Field quality in half of the main LHC dipoles

1
Field quality in half of the main LHC dipoles
FNAL, 22nd February 2005

• E. Todesco
• CERN, Accelerator Technology Departement
• Geneva, Switzerland
• B. Bellesia, P. Hagen, C. Vollinger, E.Wildner
  data validation, storage, analysis at room temp.
• L. Bottura, S. Sanfilippo, et al - data
  validation, storage, analysis at 1.9 K
• AT-MAS project engineers, cable section, L.
  Rossi, W. Scandale, J.P. Koutchouk
• AT-MTM - instrumentation section
• O. Bruning, S. Fartoukh - beam dynamics targets

2
Contents

• Introduction
• Status of field quality
• Systematics
• Random
• Correlations
• Selected topics
• Building a field quality control system
• The inverse problem
• The method
• Assembly defects
• Trends in production
• Coil plastic deformation due to first powering
• Conclusions

3
Introduction how to judge field quality

• Coordinate along the machine s
• Transverse coordinate system (x,y)
• Multipolar expansion of the field
• Byi Bx B0 10-4 ? (bni an) (xiy)/Rrefn-1
• Rrefreference radius (2/3 of aperture radius)
• B0main component (vertical field), b1 104 by
  definition
• bn, an multipolar components are grouped in
  families
• b3 b5 b7 ... up-down and left right symmetry
  (allowed components)
• b2 b4 b6 ... left right antisymmetry
• a2 a4 a6 ... up-down antisymmetry
• a3 a5 a7 ...
• A perfectly symmetric coil has only allowed
  multipoles

4
Introduction how to judge field quality

• Multipolar expansion of the field
• Byi Bx B0 10-4 ? (bni an) (xiy)/Rrefn-1
• The power series converges up to the distance of
  the first conductor from the centre (ra28 mm)
• i.e., at xiyra all terms of the series are
  approximately equal
• (bni an) ra/Rrefn-11
• therefore
• bn , an ? Rref/ ran (17/28)n(2/3)n
• The decay of the multipolar coefficients comes
  from Biot-Savart law
• Rref has no physical meaning ! it just like
  choosing a measurement unit
• Specifications are given as
• Range for the systematic (the average over one
  sector or over all LHC)
• Upper limit for random (standard deviation over
  one sector)
• Orders of magnitudes
• bn , an1 unit or less, to be controlled within
  0.1 units
• This implies a precision in coil positioning of
  less than 0.1 mm

5
Introduction baseline of measurements

• Room temperature (baseline 100)
• collared coils (coil in the collars)
• cold masses (plus iron yoke)
• Power test at 1.9 K (baseline 100)
• Magn. meas. 1.9 K (baseline 20)
• Loadline (static conditions)
• Machine cycle dynamic effects
• Magnetic measurements
• Rotating coils
• 20 times 0.75 m long coils at r.t.
• 12 times 1.12 m long coils at 1.9 K

6
Introduction available data
7
Introduction use of magnetic measurements

• Steer the production towards the beam dynamics
  targets
• Definition of corrective actions when needed
• Warm measurements, and warm-cold correlations
• Build the database of the field quality of the
  machine
• Needed for beam dynamics
• Both warm and cold measurements
• Carry out a quality control of the production
• Warm measurements can be used as an X-ray to
  determine the conductor position
• Up to now, 15 cases of assembly errors detected
  in this way
• 10 electrical shorts located in this way
• This allows intercepting assembly faults at a
  very early stage
• Saving for the manufacturer (and motivation in
  carrying out the measurements)
• Saving for CERN (cryostating, test at cold, time)

8
Contents

• Introduction
• Status of field quality
• Systematics
• Random
• Correlations
• Selected topics
• Building a field quality control system
• The inverse problem
• The method
• Assembly defects
• Trends in production
• Coil plastic deformation due to first powering
• Conclusions

9
Status of field quality allowed systematics

• The most difficult task
• b1, b3, b5, b7 are linked together any change
  affects all of them
• 3 coil cross-sections
• X-section 1 (34 magnets) the prototype baseline
• X-section 2 (147 magnets)
• modification of copper wedges of up to 0.4 mm to
  correct b3 b5 (March 2002)
• X-section 3 (361 magnets) present baseline
• Additional 0.125 mm insulation sheet in coil
  mid-plane (August 2003)
• to correct b3 b5 b7
• Present situation
• b3 optimal, b5 marginal, b7 out

10
Status of field quality unallowed systematics
11
Status of field quality random components

• spread of bending strength under control
• random b3 marginal, but the specification is for
  one sector 1/8 of the LHC, independent power
  supply of dipoles and correctors

12
Status of field quality warm-cold correlations

• Standard way of evaluating correlations
• Linear fit
• Correlation coefficient
• This can be very misleading
• It strongly depends on the range of multipoles
  that have been explored in the design
• If we had made no X-section changes, worse
  correlations ?

