Measuring multipoles of small-aperture magnets by Rotated Vibrating Wire

(RVW)

IMMW17 La Mola, Terrassa-Barcelona, 18-23 September 2011 carlo.petrone@cern.ch

1 CERN, TE-MSC-MM, Switzerland 2 University of Sannio, Italy

P. Arpaia2, M. Buzio1, J. García1, Carlo Petrone12, L. Walckiers1

Outline

¨  Requirements ¨  Rotated Vibrating Wire method (RVW)

¨  Basic idea ¨  Mathematical model q  Measurement procedure

q  Experimental proof demonstration ¨  Conclusions

Outline

IMMW17 La Mola, Terrassa-Barcelona, 18-23 September 2011 carlo.petrone@cern.ch

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To measure multipoles:

1.  in magnets with very small aperture (~mm) critical for coils

2.  for different magnets at different radii (flexibility)

Requirements

Requirements

~ Ø 8 mm

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Measure multipoles: 1.  by means of a vibrating wire 2.  by measuring in different positions on a circle through a simple mathematical model relating oscillation and field components

Rotated Vibrating Wire (RVW) Basic idea

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Rotated Vibrating Wire method

Magnetic field (B)

Io

Y

X Z

How to measure the multipoles by vibrating wire?

Io

Tension (T)

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Rotated Vibrating Wire method

Magnetic field (B)

Tension (T)

Io

Y

X Z Io

How to measure the multipoles by vibrating wire?

The wire displacement is proportional to the strength of the magnetic field

( )BvqF ×=

7/35 Mathematical model

xyyx BABA ∝∝

Rotated Vibrating Wire method

The wire displacement components are proportional to the magnetic field components

8/35 Mathematical model

xyyx BABA ∝∝

( ) ∑∞

=

−

⎟⎟⎠

⎞⎜⎜⎝

⎛=+=

1

1

n

n

refnyx R

iAAz zVA

:reference radius refR

Rotated Vibrating Wire method

The wire displacement components are proportional to the magnetic field components

The amplitude A can be represented in the complex plane as the magnetic field:

9/35 Mathematical model

xyyx BABA ∝∝

nnn iQP +=V nnmain

n

main

n

main

nn iab

PQi

PP

P+=⎟⎟

⎠

⎞⎜⎜⎝

⎛+== 44 1010 Vc

The wire displacement components are proportional to the magnetic field components

The relative multipoles, scaled on the main component in units, are:

:reference radius refR

Rotated Vibrating Wire method

The amplitude A can be represented in the complex plane as the magnetic field: ( ) ∑

∞

=

−

⎟⎟⎠

⎞⎜⎜⎝

⎛=+=

1

1

n

n

refnyx R

iAAz zVA

10/35 How to measure multipoles by vibrating wire?

Rotated Vibrating Wire procedure

Moving a wire on a circle fed by a sinusoidal current (in order to increase the measurement significativity)

On each position there are two components of the wire displacement

11/35 How to measure multipoles by vibrating wire?

Rotated Vibrating Wire procedure

On each position there are two components of the wire displacement

12/35 How to measure multipoles by vibrating wire?

1.  The amplitude components are proportional to the magnetic field

2.  The phase differences among current and displacements give the sign of the reconstructed signal

1

2

On each position there are two components of the wire displacement

Rotated Vibrating Wire procedure

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1

Rotated Vibrating Wire procedure How to measure multipoles by vibrating wire?

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The wire amplitude displacement on a number of points into a circle are

collected

Rotated Vibrating Wire procedure How to measure multipoles by vibrating wire?

1

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2

Rotated Vibrating Wire procedure How to measure multipoles by vibrating wire?

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On each point on a circle there are differences among current and

wire displacements

2

Rotated Vibrating Wire procedure How to measure multipoles by vibrating wire?

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The phase differences among current and displacements give sign information

Rotated Vibrating Wire procedure How to measure multipoles by vibrating wire?

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Rotated Vibrating Wire procedure How to measure multipoles by vibrating wire?

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xRad = x + R !cos!( ) !cos! + y+ R ! sin!( ) ! sin!yTan = " x + R !cos!( ) ! sin! + y+ R ! sin!( ) !cos!

