# Presentation: 297181

## Field quality in half of the main LHC dipoles

- 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

*FNAL, 22**nd** February 2005*

## 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

- 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

- Contents

- Ezio Todesco, LHC-MMS-MA

## Coordinate along the machine: s
Transverse coordinate system: (x,y)
Multipolar expansion of the field

By+i Bx= B0 10-4  (bn+i an) [(x+iy)/Rref]n-1
Rref=reference radius (~2/3 of aperture radius)
B0=main 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

- Transverse coordinate system: (x,y)
- Multipolar expansion of the field
- By+i Bx= B0 10-4  (bn+i an) [(x+iy)/Rref]n-1
- Rref=reference radius (~2/3 of aperture radius)
- B0=main 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

- Introduction: how to judge field quality

- Ezio Todesco, LHC-MMS-MA

## Multipolar expansion of the field
By+i Bx= B0 10-4  (bn+i an) [(x+iy)/Rref]n-1
The power series converges up to the distance of the first conductor from the centre (ra=28 mm) 
i.e., at ¦x+iy¦=ra all terms of the series are approximately equal
(bn+i an) [ra/Rref]n-1~1
therefore 
bn , an  [Rref/ ra]n ~(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 , an~1 unit or less, to be controlled within 0.1 units
This implies a precision in coil positioning of less than 0.1 mm

- By+i Bx= B0 10-4  (bn+i an) [(x+iy)/Rref]n-1
- The power series converges up to the distance of the first conductor from the centre (ra=28 mm)
- i.e., at ¦x+iy¦=ra all terms of the series are approximately equal
- (bn+i an) [ra/Rref]n-1~1
- therefore
- bn , an  [Rref/ ra]n ~(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 , an~1 unit or less, to be controlled within 0.1 units
- This implies a precision in coil positioning of less than 0.1 mm

- Introduction: how to judge field quality

- Ezio Todesco, LHC-MMS-MA

## 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

- 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

- Introduction: baseline of measurements

- Ezio Todesco, LHC-MMS-MA

## Introduction: available data

- Ezio Todesco, LHC-MMS-MA

## 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)

- 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)

- Introduction: use of magnetic measurements

- Ezio Todesco, LHC-MMS-MA

## 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

- 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

- Contents

- Ezio Todesco, LHC-MMS-MA

## 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

- 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

- Status of field quality: allowed systematics

- Ezio Todesco, LHC-MMS-MA

## Status of field quality: unallowed systematics

- Ezio Todesco, LHC-MMS-MA

## 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]

- random b3 marginal, but the specification is for one sector [1/8 of the LHC, independent power supply of dipoles and correctors]

- Status of field quality: random components

- Ezio Todesco, LHC-MMS-MA

## 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 ?

- 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 ?

- Status of field quality – warm-cold correlations

- Ezio Todesco, LHC-MMS-MA

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

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

- Status of field quality – warm-cold correlations

- Ezio Todesco, LHC-MMS-MA

## 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

- 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

- Status of field quality – warm-cold correlations

- Ezio Todesco, LHC-MMS-MA

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

- Results of measurements at room temperature

- Status of field quality – warm-cold correlations

- Ezio Todesco, LHC-MMS-MA

## 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)

- Results of the offset from warm to cold (injection) along the production
- Cool-down and persistent currents very stable (effective cable control)

- Status of field quality – warm-cold correlations

- Ezio Todesco, LHC-MMS-MA

## 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

- 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

- Contents

- Ezio Todesco, LHC-MMS-MA

## 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

- 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

- Building a field quality control system

**Tokyo Town Hall, K.Tange associates**

- Ezio Todesco, LHC-MMS-MA

## 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)

- 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)

- Building a field quality control system

**Tokyo Town Hall, K.Tange associates**

- Ezio Todesco, LHC-MMS-MA

## 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

- 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

- Building a field quality control system - example

- Ezio Todesco, LHC-MMS-MA

## 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

- 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

- Field quality in the technical specification

- Ezio Todesco, LHC-MMS-MA

## 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

- 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

- Contents

- Ezio Todesco, LHC-MMS-MA

## 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 ? 

- 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 ?

- The inverse problem

- Ezio Todesco, LHC-MMS-MA

## 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

- 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

- The inverse problem

- Ezio Todesco, LHC-MMS-MA

## Proposed approach to the inverse problem
We do not use a norm of the distance, but rather a norm of the maximum
Max [vn¦bns-bne¦ ,wn¦ans-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 !

