matrix of 17 NMR Probes

18. The wa(precession)andEDM Measurements

19. NA2 digitized samples N A <A>=0.4 An “event” is an isolated positron above a threshold. e+

20. digitized samples An “event” is an isolated positron above a threshold. e+

21. Geant Event Method NA2 N A <A>=0.4 Traditional method of determining wa is to plot Numberof events above threshold vs. Time Here, Asym is the average asymmetry of events above energy threshold cut

22. Geant Event Method Same GEANT simulation Energy Method A complementary (integrating) method of determining wa is to plot Energy vs. Time We will operate this mode in parallel to above

23. Parasitic Muon EDM Measurement using straw tube arrays BNL statistics limited • 1 tracking station • Late turn-on time • Small acceptance • Ran 2 out of 3 years FNAL: many stations, long runs, expect ~10,000 x the events The EDM tips the precession plane, producing an up-down oscillation with time (out of phase with wa) Technique: Measureup-going/down-going tracks vs. time, (modulo g-2): See: B. Casey in “extra” materials

24. CALO X hodoscope e+ Hodoscope Detector systems • Calos: time and energy of decays • Hodoscopes: beam profiles, calo seeds, muon loss monitor • In-vacuum Straws: stored muon profile & independent EDM measurement E821

25. New W/SciFi calorimeter development aimed at transverse segmentation, high density and fast response • Original prototype encouraging, results in NIM • New 25-channel array built and tested in beam • Magnetically immune SiPMs* used on 1 channel • Excellent performance, comparable to PMTs • GEANT 4 and neural-net modeling mature • Lead tungstate crystal alternative being explored *a.k.a, Silicon Photomultipliers, “Geiger mode APDs, Multi-Pixel Photon Counter, …

26. W/SciFi Calorimeter Development 15 cm Chris Mandy 6 x 6 mm2 SiPM array used on 1 channel 17 X0 12 cm Brendan MTest with many young physicists and students DOE Intensity Frontier Review

27. Early analysis shows promising performance of large array 1 RM = 1.7 cm s/E @ 2 GeV S of elements 8.5% DOE Intensity Frontier Review

28. time Simple, single pulse SiPM readout using Paul Rubinov’s custom digitizer board prototypes time Example with pileup 2 GeV Pulse area Energy resolution same as with PMTs DOE Intensity Frontier Review

29. Systematic error projections are in-line with statistical goal Magnetic field For more details, Lee has a few slides To here, requires “no” improvements. To 0.07 requires some R&D Improvement vs time  More details in slides posted at the end of this talk Precession

30. Conclusions: The experimental method is mature • New challenges: • Increased rate and total data volume • Systematic error demands on “stability” • The “ring” must be put back together • It must be shimmed to even higher uniformity • R&D efforts • Calorimeters • SiPMs • NMR Probe placement • Kicker waveform • Inflector opening • In-vacuum straws • Simulations efforts • End-to-end beam transport • Ring dynamics • Calorimeter optimization • Many young people are enjoying these development opportunities and, like us, look forward to the experiment

31. Backup materials

32. Digitizers and DAQ: Basic Plan • 500 MHz, 8 – 12 bit, continuous digitization on all calorimeter channels • For SiPMs, includes onboard voltage control • 24 frontend computers each service one of the detector stations • High-level language control of event acceptance and formatting • Built-in pileup control and diagnostic histograms • We have considerable experience with these data rates and volumes for similar precision experiments (g-2, MuLan, MuCap, …) DOE Intensity Frontier Review

33. Error due to gain shifts in the calorimeters • Systematic error on wa previously ~ 0.13 ppm., goal <0.03 ppm • Gain was controlled to ~0.25%; shifts partially caused by ‘flash’ and / or PMT gating (or rate changes) • Laser calibration system was not sufficiently pulse height stable, so electron data early-to-late were used. • If gain does not oscillate at g-2 frequency, it does not correlate very much to wa • Presence of CBO leads to larger correlation to gain shift • Solutions: • Reduce CBO • Lower average rates • Reduce flash • Better laser monitoring system (already demonstrated in MuLan experiment at PSI)

34. Coherent betatron oscillations (CBO) • Focusing and defocusing of stored muon beam can lead to a systematic error in wa. • The horizontal aperture of the inflector is narrow, so the beam is focused in the horizontal direction at the time of injection. The full-aperture ‘kick’ is not fully efficient, so the average radius is off-center. As a result, the average radial position of the beam, at a fixed location in the ring, oscillates: • The acceptance of electrons depends on radius, therefore an oscillation with frequency near fCBO appears in the electron time spectrum. This leads to an error when the spectrum is fit; the closer to 2fa, the larger the error. • Potential improvements: • Improve the efficiency of the full-aperture kick, so that beam does not ‘wobble • RF to reduce CBO amplitude • Add higher multipoles to wash out the CBO more rapidly • Adjust the quadrupole E-field to keep fCBO as far away from 2fa as possible.

35. 3 categories of pileup systematics • Uncertainty in pileup fraction, • ~ 8% for E821, 0.038 ppm error on wa. • Decreases with more statistics available to construct the pileup spectrum • Uncertainty in the constructed pileup phase: • 0.036 ppm • Decreases with increased statistics • ‘Unseen’ pileup: (from pulses too small to be seen) • ~0.026 ppm • Reduce backgrounds and use lower thresholds for pileup spectrum reconstruction • In general: • A more highly segmented detector will reduce errors by about a factor of 2 – 3 , and with the same rate/burst we get a similar reduction in pileup. • Increased number of beam pulses minimizes the instantaneous rate • New digitizers will operate with lower threshold and longer sampling, which greatly improves correction algorithm

36. What drives the detector choice? • Compact based on fixed space • Non-magnetic to avoid field perturbations • Resolution is not critical for dwa • Useful for pileup & gain monitoring • E821 “8%”; We propose 10% for tungsten-based calorimeter • Pileup depends on signal speed and shower separation • 4/5 events separated was goal • GEANT sim work in good shape Many more details and studies available. See also,

37. How was event rate obtained? Proton complex parameters and plans Compared to achieved BNL stored muon per proton rate and detailed factors for beamline differences Monte Carlo and simple calculations This is the key factor. We have calculated 11.5 so far, so we have included a “100% contingency” in estimating the beam time request to allow for something to go wrong. MARS15 model of target, beamline simulation to capture / decay pions

38. Electrons from g-2 ring strike calo at energy-dependent angle. T/he energy vs. average striking angle

39. Positron entrance angle depends on energy: low-E showers are “wider” TOP DOWN VIEW High E Low E m central radius vacuum

40. Precision field improvements: The New Muon (g-2) Collaboration, DOE – HEP – 5 February 2010

41. Calibration of the trolley probes: 0.09 → 0.06 • Issues: • position of the probes inside the trolley • uniformity of the field at the place where the trolley probes are calibrated • position of the plunging probe that transfers the calibration • Solutions • better shimming of the field in the calibration point. • an indexing scheme needs to be developed that will permit us to know more accurately where the active part of the probes are inside of the trolley

42. Interpolation with the fixed probes: 0.07 → 0.05 • Only 150 of the 370 fixed probes gave useful signals because they were near pole boundaries • Need to move probes, or shim at pole boundaries, so that we have more points constantly monitoring the field. pole piece pole piece fixed probe beam vacuum chamber The New Muon (g-2) Collaboration, DOE – HEP – 5 February 2010