1. Saw Tooth Pattern Dipole Axis Measurements. Vertical Plane Natalia Emelianenko February 2006

2. Example 1 Visible difference of the measurements precision: “oscillations” for the dipole 1165 All examples were found after the analysis was made using specific criteria.

3. Example 2 Visible difference of the measurements precision Dipole 1643, aperture 2 Upper points are measured when mole ran from the connection side

4. What to Do About This ?  Check and assess all measurements  Find the reason  Find whether it is bad Does this cause errors in the GA calculation ?  If it is bad – find a remedy if it is possible Now, a method for the measurement evaluation and its results are presented

5. Population All valid measurements with minimum 20 points measured from each side, steps ITP15, ITP20-GEO and WP08-FID, have been analyzed. The sample size is: 716 dipoles (1432 apertures) ITP15 – 716 dipoles (1432 apertures) 708 dipoles (1416 apertures) ITP20-GEO – 708 dipoles (1416 apertures) 657 dipoles (1314 apertures) WP08-FID – 657 dipoles (1314 apertures) 300 dipoles WP08B-FID – 300 dipoles 158 dipoles WP08C-FID – 158 dipoles Analysis tools – Oracle SQL (~ 1 hour running SQL), Excel Charts, web tool http://cern.ch/pda-dipoles-followup/servlet/getQueryData All distances in the X and Z direction are given in mm, Y – in m.

6. Overall Picture Dipoles of firm 1 tested during last 5 months of 2005, aperture 1

7. How to Assess the Measurements Calculate The average and max saw tooth height –Fit each curve by a polynomial, use the function to calculate the difference –Use interpolation to calculate the difference in each longitudinal position The linear regression analysis for the difference – slope, intercept, r.m.s.* The correlation between two runs’ results

8. Saw Tooth Height The “Y-mate” point should be calculated for each point measured from another side by means of interpolation difference

9. Saw Tooth Height – Average To calculate the average saw tooth height the area between the curves should be divided by the length on which the both points are known at each y i If the connection curve lies below the lyre one, the area is negative. We can sum up signed or absolute values. Since the points are evenly spread this differs from simple average by max 0.02 mm — +

10. Average Height WP08-FID TotalFirm 1Firm 2Firm 3 Mean0.050.04 0.05 St. Deviation0.09 Range0.650.620.630.58 Minimum-0.26-0.24-0.26-0.25 Maximum0.40 0.380.33 Count1316356326634 ITP20-GEO TotalFirm 1Firm 2Firm 3 Mean0.030.020.050.03 St. Deviation0.070.060.100.04 Range0.790.390.790.40 Minimum-0.41-0.25-0.42-0.09 Maximum0.390.140.3880.310 Count1416436428552

11. Average Absolute Height WP08-FID TotalFirm 1Firm 2Firm 3 Mean 0.120.110.12 St. Deviation 0.06 Range 0.40 0.350.32 Minimum 0.02 Maximum 0.41 0.380.35 Count1316356326634 ITP20-GEO TotalFirm 1Firm 2Firm 3 Mean0.080.070.110.06 St. Deviation 0.080.030.060.03 Range0.390.230.380.30 Minimum0.01 0.02 Maximum0.410.250.410.31 Count1416436428552

12. Average Tooth Height over Time Absolute “With sign”

13. Average Absolute Height: Firms Step ITP15

14. Average Absolute Height: Firms Step ITP20-GEO

15. Analysis of the Difference The difference connection – lyre is fitted with a first order polynomial (linear regression). Correlation – 0.74 Slope – 4.62E-05 Intercept – - 0.2 R.M.S. – 0.03 Average h – 0.18 Range h – 0.002 - 0.489

16. Analysis of the Difference Linear regression slope Step μ σ ITP20 1.38E-06 1.46E-05 WP08 2.18E-051.74E-05

17. Analysis of the Difference Linear regression Y-intercept (shift) Step μ σ ITP20 0.020 0.125 WP08-0.1190.121

18. Difference Linear Fit Summary StepFirmNumSlope μ Slope σShift μ Shift σ ITP15 1432-4.06E-071.09E-050.0050.095 24421.29E-051.49E-05-0.0760.142 3558-1.66E-079.69E-060.0160.080 Total14323.79E-061.33E-05-0.0160.114 ITP15* 4.40E-061.35E-05-0.0190.017 ITP20 1436-7.96E-061.11E-050.0750.101 24289.48E-061.81E-05-0.0250.173 35522.47E-068.37E-060.0110.072 Total14161.38E-061.46E-050.0200.125 ITP20* 2.14E-061.39E-050.0140.122 WP08 13561.87E-051.78E-05-0.1050.119 23262.17E-051.73E-05-0.1210.131 36342.36E-051.70E-05-0.1260.115 Total13162.18E-051.74E-05-0.1190.121 WP08* 2.25E-052.10E-05-0.1210.146 * The results when tilt and shift are calculated from linear fits of two curves

19. Difference over Time, CERN

20. Difference is not Linear: Example 1 For many magnets the difference in the middle is constant or decreasing when the global slope is positive. Example: 3428 A1 WP08-FID Diff > 0

21. Difference is not Linear: Example 2 Example: 2003 A2 Step WP08F-FID Diff < 0

22. Difference is not Linear: Example 3 Example: 1045 A2 Step WP08-FID Unusual pattern

23. Difference is not Linear: Test WP08 Whole production average slope: sides and middle

24. Correlation between 2 Runs After calculating the “y-mate” points the points measured from the connection side are laid out on the abscissa, and from the lyre side – on the ordinate (each point represent one Y value). Dipoles of firm 1 tested during last 5 months of 2005, aperture 1 Where does this happen ?

