1. Elena Wildner and Natalia Emelianenko AT/MAS
Impact of saw-tooth effect on GA calculation for MB and possible remedies
Elena Wildner and Natalia Emelianenko AT/MAS

2. Outline I. Description of problem II. Reasons for the effect
III. Correction of the saw tooth
IV. Testing the method
V. Results
Concepts - Look and feel
Each subject could fill a whole term if I tried to give the full formalism
Consider it a guided tour through the antimatter universe
A bit of everything
I hope that everybody will hear something new, although I am sure that most of you have heard many of the things I am talking about. However, if somebody finds out at the end of the lectures that he or she knew already everything I mentioned - please come to me and you will find yourself giving these lectures next year.
VI. Conclusion

3. Measurements with saw tooth
The analysis is made for the Dipole where the effect is significant (longer magnet)
Magnet 2248, vertical plane
Questions:
Why do the spools “move” by up to 0.5 mm from industry measurement to CERN measurement?
Why are measurements varying up to 1 mm along the axis?
The two measurements from both sides of the magnet separated:
Red: connection side
Blue: lyre side
I. Description of the problem

4. Saw tooth: “3D” visualization of measurement
The effect is present for all magnets, for long magnets the effect is more important
Points measured
starting from the
connection side
Points measured
from the lyre side
The band joins the
points of the two
apertures
Magnet MB 2273,
rejected measurement
at ITP20-GEO
I. Description of the problem

5. The saw tooth
Far from tracker
Close to Tracker
We use the term “saw tooth” for measurement value variations coming from the fact that we use measurements from both sides of the cold bore tube.
To really see the effect, the two measurements have to be separated.
I. Description of the problem

6. Effects on the machine
Corrector position error to be estimated (industry data)
Correctors may be misplaced due to wrong positioning of magnet (CERN)
Shifts meant for aperture gain not in the good direction?
Misalignment: Degradation in the vertical plane of the so called geometry classes
All golden magnets degraded if 0.1 mm shift in GA in firm 2!!!
fraction
fraction v h
h [0.01mm]
v [0.01 mm]
0.01 mm
I. Description of the problem

7. II. Reason for the effect
Measurement errors, recommendation 2002
D.Missiaen, M.Plusquellec, M.Dupont
Measuring The Mechanical Axis Of Lhc Dipoles Using A Laser Tracker.
Installation Procedure. LHC-G-IP-0015 rev 1.0. EDMS
II. Reason for the effect

8. II. Reasons of the effect
Measurement errors, recommendation 2004
D.Missiaen, M, Dupont, P. Winkes:
The Laser Tracker: a major tool for the metrology of the LHC, IWAA2004, CERN, Geneva, 4-7 October 2004
Recommended limit is 0.47 mm
II. Reasons of the effect

9. The bundle G. Gubello, M. La China, W. Scandale
Instrumental Uncertainty In Measuring The Geometry Of The LHC Main Dipoles.
LHC Project Report 732. Presented at the 9th European
Particle Accelerator Conference (EPAC'04)
5-9 July 2004, Lucerne, Switzerland
“The largest loss of accuracy is in fact due to the definition of the common reference system that is not directly measured … but it is worked out from the network points measured by opposite stations (and thus affected by a combination of the related errors).
After one hundred iterations the simulation provided the statistical discrepancy between the axis profiles obtained by two opposite stations as a function of laser accuracy and network point dispositions”
Roto-translation: p - slope, q – shift, h – tooth
II. Reasons for the Effect

10. The bundle
The best possible guess of the tube position is the “mean” of the measurements.
“Uncertainty” of corrector position
GA on which the spool is mounted and measured, itp15bis.
Best fit
II. Reasons for the Effect

11. The bundle
The best possible guess of the tube position is the “mean” of the measurements.
“Uncertainty” of corrector position
GA on which the spool is mounted and measured, itp15bis.
Best fit
II. Reasons for the Effect

