WP2 ESR 2.2 WP2 ESR2.2 Giordana Severino PACMAN WORKSHOP - CERN PCB technology for small diameter field sensing

WP2ESR 2.2

PARTICLEACCELERATOR COMPONENTS’

METROLOGY and ALIGNEMENT to the NANOMETER scale WP2 ESR2.2

Giordana SeverinoPACMAN WORKSHOP - CERN

PCB technology for small diameter field sensing

WP2ESR 2.2 OUTLINE

PACMAN INNOVATIVE DOCTORAL PROGRAM FOR CLIC

FIELD QUALITY IN ACCELERATOR MAGNETS

ROTATING COILS FOR SMALL DIMENSIONS APERTURES• Coil production error COIL CALIBRATION • In situ calibration

COIL ROTATION CENTER and MAGNET GEOMETRICAL CENTER• Metrology measurements

• Polygonal and cylindrical reference magnet• Coil sag evaluation

FUTURE STUDIES AND DEVELOPMENTS

WP2ESR 2.2 INNOVATIVE DOCTORAL PROGRAMME FOR CLIC

The GOAL of the PACMAN program is to develop very high accuracy metrology

and alignment tools and integrate them in a single automatic test stand

The Compact Linear Collider (CLIC) is a study to implement the future electron-positron Linear Collider

for Physics up to the multi-TeV

Help of leader companies

Hexagon Metrology

DMP

ETALON

ELTOS

METROLAB

TNO SIGMAPHI

NI

WP2ESR 2.2

FIELD QUALITY IN ACCELERATOR MAGNETS

“The field quality in accelerator magnets is conveniently described by a set of Fourier coefficients

known as

field harmonics or multipoles coefficients”1

How to measure Multipoles

coefficients?

Oscillating wire Rotating coil

1: S.Russenschuck, "Field Computation for Accelerator Magnets: Analytical and Numerical Methods for Electromagnetic Design and Optimization", Wiley (2011)

“All the undesired magnetic field harmonic components in a magnet”

WP2ESR 2.2

ROTATING COILS FOR SMALL DIMENSIONSAPERTURESUpgrade of LHC

(Linear Accelerator 4)Future accelerators

(Compact Linear Collider)Existing large accelerators

(Large Hadron Collider)

Ø 50 mm Ø 20 mm Ø 8 mm

Now 2014 20202.5 x 2.5 x

WP2ESR 2.2 MULTI-WIRE VS PCB COIL

MULTI-WIRE COIL

PCB COIL

• PCB layer misalignment

• Coil deformation

• More expensive

• Limited stiffness

ADVANTAGES

DISADVANTAGES

• Stiffness

• cheap

• Used for aperture above Ø 19mm: Possibility to use an inclinometer (bubble level)

ADVANTAGES

DISADVANTAGES

• Hand made connections are difficult: Both with multifilar wire colour coded (MWS) and LIZ wire

• Limited downsizing

• Imperfect coil section

• Good downsizing

• Fast to produce

• Connection on PCB

WP2ESR 2.2 USEFUL BACKGROUND INFORMATION

Based on Faraday law:

A change of flux induces, by Faradays law, a voltage signal U on the terminal of the coil:

A magnetic flux measurement by means of the rotating coils thus requires the integration of the voltage induced on the coil:

Which can be reparametrized to the angular position using an angular encoder.

The field harmonics (multipoles) are derived using knowledge of the coil geometry.

WP2ESR 2.2 COIL SENSITIVITY COEFFICIENTS

Single filament approximation: the crossing section is reduced to a single filament

correction factor

kn are the complex coil sensitivity coefficients to the harmonic n

• General: ) = )

• Tangential:

• Radial:

WP2ESR 2.2 COIL CALIBRATION

Design Parameters

Calibration

Real Parameters

Parameters to calibrate:• R0: Coil Center radius• A: coil magnetic

surface• Θ: coil tilt

Accurate parameters:• L: Coil length (10-4)• Nt: Number of turns • Number of layer

Kn sensitivity factor Computation of Kn sensitivity

factors, used for the computation of Multipole field harmonics

In-situ calibration1:Procedure for calibrating equivalent magnetic area and rotation radius of coil 1 In-situ calibration of rotating coil magnetic measurement systems: a case study on Linac4 magnets at CERN Pasquale Arpaia, Marco Buzio, Giancarlo Golluccio, Fernando Mateo 17th Symposium IMEKO TC

WP2ESR 2.2 IN-SITU CALIBRATION1 Radius calibration

𝑅=∆𝑥~𝐵3 (𝑧𝑎 )