25. Correlation Example 1 Very good measurement 1031, A2, WP08-FID Correlation 0.97 Slope = - 3.23E-06 Shift = - 0.06 Avg h = 0.09, Std h = 0.05 Max h = 0.22

26. Correlation Example 2 Bad measurement 2214, A1, WP08-FID Correlation 0.15 Slope = 5.75E-05 Shift = - 0.25 Avg h = 0.23, Std h = 0.17 Max h = 0.61

27. Correlation Example 3 Awful measurement 2248, A1, WP08-FID Correlation – 0.33 Slope = 9.42E-05 Shift = - 0.82 Avg h = 0.33, Std h = 0.23 Max h = 0.85

28. Correlation for Each Aperture

29. Correlation coefficient between the two runs over each meter, all magnets Firm 1 Firm 2 Firm 3 Correlation per Meter

30. Correlation versus Slope Correlation over the whole aperture length This is a simulation result when one curve was rotated

31. Saw Tooth Effect Reason From the study of G.Gubello et al. (Instrumental uncertainty in measuring the geometry of the LHC main dipoles, EPAC 2004). From the report by M.Dupont et al. (The laser tracker: A Major Tool for the Metrology of the LHC. IWAA2004) “ Finite roto-translation between the curves is intrinsic in the ideal measuring procedure…” (“…due to the definition of the common reference system that is not directly measured…”) “The potential cause [ for larger errors ] was identified in small laser tracker displacements due to interaction with the ground…” “This phenomena [ saw toothed effect ] is due to a combination of errors: … bundle adjustment 0.08mm, …tracker error 5ppm, … centering error of the ‘mole’ 0.07mm… This gives the limit [ for the saw tooth height ] of 0.47mm at 3σ…”

32. Horizontal Plane Whole production statistics is very close to the simulation results* (G.Gubello et al. 2004) Here p - slope, q – shift, h – tooth * They did not make simulations for the vertical plane. STEPHeight* averageHeight stdSlope avgSlope stdShift avgShift std ITP150.0830.050-9.51E-087.04E-060.0160.110 ITP20-GEO0.0850.0489.33E-078.40E-060.0110.112 WP08-FID0.0910.0533.17E-066.91E-06-0.0160.112

33. Compare with the Horizontal Plane Effect in the vertical plane is close to that in the horizontal one with the exception of tests at WP08 whole production

34. Compare with the Horizontal Plane whole production by firm

35. Saw Tooth at WP08 The above analysis shows that the saw tooth effect for many measurements at WP08 is not random and cannot be explained by the errors intrinsic to the measurement procedure. Alarms: 1.Saw tooth height μ + 3σ > 0.47 mm ( 314 apertures ) 2.Big rotation (difference slope) … 3.Large local saw tooth with unusual pattern for the difference …

36. Temperature Effects ? For the measurements after cold test the larger saw tooth effect can be explained by the beam deflection in the tube:  There can be a temperature gradient.  Convection cells establish near the dipole extremities.  Such cell can act like a lens. Similar effect was studied by MTA team on the dipole model. (E.Ainardi et al. Light Beam Deflection through a 10m Long Dipole Model. MTA-IN-99-070, L.Bottura et al. The Methods of the LHC Magnets’ Magnetic Axis Location Measurement. IWAA99)

37. Temperature Effect Analysis Here the statistics is calculated for the three populations: cold magnet (1), hot magnet (-1), magnet and room temperature are equal (0) (abs.diff. < 0.1 deg) Average temperature room and magnet % of tests

38. Other Factors Nothing found so far. For the CERN tests have been tried:  Operator (listed only operators with more than 30 tests)  Laser tracker (for 606 tests the tracker is unknown)  Bundle RMS OperatorTestsAvg hStd hAvg slopeStd slopeAvg shiftStd shift SETIS1720.100.061.08E-052.01E-05-0.080.16 SIMCO20660.110.061.96E-051.89E-05-0.120.13 TrackerTestsAvg hStd hAvg slopeStd slopeAvg shiftStd shift 5664800.120.062.36E-051.63E-05-0.120.11 7387540.090.051.32E-051.66E-05-0.100.13 9374820.120.062.31E-052.38E-05-0.120.11 Average tooth height over bundle RMS

39. Conclusions The saw tooth effect is In the horizontal plane: –small and rather constant at firms and at CERN In the vertical plane: –close to that in the horizontal plane –much larger at CERN (first tests after the cold one) and at firm 2 –in general is the result of a roto-translation between the two curves with, at CERN, mostly positive slope and is larger near the lyre side –there are many exception from the above statement

40. ? ? ? † Does the saw tooth effect deteriorate the accuracy of the GA calculation ? † Is it curable without re-measurement ?