12. Separating the measurements
Let us have a look at the saw tooth statistics of the whole production
First glance:
Dipoles of firm 1 tested during last 5 months of 2005, aperture 1
II. Reasons of the effect

13. Saw tooth height value The “Y-mate” point should be
calculated for each point
measured from another side
by means of interpolation
difference
II. Reasons of the effect

14. Defining the average saw tooth height
Sdiff is the sum of the interpolated difference between the two curves
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
II. Reasons of the effect

15. Average saw tooth height over time, firms and CERN
Absolute
Vertical plane
“With sign”
II. Reasons of the effect

16. Average saw tooth height over time, firms and CERN
Industry - ITP15 (corr. positioning)
CERN – WP08 (final aperture and corr. Positioning)
Vertical plane
We see that the situation is
stable and rather good in industry,
but much worse and degrading at CERN
(increasing production rate)
Firm 1 and 3 are similar
II. Reasons of the effect

17. Average saw tooth height at CERN
Saw tooth height at CERN over time
The dates of the
related presentations !!!
20 Dec 2005
9 Feb 2006
II. Reasons of the effect

18. Saw tooth height, firms and CERN
Horizontal Plane
Statistics (for February 2006):
ITP15 – 716 dipoles (1432 apertures)
ITP20-GEO – 708 dipoles (1416 apertures)
WP08-FID – 657 dipoles (1314 apertures)
Measurement results better (!) than
non-steady simulation
STEP
Height avg
Height std
Slope avg
Slope std
Shift avg
Shift std
Simulation (steady)
0.065
0.010
-3.0E-07
4.6E-06
0.040
Simulation (non-steady)
0.125
0.095
-2.4E-07
4.0E-06
-0.015
0.160
ITP15
0.083
0.050
-9.5E-08
7.0E-06
0.016
0.110
ITP20-GEO
0.085
0.048
9.3E-07
8.4E-06
0.011
0.112
WP08-FID
0.091
0.053
3.2E-06
6.9E-06
-0.016
II. Reasons of the effect

19. Bundle Error Simulation in the Vertical Plane
Other networks:
n.p. 1         3        4
x:    4.25     4.25     13.25     13.25   (longitudinal)
z:     -1            1         -1             1    (vertical)
                    m                   q
avg      -3.00e-007    2.56e-006 std       4.35e-006    3.39e-005
n.p. 1   2    3    4     5      6     7     8
x:   .5  .5    5    5    15    15   ;
z:    1   -1  2    -2    2    -2       1    -1;
                   m                     q
avg       1.86e-007   -1.23e-006 std       2.21e-006    2.14e-005
m is the rotation between the
bore axes measured from opposite
stations and q is the translation
Network: p x: z: ?
M. La China made the Monte Carlo simulation for the vertical plane, and the results are very close to those for the horizontal plane and does not strongly depend on the network points configuration.
II. Reasons of the effect

20. Saw tooth height, firms and CERN
Vertical plane:
Strange increase for the CERN tests
II. Reasons of the effect

21. Large saw tooth in firms and CERN
Criterion
Amount
Percentage
μ + 1σ > 0.47 12
0.2
μ + 2σ > 0.47 47
1.0
μ + 3σ > 0.47
144
3.0
max > 0.47 83
1.7
Industry
CERN
Criterion
Amount
Percentage
μ + 1σ > 0.47 32
1.3
μ + 2σ > 0.47
209
8.3
μ + 3σ > 0.47
474
18.9
max > 0.47
291
11.6
μ - the average saw tooth height along the aperture, σ – its standard deviation
II. Reasons of the effect

22. Large saw tooth in CERN Vertical plane (statistics by firm):
Strange increase for the CERN tests
Temperature?
Recent tests on the external point
measured through and ”around” the
tube show that the beam is really
deflecting for the measurement
with big saw tooth (thanks to
P.Winkes)
Temperature measurement made
at Ansaldo shows that at normal
conditions the temperature gradient
can be up to 2 degrees, and the
temperature inside the tube is
constant and low with respect to
the room temperature.
II. Reasons of the effect