~𝐵2 (𝑧𝑏 ) −~

𝐵2 (𝑧𝑎 )Formula to calculate Radius and area in case

of zero initial phase, pure delta x displacement on x axis and no coil tilt

Procedure for calibrating equivalent magnetic area and rotation radius with a mechanical displacement inside reference quadrupole magnet

In particular focusing on the radius calibration it is possible to determine it from the dipole and quadrupole FFT coefficients of flux

• Δx stage-x movement• quadrupole coefficient of Flux DFT• dipole coefficient of Flux DFT

STUDY THE EFFECT OF ONE SINGLE HIGHER HARMONICS ON THE CALIBRATION

1: In-situ calibration of rotating coil magnetic measurement systems: a case study on Linac4 magnets at CERN Pasqual Arpaia, Marco Buzio, Giancarlo Golluccio, Fernando Mateo 17th Symposium IMEKO TC4 2014

WP2ESR 2.2 Single Higher Harmonics effect on radius computation

Feed-down of a quadrupole with sextupolar multipole field error

Purely horizontal translation no skew field harmonics excited

Substituting the sensitivity coefficient for an ideal radial coil with zero initial phase, we get:

WP2ESR 2.2 ROXIE SIMULATION

A sextupole current shell is nested within the quadrupole.

NEXT STEP TEST ON REAL MEASURAMENTS

To simulate flux measurement:• Perform a parametric analysis by rotating the coil 360 degrees in N steps

• Move the coil rotation center• Set the desired coil radius

2D simulation is sufficient by assuming longitudinal homogeneity both in the magnet and the sensing coil

WP2ESR 2.2 IN-SITU CALIBRATION Radius calibration

Radius calibration independent from alignment error

Linear stagesfor precise

displacement

From the feed-down formula:

For a movement from to :

The complex numbers can be transformed in a modulus and phase notation

• Δz stage movement• Ck harmonic coefficient• R coil rotation radius

The quadrupole is not affected by feed-down

WP2ESR 2.2 COIL ROTATION CENTER and MECHANICAL CENTER

The magnet geometric axis G and the coil rotation axis C

are coincident

The magnet is rotated by successive angular steps until a

complete rotation is performed…

The coil rotation axis C is not coincident with the magnet

geometric axis

WP2ESR 2.2 METROLOGY MEASURAMENT

d represents the distance between the coil rotation axis and geometrical magnet axis

• If with metrology measurements the distance d between the magnet geometric center and the coil rotation center is evaluated precisely, the distance obtained from the magnet rotation should be the same.

If there is a difference between these values …

MORE GENERAL CASE: COIL FRAME AND MAGNET FRAME ARE NOT COINCIDENT THERE IS A COIL INITIAL

PHASE

WP2ESR 2.2 POLYGONAL AND CYLINDRICAL REFERENCE MAGNET

Polygonal shape magnet Cylindrical shape magnet Less machining error

More precise

Impossible to calibrate the initial phase

More machining error

Less precise

It is possible to calibrate the initial phase

WP2ESR 2.2 COIL SAG EVALUATION

• CHECK DEFORMATION (COIL BEND: In particular in case of absence of an external rigid shaft)

• EVALUTION OF COIL SAG WITH A THIN MAGNET OF SMALL APERTURE

The effect of sag can be corrected in calculation

of harmonics

Each coil subsection rotates about its local

geometric centerIt is a problem for magnetic

axis measurements.1

2: CAS Accelerator school “Measurement and alignment of accelerator and detector magnets”.11-17 April 1997

WP2ESR 2.2 FUTURE STUDIES AND DEVELOPMENT

• Bearings to reduce torsion • AIR BEARINGS FOR REALLY SMALL SHAFT Ø8 mm

Ruby and sapphire can attain very high surface finish. The finish can be routinely maintained at 2 micro-inch and under

• RING JEWEL BEARINGS

• Study on extra-small shaftTo improve stiffness

• CARBON FIBER SHAFT ?• Comparison of different shafts to find best

performance on small dimension

• Study on fiducialization to be optimized for small

aperture test-bench

Fiducialization with small shaft is complex

WP2ESR 2.2

• Study of effects of PCB fabrication error (misalignment of planes ..) on the value of sensitivity coefficients

• Study of new possible pcb coil configuration optimized for small dimensions

• Studies to improve coil calibration focus on PCB coil

FUTURE STUDIES AND DEVELOPMENT

WP2ESR 2.2 WP2ESR 2.2

Thank you for your attention

WP2ESR 2.2

FLIP COIL METHOD FOR THE EVALUATION OF COIL AREA

The coil is flip two times inside a reference dipole with a magnetic field B known precisely