13
Status of field quality warm-cold correlations

• Example
• We look at the recent production of one firm,
  which is stable within 2 units
• The correlation looks much worse
• Same data !

14
Status of field quality warm-cold correlations

• Example
• If the manufacturer had such a good quality
  control, and pieces always nominal, so to produce
  magnet with very similar b3
• We would conclude no correlation !
• Better way
• The relevant quantity is the spread of the
  offsets
• To be compared to the beam dynamics targets

15
Status of field quality warm-cold correlations

• Main allowed harmonic normal sextupole b3
• Results of measurements at room temperature

16
Status of field quality warm-cold correlations

• Main allowed harmonic normal sextupole b3
• Results of the offset from warm to cold
  (injection) along the production
• Cool-down and persistent currents very stable
  (effective cable control)

17
Contents

• Introduction
• Status of field quality
• Systematics
• Random
• Correlations
• Selected topics
• Building a field quality control system
• The inverse problem
• The method
• Assembly defects
• Trends in production
• Coil plastic deformation due to first powering
• Conclusions

18
Building a field quality control system

• The Lego model for FQ control
• The right tower high field (11850 A)
• at 1.9 K
• Iron yoke saturation
• Lorentz forces deformations
• The left tower injection (760 A) at 1.9 K
• Persistent currents
• The second floor geometric at 1.9 K
• Cool-down deformations
• The first floor cold mass at r.t.
• Iron yoke effect
• The ground floor collared coil at r.t.
• Coil lay-out
• Assembly deformations

Tokyo Town Hall, K.Tange associates
19
Building a field quality control system

• Each floor is controlled independently
• At each stage, we do not control all the
  building, but only the floor the we added
• The main sources of variability are
• The collared coil (coil geometry)
• What we add at injection (persistent currents)
• Once the production is started
• Once we have enough statistics (30 magnets)
• We drop the anomalous known cases
• We compute average and sigma
• We define a acceptance range as ??3.5 ?
• Alarm is set beyond 3.5 ? (yellow) and 7 ? (red)
• Major problem distinguish false measurements
  from true problems (human needed)

Tokyo Town Hall, K.Tange associates
20
Building a field quality control system - example

• Example (a4, Firm3)
• After 11 Firm3 magnets
• ? and ? evaluated,
• bound at ??3.5 ?
• Revision of limits
• after 100 magnets
• Collared coil - bounds by S. Pauletta (2002),
  revision by C. Vollinger (2004)
• Cold mass - bounds by E. Wildner (2003)
• IEEE Trans. Appl. Supercond. 14 (2004) no. 2,
  pp.173-176
• W/C correlations - bounds by P. Hagen (2004)
• Control limits and model are independent
• Control limits and beam dynamic targets are
  independent
• we use measurements to define what is normal
  control limits point out anomalies
• If targets are not met corrective actions are
  taken

21
Field quality in the technical specification

• The problem should field quality targets be in
  the technical specifications for the Firms ?
• The manufacturer can guarantee procedures and
  tolerances
• But it has little experience in the field quality
  analysis
• The solution adopted
• No tolerances on multipoles (we do not pay for
  multipoles)
• A decollaring or unwelding can be asked by CERN
  if the field quality anomalies indicate a wrong
  procedure (holding point)
• Corrective actions to steer multipoles towards
  targets can be asked by CERN
• A posteriori, we found that
• The signatures of assembly errors are large
  variations of field quality along the magnet axis
  (errors localized in some positions), that do not
  affect the average
• It is practically impossible to give acceptance
  windows on multipoles

22
Contents

• Introduction
• Status of field quality
• Systematics
• Random
• Correlations
• Selected topics
• Building a field quality control system
• The inverse problem
• The method
• Assembly defects
• Trends in production
• Coil plastic deformation due to first powering
• Conclusions