23. Mirages Refraction or reflection: layers of the hot and cold air
*image sources – Wikipedia, graphics.stanford.edu, hypertextbook.com/physics/waves/refraction
II. Reasons of the effect

24. Temperature difference in the cold bore tune
E. Ainardi, L.Bottura, and N.Smirnov, “Light beam deflection through a 10m long dipole model”, CERN LHC-MTA, Tech. Rep. May 1999.
N. Smirnov et al. “The methods of the LHC Magnets’ Magnetic Axis Location Measurement”. IWAA 1999.
P.Schnizer et al. “Experience from measuring the LHC Quadrupole axes”. IWAA 2004.
lens
We may have a longitudinal temperature difference along the magnet
This may cause a convection cell at the ends of the magnet at ~ 0.2 m from the cold bore ends.
The convection cells deflect the light beam up/down, if magnet warm/cold inside
Act only in the vertical plane
tracker
error
0.2
II. Reasons for the Effect

25. Non detectable bias!! Magnets too high by 0.1 mm?
Mole centering
Lyre side
Connection side
Horizontal plane, saw tooth, mean value of the two measurements is a good estimation
Vertical plane, no saw tooth, we have a bias of 0.1 mm (from comparison AC-GEO mole for SSS) if AC mole correctly centered.
Non detectable bias!! Magnets too high by 0.1 mm?
II. Reasons for the Effect

26. Error contributions, summary
To sum up the reasons of the saw tooth effect:
__________________________________________________
Bundle adjustment (best fit on network points to translate the measurements in the same reference system): 0.08 mm rms at any position (3s ~ 0.2 mm).
>>> Negligible for the bad measurement at WP08 !
Calibration mole centring error: 0.07 mm. This is not visible in the vertical plane and considered = 0 in this plane
Random mole centring error can be estimated from the data. Must be small (from comparison with the simulation results).
Thumb estimation gives 0.06 mm and 4ppm.
Beam deflection in the tube
Note:
Laser tracker errors: 5 ppm cannot explain the roto-translation between the curves.
II. Reasons of the effect

27. Simulation of bundle contribution
Vertical Plane
Monte Carlo simulation for ideal measurement and “non-steady”; results do not strongly depend on the network points configuration.
In the table from measurements in the horizontal plane the mole error is included (0.07 mm rms as stated by SU )
This means that we are conservative by taking the same values in the vertical plane (mole centering error the same for the two measurements from the two sides, doe not contribute to saw tooth)
II. Reasons of the effect

28. The idea for correction for temperature effect
Points close to the Tracker more correct than points far from the Tracker.
Superposing the curves while keeping fix the points close to the tracker
No change in the reference system for this correction
When both curves corrected a new GA is constructed (3 dimensions with weighted best fit)
Shape and corrector positions recovered
Far from tracker
Close to Tracker
III. Correction of the saw tooth

29. Description of the problem
Apertures treated individually z
Linear interpolation from “knee” at 0.2 cm, from ends y
Reference line for the correction
0.2 m
0.2 m
Convection cell position
Crossover straight line from best fit and the 0.2 m boundary (rotation point)
Measurement from Connection Side
Measurement from Lyre Side
III. Correction of the saw tooth

30. Description of the problem 2
Procedure proposed for the correction:
Connection side
Non Connection side z y
III. Correction of the saw tooth

31. Description of the problem 3
III. Correction of the saw tooth

32. Difference not always linear, Example 1
For many magnets the difference
in the middle is constant or
decreasing when the global
slope is positive.
At least 0.2 mm measurement error
Temperature?
Example: 3428 A1 WP08-FID
Diff > 0
III. Correction of the saw tooth