= Flipping the coil one side of 180˚and after on the opposite side coming back to the same position it is possible to calculate the area if the Dipole field B in known precisely

With calibration in situ

The dipole magnet should be controlled with a NMRMonitor temperature and current during the measurement

Weff

The reference value of the focusing strength1 GdL must be obtained with independent measurement → SSW single stretch wire

WP2ESR 2.2

Single Higher Harmonics effect on radius computation of in-situ calibration

ROXIE simulation: quadrupole with a sextupole harmonic error

The magnet is modelled by means of current shells of an ideal distribution that generates a pure multipole field of order n



SOME OF CALIBRATION

CASE STUDIES

IDEAL QUADRUPOLE

QUADRUPOLE WITH A SEXTUPOLE HARMONIC ERROR

NEXT STEP TEST ON REAL MEASURAMENTS

WP2ESR 2.2 Calibration method with sextupole harmonic

20th IMEKO TC4 International Symposium – Benevento (Italy) 23

𝐵3 (𝑧𝑎 )(∆ 𝑥𝑅 )=12 (𝐵¿¿2 ( 𝑧𝑏) −𝐵2 ( 𝑧𝑎 ))¿

Feed-down of a quadrupole with sextupolar multipole field error:

In the special case of a translation in the horizontal plane, there will be no skew field harmonics excited:

Proposed calibration in a quadrupole with sextupole error harmonic

WP2ESR 2.2 Calibration method with sextupole harmonic


The relation between the Fourier coefficients of the vector potential and the multipole field errors is given by:

Substituting the sensitivity coefficient for an ideal radial coil with zero initial phase.

~𝐵2 (𝑧𝑏 )=~𝐵2 (𝑧𝑎 )+ 12~𝐵3

(𝑧𝑎 )(∆ 𝑥𝑅 )+ 12~𝐵3

(𝑧𝑏)( ∆𝑥𝑅 )

= 𝑘2=𝐴𝐶 𝑅• Ac calibrated area • L coil lenght • W coil width

=

𝐵1 (𝑧𝑏 )=𝐵1 (𝑧𝑎 )+ 12𝐵2 (𝑧𝑎) (∆ 𝑥

𝑅 )+ 12 𝐵2 (𝑧𝑏 )(∆ 𝑥𝑅 )

WP2ESR 2.2 Calibration method with one higher multiple harmonic

The same procedure can be applied with an octupole error harmonic and a negligible sextupole :

One should keep the coil positions as close as possible to the magnet center, as the sextupole harmonic is not negligible otherwise:

WP2ESR 2.2 2D simulation with ROXIE



CALIBRATION CASE STUDIES

IDEAL QUADRUPOLE

QUADRUPOLE WITH A SEXTUPOLE HARMONIC ERROR

QUADRUPOLE WITH AN OCTUPOLE HARMONIC ERROR

WP2ESR 2.2 Roxie simulation


For the numerical simulation the CERN field computation program ROXIE was used

One of the innovative aspect of ROXIE is that it allows to simulate a rotating coil both hand wound and PCB.

WP2ESR 2.2 ROXIE SIMULATION: QUADRUPOLE WITH A SEXTUPOLE HARMONIC ERROR



To simulate flux measurement:• Perform a parametric analysis by rotating the coil 360 degrees in N steps

• Move the coil rotation center• Set the desired coil radius

The magnet is modelled by means of current shells of an ideal distribution that generates a pure multipole field of order n

WP2ESR 2.2 ROXIE SIMULATION: QUADRUPOLE WITH A SEXTUPOLE HARMONIC ERROR


WP2ESR 2.2 COIL SAG EVALUATION

• CHECK DEFORMATION (COIL BEND: In particular in case of absence of an external rigid shaft)

Check the coil profile along the z axis in four position (one every rotation of 90˚) • EVALUTION OF COIL SAG WITH A THIN MAGNET OF SMALL APERTURE

The sag of a measuring coil due to its own weight changes along the coil the distance between the mechanical center and the rotation axis. It could be interesting to check the distance in three position of the coil

The effect of sag can be corrected in calculation

of harmonics

Each coil subsection rotates about its local

geometric center

It is a problem for magnetic axis measurements.

Difficult to distinguish between true offset of magnetic axis and apparent due to sag2

2: CAS Accelerator school “Measurement and alignment of accelerator and detector magnets”.11-17 April 1997

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WP2 ESR 2.2 WP2 ESR2.2 Giordana Severino PACMAN WORKSHOP - CERN PCB technology for small diameter field sensing