Enhancement of Single Stretched Wire Measurements

of LHC Short Straight Sections

Guy Deferne, Nikolay Smirnov, CERN

Joe DiMarco, FNAL

14th International Magnetic Measurement Workshop26-29 September 2005, Geneva, Switzerland

28.09.2005 IMMW14 2

Content

Introduction – The Single Stretched Wire (SSW) at CERN Part I - Roll Angle Offset Calibration

Introduction Case of a centered magnet Case of a non-centered magnet Example of calibration

Part II - Integrated Strength (Gdl) Measurements For more details, please see the presentation of N. Smirnov et al, « Focusing strength measurements of the main quadrupoles for the LHC », submitted at the MT19 Conference, 2005)

Introduction Shape of the wire Gdl Measurement procedure Magnetic properties of the wire System performance

Conclusion

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• The Single Stretched Wire (SSW) are the reference systems used for the integrated strength and field direction measurements

– Three systems operational– All three are similar to the

ones used at DESY and at FNAL

One of the two stages

System installed on a cold bench

Introduction

The SSW features used at CERN:

• Warm and cold integrated axis of MQ and associated correctors• Integrated strength of MQ and MB at cold• Warm and cold integrated roll angle of MQ, correctors and MB

Nearly 500 Short Straight Section (SSS) for the LHC. All of them are an assembly of different magnets 10 % of those must be magnetically measured

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Roll angle offset calibration (1) Introduction

The field direction is one of the essential parameters of the measurement campaign

The SSW systems must be periodically calibrated in sense of roll angle in order to perform fast measurements that fulfill the requirements

Two different type of calibration can be used, depending if the measured magnet is centered or not in between the stages

Part I – Roll angle offset calibration

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aField (normal offset) (swapped offset)

2

Roll angle offset calibration (2)

Stages are aligned w/r to gravity with 5µrad

resolution Wyler inclinometers

etSystemOffsaswappednormal

measured

2

)(

zA

zB

offsetstageA

offsetstageB

αgravity

αgravity

αfield αgravity

Stage A

Magnet

Stage B

If zA=zB AND αfield=αgravity (reference magnet), then

Swapping stages

• Introducing the system offset in the calculation allows to perform absolute angle measurement without swapping the stages

Case of a centered magnet

If zA=zB, then

Absolute field direction w/r to gravity:

System offset:

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On cold benches, the magnet is NOT centered in between the stages

• Inside an SSS, the different magnets are located at different longitudinal positions

Layout of the magnets inside an SSS

Stage AStage B

MQ

MSCB

MO/MQT

2.94m

4.975m

6.849m

11.68m

Roll angle offset calibration (3) Case of a non-centered magnet (1)

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Roll angle offset calibration (4)

• Simply swapping the two stages as for a regular absolute offset calibration is not sufficient; the variation of the offset along the longitudinal position must be taken into account

• During the calibration, one of the stage is placed closer to the magnet

A stage

B stage

Reference quadrupole

SSW stages installed on the calibration bench

Case of a non-centered magnet (2)

If zA≠zB, then

where: z is the distance from stage A to the magnet center and

l is the distance between the stages

Offset(z) normal (1z

l) swapped

z

l

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Roll angle offset calibration (5)

System offset vs longitudinal position

-0.4

-0.2

0

0.20.4

0.6

0.8

1

1.2

2 3 4 5 6 7

Z distance from stage A [m]

Ro

ll a

ng

le o

ffs

et

[mra

d]

SSW1_09.2004

SSW1_11.2004

SSW2_09.2004

SSW2_01.2005

• The roll angle offset parameter is updated for each type of magnet, in each SSW system.

Example of calibration

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Integrated Strength (Gdl) (1)

• A second essential parameter of the measurement campaign is the integrated gradient (Gdl) of quadrupoles

• This is one of the most challenging magnetic parameters of the LHC magnets

– Required absolute error (Magnetic measurement): 5 [units]– Required repeatability (Magnetic measurement): < 5 [units]

• For the Stretched Wire Systems, this means an error on the wire positioning less than 2.5µm over 12m!

Introduction

Only a proper method and good properties of the wire can give results inside specifications

Part II – Integrated Strength (Gdl) measurement

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Integrated Strength (Gdl) (2) Shape of the wire (1)

The position of the wire at the stages is known within 1 µm,

but inside the magnet, the wire is deflected by magnetic forces and gravity

Therefore, the weight of the wire and its magnetic properties must be taken into account.

Magnetic forces

Gravity

Stretched wire

)()(

)()(

2

2

2

2

zFz

zXT

zFwgz

zYT

magx

magy

Vertical position of the wire:

Horizontal position of the wire:

• T is the wire tension

• w is the mass per unit of length

• Fmag is the magnetic force.