33. Difference not always linear, Example 2
Example: 1045 A2
Step WP08-FID
Local measurement problem for at least
one of the measurement directions
(several points):
At least 0.4 mm at the connection end
and locally along the tube 0.3 mm.
III. Correction of the saw tooth

34. I. Description of the problem 2
1. Why do we choose 0.2 m from the ends?
The position of the convection cell is difficult to estimate by analysis (very few measurement points). The value is chosen from MTM reports.
Check for 10 and 100 cm in plots below.
III. Correction of the saw tooth

35. I. Description of the problem 2
2. Why do we make a linear interpolation of the measurement?
The linear interpolation is chosen due to the similarity with the GA construction which is a best fit of a plane (however 3D).
3. Why is the reference line taken between the two knee points?
We estimate that the two knee-points are the two last points where the data is not affected by the light deflection (corresponding to the position of the convection cell). So from these points onward we should superpose the two curves best fitted with straight lines.
III. Correction of the saw tooth

36. Saw tooth before and after the correction
III. Correction of the saw tooth

37. Testing the method
We believe that we can treat the data so as to get a better idea of the magnet shape by compensating for the temperature effects
How to proceed to check this assumption?
Check the corrected value of the saw tooth. It should be small (comparable to the measurement errors for one measurement, from one side).
Compare shape at WP08 with shape at itp20, including position of end cover. If we can recover the shape at ITP20 by this method we believe the idea makes sense. Checks are made also for one case in industry where two measurements were made for magnet 2273.
A set of magnets have been chosen:
> big saw tooth in CERN measurements (WP08),
> perfect measurement in industry (step ITP20-GEO) and
> adjusted at CERN to their industry shape (itp20).
Another test on 174 magnets with big saw tooth at last step at WP08, ready to be installed in the tunnel.
IV. Testing the method

38. Results for end cover positions (1)
Lyre
Connection
The uncertainty of the mid-plane correction for the end covers positions is about 0.01 mm at 1σ
V. Results

39. Results for end cover positions (2)
Shape change due to diffence in positioning firm CERN included.
End cover position recuperated with the 3D correction.
Difference CERN-industry
Orig conn
Orig lyre
Corr conn
Corr lyre
Average
-0.10
-0.17
0.02
0.01
Stdev
0.21
0.19
0.17
0.16
V. Results

40. Results for the aperture classification
mag
orig
Corr/itp20
1080
silver
Golden/Golden
1105
1123
1135
1153
mid cell
Silver/Silver left right
1154
1163
1178
silver right
Silver/Silver
1211
Golden/Silver
1213
silver left
1221
golden
1246
1279
2056
2086
2096
2118
silver left right
2133
Silver right/Silver right
2152
2195
Silver
mag
orig
Corr/itp20
2216
silver right
Silver/silver
2247
silver
3035
silver left right
Silver/Silver
3102
Silver/Silver Left right
3152
Golden/Golden
3158
Silver/Golden
3203
3209
Golden/Silver
3238
3244
golden
3348
3392
3395
silver left
15 magnets recuperate their class (red),
5 are better after correction (blue),
1 is degraded (green)
12 magnets keep their class (black).
V. Results

41. Closer look on the classes
Why do the 5 magnets become better at CERN after correction?
1153, horizontal adjustment not good at CERN, combined sensitive point 1211, saw tooth in industry 2086, minor saw tooth in industry 3102, magnet better adjusted horizontally at CERN 3209, horizontal adjustment not good at CERN, combined sensitive point
Why is one degrading?
3158, magnet not well adjusted horizontally at CERN
V. Results

42. Magnet alignment, 2086 example (1)
V. Results

43. Magnet alignment, 2086 example (2)
Magnet shift
1153 0
1154 0
2096 0
2152 0
3203 0
3209 0
3395 0
1221 0
1246 0
3158 0
3392 0
2056 0
3348 0
1123 0
1213 0
1211 0
2216 0
2118 0
The mean plane after correction in the old reference
The magnet should be shifted in the positive direction!!!
V. Results