23
The inverse problem

• Inverse problem finding the coil displacement
  that gives rise to the measured field anomalies
• The space of solutions is very large - coil
  movements - but only a few are physical
• Field anomaly is a vector (b2, b3, b4, b5 ... a2,
  a3, a4, ...) - how to weight field anomalies ?
• Same problem for the coil optimization - usually
  solved but putting weights (vn,wn) by
  experience
• Usually one tries to minimize a scalar quantity
• ? vn(bns-bne)2 wn(ans-ane)2
• where s is the results of the simulation, and e
  is the field anomaly
• A complete match is impossible, since there is a
  natural spread of the multipole ... but what is a
  good match ? and a bad one ?

24
The inverse problem

• Proposed approach to the inverse problem
• We restrict the solution a number of physical
  coil movements
• In this way we avoid unphysical solutions
• The weight is the inverse of the spread of the
  multipole
• I.e., we express the field anomaly not in term of
  units but in term of how many sigma is far from
  the normal value
• This is an objective criteria to set weights for
  optimizations
• The spread to be used depends on the problem
• First example anomaly in the average multipole
  spread to be used stdev of averages
• Second example spike along the magnet axis
  spread to be used stdev of multipole along axis
• Third example variation before and after thermal
  cycle spread to be used reproducibility of the
  measurement

25
The inverse problem

• Proposed approach to the inverse problem
• We do not use a norm of the distance, but rather
  a norm of the maximum
• Max vnbns-bne ,wnans-ane
• Any solution that brings back all anomalies below
  three sigma is considered a good solution
• We do not look for an exact match, but for a
  match within three sigma
• Within three sigma, everything is to be
  considered as normal ...
• This also avoids unphysical solutions !

26
The inverse problem assembly defects

• 13 defects found at the level of collared coil
  analyzing field anomalies at warm over 650
  magnets (2.2)
• 9 cases of bad gluing of the coil, leading to
  block6 radial movements of 0.5 to 1 mm
• 4 assembly defects
• All cases cured
• at the level of
• collared coil

27
The inverse problem assembly defects

• Three types of assembly defects found

A folded outer shim (2 times)
A missing outer shim
A double coil protection sheet
28
The inverse problem assembly defects

• 9 cases of bad gluing of block6, leading to
  radial movement of 0.3 to 1 mm
• Small anomalies in b8, a6 (0.5 units)
• Detected in all Firms, now solved

A badly glued coil after disassembly
29
The inverse problem trends in production

• Since the beginning of the series in Firm2 we had
  a large systematic a4, not associated to a2 -
  hard to obtain with simulations
• The bad cases of May 2004 suggested to explore
  the possibilty that this effect was due to block6

• A radial movement of 0.1 mm inward of block6 of
  the upper pole, and nothing on the lower, gives
  the observed a4 (0.5 units) and practically no a2

30
The inverse problem trends in production

• In summer 2004, we had a large negative trend in
  average b3
• risky for the beam dynamics
• associated to higher b5, and no variations of
  transfer function

• A movement of up to 0.3 mm inward of block6 of
  all poles, gives the observed b3, b5 and no main
  field as observed

31
Electrical short localization with room
temperature magnetic measurements

• Cases of electrical shorts - some of them only
  during collaring
• We started use magnetic measurements to locate
  shorts
• Large anomaly (a2 70 units), easy to locate pole
  and along the axis
• Exact location in cross-section though comparison
  with model
• In general, good agreement, locations confirmed
  by disassembly
• 7 shorts located
• All in head
• connection
• side

32
Contents

• Introduction
• Status of field quality
• Systematics
• Random
• Correlations
• Selected topics
• Building a field quality control system
• The inverse problem
• The method
• Assembly defects
• Trends in production
• Coil plastic deformation due to first powering
• Conclusions

33
The inverse problem effect of first powering

• Analysis of changes in the coil geometry induced
  by the first powering
• Data of 13 magnets measured after cold test at
  r.t.
• Small systematic difference in b3, b5, b7 before
  and after power test
• Strong correlation b3, b5, b7 only one movement
  responsible

34
The inverse problem effect of first powering

• Difference before and after power test - magnet
  2096
• Field anomaly expressed in units of sigma
• The effect of the movement of block6 of 0 micron
  is subtracted

