1. FIELD MAPPING V. Blackmore CM38 23rd February 2014 1/70

2. There is a lot of information in these slides, and not enough time to say it all. A lot of this will be revisited in future analysis meetings. I have added notes to most slides (if you download the.ppt version), so they should be understandable “offline.” As for now, we’ll see just how far we get... 2/70

3. Contents Survey plots presented at CM37. Today:  Coordinate systems  Effect of the shielding plate  Linearity of field with current  Residual magnetic field  Probe Jitter  Hysteresis  Magnetic axis fits Mode Sol (Solenoid) 100281256234274253 95266.95243.20222.30260.30240.35 80224.80204.80187.20219.20202.40 50140.50128.00117.00137.00126.50 Flip 100265280234278249 95251.75266.00222.30264.10236.55 80212.00224.00287.20222.40199.20 50132.50140.00117.00139.00124.50 Runs cover the above currents, plus: 0A measurements (residual field) 30A individual coil measurements (superposition) With and without Virostek plate A lot of data Mapped Currents 3/70 4 17 24 29 41 48 50

4. COORDINATE SYSTEMS Until the end of this talk... 4/70

5. The “Mapper” Co-ordinate System To avoid changing too many variables at once, all of the data (until it says otherwise) is in the “mapper co-ordinate system.” No survey corrections (as described at CM37) have been applied. Mapper: Movement example video* Mapper: Rotation example video * Probes numbered from 0 to 6 in order of increasing radius Probe “0” on axis “Spectrometer Solenoid” “Upstream” end and Virostek Plate Hall probe card “Conveyor belt” “Carriage” *Thanks to F. Bergsma 5/70

6. The “Mapper” Co-ordinate System To avoid changing too many variables at once, all of the data (until it says otherwise) is in the “mapper co-ordinate system.” No survey corrections (as described at CM37) have been applied. Mapper: Movement example video Mapper: Rotation example video 6/70

7. The “Mapper” Co-ordinate System To avoid changing too many variables at once, all of the data (until it says otherwise) is in the “mapper co-ordinate system.” No survey corrections (as described at CM37) have been applied. Mapper: Movement example video Tick! Mapper: Rotation example video 7/70

8. The “Mapper” Co-ordinate System To avoid changing too many variables at once, all of the data (until it says otherwise) is in the “mapper co-ordinate system.” No survey corrections (as described at CM37) have been applied. Mapper: Movement example video Tick! Mapper: Rotation example video 8/70

9. The “Mapper” Co-ordinate System To avoid changing too many variables at once, all of the data (until it says otherwise) is in the “mapper co-ordinate system.” No survey corrections (as described at CM37) have been applied. Mapper: Movement example video Tick! Mapper: Rotation example video 9/70

10. The “Mapper” Co-ordinate System To avoid changing too many variables at once, all of the data (until it says otherwise) is in the “mapper co-ordinate system.” No survey corrections (as described at CM37) have been applied. Mapper: Movement example video Rotate! Tick! Mapper: Rotation example video 10/70

11. The “Mapper” Co-ordinate System To avoid changing too many variables at once, all of the data (until it says otherwise) is in the “mapper co-ordinate system.” No survey corrections (as described at CM37) have been applied. Mapper: Movement example video Reverse! Mapper: Rotation example video 11/70

12. The “Mapper” Co-ordinate System To avoid changing too many variables at once, all of the data (until it says otherwise) is in the “mapper co-ordinate system.” No survey corrections (as described at CM37) have been applied. Mapper: Movement example video Tick! Mapper: Rotation example video 12/70

13. The “Mapper” Co-ordinate System To avoid changing too many variables at once, all of the data (until it says otherwise) is in the “mapper co-ordinate system.” No survey corrections (as described at CM37) have been applied. Mapper: Movement example video Tick! Mapper: Rotation example video 13/70

14. The “Mapper” Co-ordinate System To avoid changing too many variables at once, all of the data (until it says otherwise) is in the “mapper co-ordinate system.” No survey corrections (as described at CM37) have been applied. Mapper: Movement example video Rotate! Tick! Mapper: Rotation example video 14/70

15. The “Mapper” Co-ordinate System To avoid changing too many variables at once, all of the data (until it says otherwise) is in the “mapper co-ordinate system.” No survey corrections (as described at CM37) have been applied. Mapper: Movement example video Forward! etc. Mapper: Rotation example video 15/70