44. Corrector Z Error: Estimation for the Whole Machine
Magnets ready for the installation, WP08 completed - 698
Select those having
Measurements from both sides with more than 20 points
Difference linear fit RMS < 0.07mm
Max distance between curves > 0.32mm for at least one aperture
0.07 mm is the average RMS for all difference linear fits for WP σ
0.32 mm is bundle error 0.08 plus possible mole centering error 0.07mm at 3σ
So we have 176 dipoles with big saw tooth, possibly curable.
Others are considered “perfect”.
V. Results

45. Saw tooth reduction, 176 magnets
V. Results

46. End-cover vertical position recuperation
For the 54
itp20 adjusted
magnets
Avg
Std
Connection
Original
-0.09
0.26
Corrected
0.03
0.22
Lyre
-0.12
0.24
0.01
0.23
V. Results

47. Recuperation of classes, 176 magnets
Classes after correction
Whole set
V. Results

48. End Covers Move by Z Average shift by Z – -0.09 mm and -0.004 mrad.
difference between the new and the original coordinates of the end covers
Connection mm
Lyre side mm
Average mm
This corresponds to
the mean plane
average shift of
-0.09 mm and
average slope by Y of
mrad.
Average shift: 0.82x
V. Results

49. Corrector Z Error: Estimation for the Whole Machine
176 dipoles over 698 are corrected.
If we consider the rest of the dipoles Z error close to 0 we get:
If we “extrapolate” the shift fit:
0.082 of the average saw tooth for the both apertures – 0.006
we get for all magnets:
Average
0.03 mm
Standard deviation
0.06 mm
Average
0.08 mm
Standard deviation
0.04 mm
V. Results

50. Corrector positioning error in industry
Estimation from GA shift between two measurements (bundle contribution only). Conservative approach: temperature effect treatment would give only half. Possible rolls and pitches from a temperature effect will not be considered, they are small. #
Firm
Max conn
Average conn
Std conn
Max lyre
Average lyre
Std lyre 1
0.30
-0.00
0.08
0.28
0.02
0.09 2
0.40
-0.08
0.12
0.49
0.11 3
0.19
0.07
0.26
0.01 4
All
-0.02
0.10
0.05
This has to be added to the final results for the corrector estimation at CERN
V. Results

51. Corrector (6-pole) positioning error for installation
Horizontal [mm]
Vertical [mm]
Average
Stdev
Corrector mag/mech
0.00
0.10
Corrector position after coldtest
0.13
0.26
0.07
0.29/0.23
Transports and ageing
0.09
0.18
-0.01
0.12
Down into tunnel
0.17
0.08
0.11
Precision of positioning in tunnel
Contribution from tilting
0.30 -
Cold temperature
0.00?
Interconnection
Total
0.48
0.15/0.34
0.35/0.33
Requirement
0.50
Add: 0.1 mm rms for industry Take away contribution from saw tooth
Add: 0.0 mm for industry 0.19 mm for CERN
Quadratic addition of industry contribution only: 0.37 mm rms and 0.20 mm average Total would be: 0.33 mm rms, 0.34 mm average if all saw tooth effects reduced by treatment.
V. Results

52. Conclusion
Final results adding industry, subtracting CERN saw tooth contribution change the total situation very little (0.29 to 0.23 for corrector position after cold test)
The shifts are not always in the best direction for aperture optimization.
We recover the industry shapes (classes) that have been degraded due to measurement problems (saw tooth) for correctly positioned magnets (same positioning in industry and CERN)
Contributions for saw tooth cancels the positive average for the adjustments.
The mole contribution (centering error) also contributes in a “good” way for the average (this error may be contested).
We have to look at individual magnets and their position in the machine to judge better the effect on aperture.
Pitch and roll still to be done
VI. Conclusion

53. Conclusion Magnets are displaced Measurements very good \ ‘
VI. Conclusion