- We do not use a norm of the distance, but rather a norm of the maximum
- Max [vn¦bns-bne¦ ,wn¦ans-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 !

- The inverse problem

- Ezio Todesco, LHC-MMS-MA

## 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

- 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

- The inverse problem: assembly defects

- Ezio Todesco, LHC-MMS-MA

## Three types of assembly defects found

- The inverse problem:
- assembly defects

**A missing outer shim**

**A double coil protection sheet**

**A folded outer shim (2 times)**

- Ezio Todesco, LHC-MMS-MA

## 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

- Small anomalies in b8, a6 (0.5 units)
- Detected in all Firms, now solved

- The inverse problem: assembly defects

**A badly glued coil after disassembly**

- Ezio Todesco, LHC-MMS-MA

## 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

- The bad cases of May 2004 suggested to explore the possibilty that this effect was due to block6

- The inverse problem: trends in production

- 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

- Ezio Todesco, LHC-MMS-MA

## 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

- risky for the beam dynamics
- associated to higher b5, and no variations of transfer function

- The inverse problem: trends in production

- 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

- Ezio Todesco, LHC-MMS-MA

## 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

- 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

- Electrical short localization with room temperature magnetic measurements

- Ezio Todesco, LHC-MMS-MA

## 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

- 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

- Contents

- Ezio Todesco, LHC-MMS-MA

## 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

- 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

- The inverse problem: effect of first powering

- Ezio Todesco, LHC-MMS-MA

## 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

- Field anomaly expressed in units of sigma
- The effect of the movement of block6 of  0 micron is subtracted

- The inverse problem: effect of first powering

- Ezio Todesco, LHC-MMS-MA

## 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

- Field anomaly expressed in units of sigma
- The effect of the movement of block6 of  5 micron is subtracted

- The inverse problem: effect of first powering

- Ezio Todesco, LHC-MMS-MA

## 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

- Field anomaly expressed in units of sigma
- The effect of the movement of block6 of 10 micron is subtracted

- The inverse problem: effect of first powering

- Ezio Todesco, LHC-MMS-MA

## 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

- Field anomaly expressed in units of sigma
- The effect of the movement of block6 of 15 micron is subtracted

- The inverse problem: effect of first powering

- Ezio Todesco, LHC-MMS-MA

## 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

- Field anomaly expressed in units of sigma
- The effect of the movement of block6 of 20 micron is subtracted

- The inverse problem: effect of first powering

- Ezio Todesco, LHC-MMS-MA

## 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

- Field anomaly expressed in units of sigma
- The effect of the movement of block6 of 25 micron is subtracted

- The inverse problem: effect of first powering

- Ezio Todesco, LHC-MMS-MA

## 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

- Field anomaly expressed in units of sigma
- The effect of the movement of block6 of 30 micron is subtracted

- The inverse problem: effect of first powering

- Ezio Todesco, LHC-MMS-MA

## 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

- Field anomaly expressed in units of sigma
- The effect of the movement of block6 of 35 micron is subtracted

- The inverse problem: effect of first powering

- Ezio Todesco, LHC-MMS-MA

## Slide 42

## 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 !)

- 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 !)

- The inverse problem: effect of first powering

- Ezio Todesco, LHC-MMS-MA

## 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

- Field anomaly expressed in units of sigma
- The effect of the movement of block5 of  5 micron is subtracted

- The inverse problem: effect of first powering

- Ezio Todesco, LHC-MMS-MA

## 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 !

- 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 !

- The inverse problem: effect of first powering

- Ezio Todesco, LHC-MMS-MA

## 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

- 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

- The inverse problem: effect of first powering

- Ezio Todesco, LHC-MMS-MA

## 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 ?

- 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 ?

- Conclusions

- Ezio Todesco, LHC-MMS-MA

## 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 ?

- 	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 ?

- Are all firms equal ?

- Ezio Todesco, LHC-MMS-MA

## Bending strength: magnetic length * transfer function
Negligible differences between firms

- Negligible differences between firms

- Are all firms equal ?

- Ezio Todesco, LHC-MMS-MA

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

- Large difference between Firm1 and Firm2-3 (3 sigma)
- The origin of this difference is not explained

- Are all firms equal ?

- Ezio Todesco, LHC-MMS-MA

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

- Large difference between Firm2 and Firm1-3 (3 sigma)
- The origin of this difference is not explained

- Are all firms equal ?

- Ezio Todesco, LHC-MMS-MA

## 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

- 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

- Are all firms equal ?

- Ezio Todesco, LHC-MMS-MA