35
The inverse problem effect of first powering

• Difference before and after power test - magnet
  2096
• Field anomaly expressed in units of sigma
• The effect of the movement of block6 of 5 micron
  is subtracted

36
The inverse problem effect of first powering

• Difference before and after power test - magnet
  2096
• Field anomaly expressed in units of sigma
• The effect of the movement of block6 of 10 micron
  is subtracted

37
The inverse problem effect of first powering

• Difference before and after power test - magnet
  2096
• Field anomaly expressed in units of sigma
• The effect of the movement of block6 of 15 micron
  is subtracted

38
The inverse problem effect of first powering

• Difference before and after power test - magnet
  2096
• Field anomaly expressed in units of sigma
• The effect of the movement of block6 of 20 micron
  is subtracted

39
The inverse problem effect of first powering

• Difference before and after power test - magnet
  2096
• Field anomaly expressed in units of sigma
• The effect of the movement of block6 of 25 micron
  is subtracted

40
The inverse problem effect of first powering

• Difference before and after power test - magnet
  2096
• Field anomaly expressed in units of sigma
• The effect of the movement of block6 of 30 micron
  is subtracted

41
The inverse problem effect of first powering

• Difference before and after power test - magnet
  2096
• Field anomaly expressed in units of sigma
• The effect of the movement of block6 of 35 micron
  is subtracted

42
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43
The inverse problem effect of first powering

• Difference before and after power test - magnet
  2096
• Field anomaly expressed in units of sigma
• The effect of the movement of block5 of 0 micron
  is subtracted
• (just to prove that winning the multipole bingo
  is not so easy !)

44
The inverse problem effect of first powering

• Difference before and after power test - magnet
  2096
• Field anomaly expressed in units of sigma
• The effect of the movement of block5 of 5 micron
  is subtracted

45
The inverse problem effect of first powering

• Difference before and after power test - magnet
  2096
• Field anomaly expressed in units of sigma
• The effect of the movement of block5 of 10 micron
  is subtracted
• It does not work - b7 goes out and b5 does not
  change !

46
The inverse problem effect of first powering

• Interpretation through model
• outward radial movement of
• block6 of 20 to 30 ?
• or block6 inward compression
• of 30 to 50 ?
• Comments
• The shift is not related to quench
• The shift smoothly depends on current
• The shift could be related to the spike
• activity during the first powering
• Why only block6 ?
• Small effect (0.3 units of b3), not relevant for
  the beam
• Very nice benchmark for the method (difficult
  case)
• Could be interesting to understand mechanical
  behavior during powering

47
Conclusions

• Status
• Systematics within targets except b7
• Randoms under control, further minimization of
  random b3 by installation
• Selected topics
• Quality control
• Control limits independent of targets
• Each assembly stage is analyzed as the difference
  with respect to the previous
• Field quality in the specification
• No acceptance windows for multipoles, but
  possibility of corrective actions
• Disassembly can be asked on the basis of field
  anomalies
• The inverse problem
• Try only with physical movements
• Use the natural spread of multipoles as a weight
• Do not look for exact match, but stay within 3
  sigma
• The most sensitive spot for field quality block6
  radial position
• Is it the same for other designs ?

48
Are all firms equal ?

• In HERA the two manufacturers had
• large differences in Field Quality
• (Transfer function ...)
• Based on this experience, the
• expected errors for the LHC
• included an systematic difference
• between firms (the uncertainty)
• The original baseline assumed the same firm
  installed in the same octant
• It has been broken at the beginning of the
  pre-series, thus allowing 1/3 of dipoles to be
  built per manufacturer
• For the cable manufacturer the baseline has been
  kept
• What can we say about uncertainty after 640
  magnets ?

49
Are all firms equal ?

• Bending strength magnetic length transfer
  function
• Negligible differences between firms

50
Are all firms equal ?

• Second allowed harmonic normal decapole b5
• Large difference between Firm1 and Firm2-3 (3
  sigma)
• The origin of this difference is not explained

51
Are all firms equal ?

• Third allowed harmonic normal 14th-pole b7
• Large difference between Firm2 and Firm1-3 (3
  sigma)
• The origin of this difference is not explained

52
Are all firms equal ?

• Multipoles - the firm trademark is in high orders
  !
• Small differences in b3
• Large differences in b5, b7, b9, difficult to be
  reduced because of coupling
• In skews, some differences in a3 a4 a5