Where:

Note: the sign of the force Fmag depends on the magnetic properties of the wire and its location in the field

)()()( zYzYzY maggravity )()( zXzX mag

)(2 wiregravity lzzT

wgY

)(2 0

22

zT

DGorXY magmag

with

• z is the longitudinal position

• w is the wire weight per unit of length

• G the gradient of the field

• D the wire displacement

• is the wire susceptibility

• T is the wire tension

Where:

Possible solutions of (1):

(1)

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Note:

Integrated Strength (Gdl) (3) Shape of the wire (2)

Sag of the wire:2

8wirel

T

wgSag

As tension measurement is affected by friction problems and gauge accuracy,

the SSW system measures the fundamental frequency of the wire,

which includes its mechanical properties

w

T

lf

wire2

1

Shape of stretched wire with / without magnetic forces

Z

Y p

os

itio

n

Magnetic Field

Mag Force

Mag Force

B stageA stage

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Integrated Strength (Gdl) (4) Gdl measurement procedure

-70

-68

-66

-64

-62

-60

-58

-56

-54

0 0.002 0.004 0.006 0.008

1/f**2 (s**-2)

Inte

gra

ted

Tra

sfe

r F

un

ctio

n [

T/k

A] TF @ 0.76kA (injection)

TF @ 5kA (intermediate)TF @ 11.85kA (nominal)

Dependence of transfer function as a function of wire tension with CuBe wire 0.13mm diam

• The Gdl obtained from a horizontal movement, can be calculated from the linear fit of different wire tensions.

• The Gdl obtained from a vertical movement must be calculated from the parabolic fit of different wire tensions.

The parabolic term of the polynomial expansion comes from the sag of the wire:

22 )( SagLGF stepmagy

,

To cancel the effect of the magnetic forces, the value of the strength is calculated from the extrapolation of Gdl = f(1/f2) at the interception of the axis, where 1/f2 0 (infinite tension)

1

f 2

s2

Note:

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Integrated Strength (Gdl) (5) Magnetic properties of the wire

Four different wires have been tested:

1. 0.1mm CuBe wire from California Fine Wire Co, USA

2. 0.1mm Mg wire from California Fine Wire Co, USA

3. 0.13mm CuBe wire from Goodfellow Co, UK

4. Carbon fiber strand from Toho Tenaz Europe gmbh, type HTA5241

(5). ( 0.078mm silicon carbide, type SCS-9A from Speciality Materials Co, USA)

(Note: type 5. could not be magnetically tested because of its high rigidity)

Wire 0.76kA 5kA 11.85kA χ

CuBe 0.1mm 30.4 2000 9480 >0

Mg 0.1mm 6.1 500 4977 >0

CuBe 0.13mm 2.3 50 474 <0

Multi filament Carbon strand

- - 380 <0

Slopes of strength for different types of wire in [T/s2]

CuBeCarbon fiber HTA5241

SCS-6 Silicon Carbide

Different type of tested wire

Note:

• if strength rises when tension increases, wire is diamagnetic

• If strength falls when tension increases, wire is paramagnetic

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0 1 2 3 4 5 6 7 8 9

1 0

0 2 0 0 4 0 0 6 0 0 8 0 0 I n t e g r a t e d F i e l d G r a d i e n t [ T ]

D(G

dl)

units

H y p e r b o l a E x p e r i m e n t a l r e s u l t s P a r a b o l a

The error on the extrapolation is proportional to the slope

The lower is the susceptibility, the smaller is the random error on Gdl

Integrated Strength (Gdl) (6) System performance (1)

Gdl

1/T

1. Random error

Typical random error vs Gdl

3)()/()( GdlGdlGdl snn

Gdl stdev at interception point

Total random error

Contribution of the slope (magnetization of the wire)

Qualification of two SSW systems

Parameter/SSWUnits SSW#1 SSW#2

δnoise units*T 210 400

ηslope units*T-3 2.5*10-9 5*10-9

Gdl lower acceptable limit (5units at one sigma)

T 42 80

As Gdl at injection is 44T, its measurement can be performed only with certain statistic

Inje

ctio

n

Nom

inal

Tolerance limit

Dev

(Gdl

) [u

nits

]

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Integrated Strength (Gdl) (7) System performance (2)

2. Systematic errors

Estimated contribution

Powering of the magnet: <0.1 [units]

Amplifier and integration: <0.1 [units]

Main field errors: <0.2 [units]

Stray field (on cold test benches): 2.3 [units]

Alignment of stages: <1 [units]

Wire susceptibility: <2 [units]

____

Total (rms) <3.2 [units]

A cross calibration with a system that uses a different method of Gdl measurement could give a valuable confirmation of the systematic error of the SSW systems performances

The twin shafts and the automated scanner (both are rotating coils systems) used in SM18 cannot guaranty so far better than 20 [units] of absolute error

Thus an estimation of the all possible and known sources of systematic error is used to qualify the SSW systems at CERN

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Conclusion

•A special method has been developed to measure the integrated strength (Gdl) of the LHC MQ with an accuracy within the specification (even though a statistical study is required at injection field)

•Gdl measurements:Absolute

RandomError specifications: 5 [units] 5 [units] Error obtained: est. <3.2 [units] <5 [units]

• Different wires have been tested for their magnetic and mechanical properties and one type, the 0.13mm diam. CuBe from Goodfellow Ltd, has been chosen for the LHC measurements

• As we have shown that not any wire can be used for Gdl measurements, the search for wires with a lower susceptibility will continue

•A procedure has been developed to calibrate the roll angle offset of the Single Stretched Wire systems as a function of the magnet longitudinal position.

•This allows to measure the field angle w/r to gravity of the main quadrupoles and correctors magnets installed in an Short Straight Section without any swapping of the system stages.

Roll Angle Calibration

Integrated Strength