16. The “Mapper” Co-ordinate System To avoid changing too many variables at once, all of the data (until it says otherwise) is in the “mapper co-ordinate system.” No survey corrections (as described at CM37) have been applied. Mapper: Movement example video Forward! etc. Mapper: Rotation example video 16/70

17. THE SHIELDING PLATE Compare identical measurements with and without the shielding (“Virostek”) plate “Identical”: Same currents *Photographs gratuitously stolen from S. Virostek’s talk at CM36 * 17/70

18. Spot the Shielding Plate Let’s play 18/70

19. Spot the Shielding Plate Let’s play 19/70

20. Spot the Shielding Plate Let’s play 20/70

21. Let’s play Probably due to rapidly changing field (?) 21/70

22. Spot the Difference (Again) Let’s play Field increased by shielding plate Field decreased by shielding plate Would guess the centre of the shielding plate is here! 22/70

23. Let’s play Probably due to rapidly changing field (?) 23/70

24. FIELD LINEARITY With no shielding plate, field should be linear with current. With shielding plate, field may be non-linear with current 24/70

25. Without the shielding plate… (Black) 100% current in Flip Mode (Red) 80% current in Flip Mode Scale up 80% measurements and compare… 25/70

26. Without the shielding plate… (Black) 100% current in Flip Mode (Red) 80% current in Flip Mode Scale up 80% measurements and compare… First impression is good. 26/70

27. Without the shielding plate… Majority of differences are where field is changing Scaled down field measurement Scaled field is slightly larger (difference <0) 27/70

28. With the shielding plate… Majority of differences are where field is changing, now looks more systematic Scaled down field measurement 28/70 Scaled by 1.25

29. RESIDUAL FIELD We do have data sets that allow us to naively look at the residual field Q: Does the residual field change depending on the previous operating current? 29/70

30. Residual Field Measurements Every day of measurements began/ended (or both) with a field map at “0A” Can compare measurements at 80/100% field and 0A. Still using “mapper co-ordinates” Order of measurements does matter Date (June)% Current 7th80% SM 10th0% 10th3.6% SM 11th0% 11th100% SM 13th0% 19th80% SM 19th0% No intermediate measurements carried out between these pairs of data Intermediate Flip Mode runs (not interspersed with 0A data). Shielding plate removed 15th—16th June. Colour-coded dots are meant to help those viewing later 30/70

31. 7th—10th June: Previously at 80% Sol. Mode 0A, so line should be flat – but is it? Ran at 80% Solenoid Mode, then turned everything off and took a well-deserved weekend break On-axis probe only 31/70

32. 7th—10th June: Previously at 80% Sol. Mode Scaled 80% SM measurements for general shape comparison only. Not very flat – but there are welds, which will be magnetic (hence suffer residual field). Possibly correlates with mapper carriage movement? On-axis probe only 32/70

33. 10th—11th June: Previously at 3.6% Sol. Mode Ran at 10A (3.6%) Solenoid Mode, then went home for the night The next morning, at 0A On-axis probe only 33/70

34. 10th—11th June: Previously at 3.6% Sol. Mode 3.6% SM scaled for shape comparison only Similar to before? On-axis probe only 34/70

35. Previously at 3.6% Sol. Mode 3.6% SM scaled for shape comparison only Similar to before? Yes! On-axis probe only 10th—11th June: 35/70

36. 11th—13th June: Previously at 100% Sol. Mode Now it gets interesting: After the previous slide’s 0A run, ran at 100% SM. The next day took a 0A measurement… On-axis probe only 36/70

37. 11th—13th June: Previously at 100% Sol. Mode 100% SM scaled for shape comparison only On-axis probe only Much flatter! More obvious when compared to previous 0A measurements… (Does make mapper carriage movement argument moot) 37/70

38. Previously at 100% Sol. Mode 100% SM scaled for shape comparison only On-axis probe only 11th—13th June: The only thing that happened between and is a 100% field run. 38/70

39. : Several Flip Mode runs, shielding plate removed, then back to 80%SM followed by 0A measurement. 80% SM (no shielding plate) scaled for shape comparison only On-axis probe only 19th—19th June: Previously at 100% Sol. Mode All bar consistent here 39/70

40. 80% SM (w/ & w/o shielding plate) scaled for shape comparison only On-axis probe only 7th—19th June: Shielding plate differences 40/70

41. PROBE JITTER What kind of error bars should we be imagining on the previous plots? Look at the “flat” regions of the 0A measurements and see what variation there is in probe readout. 41/70