The radial and tangential relative field components can be calculated by rotation of the reference system

Rotated Vibrating Wire procedure How to measure multipoles by vibrating wire?

20/35 Measurement setup architecture

!

Experimental proof demonstration

•  Sensors: phototransistor Sharp GP1S094HCZ0F •  Current generator: Keithley 6351 •  Unique marble support for magnets and stages

21/35 Measurement setup

Experimental proof demonstration

22/35 Measurement setup

Optical sensor linearization

GAP 3 mm, Slit 0.3 mm

Scratched surface: nonlinear response

23/35 Measurement setup

Optical sensor linearization

GAP 3 mm, Slit 0.3 mm

Scratched surface: nonlinear response

Sensor linearization

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What parameters to use?

What current frequency?

Frequency: small enough to assume almost static movement of the wire

I = 105 mA T = 950 g L = 1.86 m

Measurement setup

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Test protocol

Framework domain

Matlab domain

FFMM-Flexible Framework

for Magnetic Measurements*

drives all measurement

system

*Lucio Fiscarelli IMMW16

Data analysis off line done by using MatlabR

Measurement setup

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Experimental results Magnet Linac4

The first case study exploits magnet Linac4-R1: Diameter: 22 mm Length: 45 mm Several measurements using different radius and different configuration are carried out.

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Experimental results Magnet Linac4

The first case study exploits magnet Linac4-R1: Diameter: 22 mm Length: 45 mm Several measurements using different radius and different configuration are carried out.

Pos 1

Pos 2

The magnet is rotated in order to investigate deterministic errors

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Experimental results Magnet Linac4 R1 - Reference radius: 7.5 mm - bn

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-%+#

-$+#

-"+#

-1+#

-*+#

+#

*+#

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Differences with Linac4 measurements in units (bn / b2 ± σ @ 7.5 mm)

Differences among multipoles achieved from sensor X and sensor Y Independently and multipoles by standard rotating coil

Position 1

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Experimental results Magnet Linac4 R1 - Reference radius: 7.5 mm - an

The skew multipole components (an)

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-(#

-&#

-$#

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+#

1#

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(#

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Differences with Linac4 measurements in units (an / a2 ± σ @ 7.5 mm)

Position 1

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Experimental results Magnet Linac4 R1 - Reference radius: 7.5 mm - bn

Position 2

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-&+#

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-$+#

-"+#

-1+#

-*+#

+#

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Differences with Linac4 measurements in units (bn / b2 ± σ @ 7.5 mm)

31/35

Experimental results Magnet Linac4 R1 - Reference radius: 7.5 mm - an

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-(#

-&#

-$#

-1#

+#

1#

$#

&#

(#

*+#

34567##

Differences with Linac4 measurements in units (an / a2 ± σ @ 7.5 mm)

Position 2

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Experimental results Magnet Linac4 R1 - Reference radius: 7.5 mm - cn

Other case studies will be presented by J. García at this workshop

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23+#

+#

3+#

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&+#

(+#

*++#

*3+#

*$+#

*&+#45-67#

Multipoles comp. with Linac4 measurements in units (cn / c2 ± σ @ 7.5 mm)

Using the magnet

rotation the systematic

effect is corrected and

also b3 is comparable with rotating coil results

Conclusions 33/35

q  multipoles are measured by an original method based on vibrating wire

q  Method very flexible (easy to change measurement’s radius and magnet)

q  By rotating magnet is possible to correct deterministic effects

q  Further ongoing investigations to:

q  optimize the setup’s parameters

q  correct deterministic effects

Future…

q  Refer the magnetic axis to the local point into the magnet

q  Measure multipoles not only on a circle but on ellipse and …

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I would like to thank

Dominique Cote, Lucio Fiscarelli, Peter Galbraith, David Giloteaux,

Giancarlo Golluccio, Fernando Mateo Jimenez.

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Thank you for your attention

I would like to thank

Dominique Cote, Lucio Fiscarelli, Peter Galbraith, David Giloteaux,

Giancarlo Golluccio, Fernando Mateo Jimenez.