42. Consider dotted region Is approx flat in all 0A measurements Should have a negligible residual field Use, June 13 th 0A measurement, as it is “flattest” Compare with measurement from June 14 th (not previously shown) Calculate mean and standard deviation in this ROI Probe at 90mm sees more residual field that the others 180mm probe has a large spike here 42/70

43. Probe at 90mm sees more residual field that the others 43/70

44. 44/70

45. 45/70

46. Probe Jitter Comparison Composite of previous 3 slide’s plots 46/70

47. Probe Jitter Comparison 47/70

48. HYSTERESIS Q: Do we achieve the same field when we approach it from below the operating current and above the operating current? 48/70

49. Hysteresis Ideally, requires consecutive four measurements with the shielding plate 0% solenoid/flip 80% solenoid/flip mode 100% solenoid/flip mode 80% solenoid/flip mode We have 0%  80%, and 0%  100%, but do not have 100%  80% Mapping takes a long time Time taken by shielding plate installation and removal Judging by changes in residual field, likely there will be a (very) small hysteresis effect Should make this measurement when mapping final SS 49/70

50. FINDING THE MAGNETIC AXIS (FIRST PASS) The mapper moves about by ~ 1mm in (x,y) as it travels through the magnet To first approximation, ignore this movement and use mapper co- ordinates to get an estimate of the magnetic axis 50/70

51. Finding the Magnetic Axis x or y Bx or By Fit Magnetic axis 51/70 Simulation, 1 coil

52. 1e-12m 52/70

53. Simulation, 1 coil 1e-12m 53/70

54. Real magnets Note: No survey information has been applied to the data before the fits, and the mapper does wiggle around! 100% Solenoid Mode, w/ Shielding Plate 54/70

55. Shielding plate No shielding plate Region 1 Region 2 55/70

56. 0.5mm Mapper carriage moves around by ~ 1mm, so axis is consistent with zero Probably just the carriage moving about 56/70

57. ~0.8mm Mapper carriage moves around by ~ 1mm, so axis is consistent with zero 57/70

58. Shielding plate No shielding plate Region 1 Region 2 58/70

59. 1mm This is the upstream end, so the shielding plate should have no effect. Shape matches, but is offset... 59/70

60. 1mm Shielding plate makes a difference 60/70

61. What happens in here? Region 3 61/70

62. Region 3 0.03T 100% Solenoid Mode, w/ Shielding Plate 62/70

63. Region 3 1T 100% Solenoid Mode, w/ Shielding Plate 63/70

64. Region 3 0.06T 100% Solenoid Mode, w/ Shielding Plate 64/70

65. Region 3 0.5T 100% Solenoid Mode, w/ Shielding Plate 65/70

66. Region 3 0.03T 100% Solenoid Mode, w/ Shielding Plate 66/70

67. Region 3 0.015T 100% Solenoid Mode, w/ Shielding Plate 67/70

68. Region 3 0.5T 100% Solenoid Mode, w/ Shielding Plate 68/70

69. CONCLUSIONS

70. Conclusions & Next Steps The magnetic axis is approximately centred on zero, but this requires a significant uncertainty analysis and combination with the survey info to confirm. Next steps: Evaluation of uncertainties Cross-calibration of Hall probes Refinement of magnetic axis fits Field fits using 2-model scaling technique Evaluation of difference between fitted and measured fields (Fourier-Bessel fits) “Real magnet” model  MAUS More to come at analysis meetings!

71. BACK-UP SLIDES A. Interpolation reliability B. Mapper co-ordinate transforms

72. Interpolation reliability A1/1 4 measurements with different rotations of the mapper disc Interpolated line

73. Mapper co0rdinate transformations z y phi Direction of mapper travel (x) is out of page Bz By 0 1 2 3 4 5 6 #yz 00000 1030900 2600090 30 2700 4-1200270 5150090 6018000 B1/4

74. 0 1 2 3 4 5 6 z y phi Direction of mapper travel (x) is out of page 0 1 2 3 4 5 6 Start by working in POLAR co-ordinates (Br, Bphi, Bz) Bz By #yz 00000 1030900 2600090 30 2700 4-1200270 5150090 6018000 Mapper co0rdinate transformations B2/4

75. z y phi Direction of mapper travel (x) is out of page Start by working in POLAR co-ordinates (Br, Bphi, Bz) Bz By 0 1 2 3 4 5 6 This will be true regardless of how we rotate the disc Mapper co0rdinate transformations B3/4

76. z y phi Direction of mapper travel (x) is out of page Bz By 0 1 2 3 4 5 6 For “MICE” co-ordinates: Mapper co0rdinate transformations B4/4