Contents 1 – Rotating coils 2 – Stretched wire

“Magnetic Measurements for Particle Accelerators”International Master in Hadronteraphy, Pavia, 10 May 2013 [email protected]

/65 MAGNETIC MEASUREMENT LABORATORY cern.ch/mm

Contents

1 – Rotating coils

2 – Stretched wire

Magnetic Measurementsfor PACMANMarco Buzio, TE/MSC/MM

mailto:[email protected]



Main PACMAN WP 2.2 goal

Development of a rotating coil system (single scanning coil and/or coil train) integrated on the PACMAN test stand in bldg. 169 and aimed at field quality (strength, harmonics, direction) measurements of CLIC quadrupoles.

Magnetic measurement of the axis: if possible absolute, otherwise in relative (fixed-coil) mode with ultra-high bandwidth and resolution.

This implies, within the 3-years span: a dedicated FAME system with an optimized PCB coil(s), FDI, FFMM script etc…. Metrological qualification, cross-checks with other instruments, with documented calibration and test procedures




• Workhorse of CERN instrumentation park: most accurate and cost-effective method• Size, effective surface, number of turns, resistance, assemblies … must be adapted to the specific

requirements of each magnet no commercial solution, in-house R&D• Main parameter: total area exposed to flux change Ac, which determines the peak

induced voltage (limited by electronics, typically 5 or 10 V)

Search coils

AAA

C dAt

dAdtd

dtdV d BvnBnB

VC

A

NT

B n

A

Faraday’s law (total derivative) fixed-coil,time-varying field

coil rotating, translatingor deforming (wire)

BvABABA

tV

c

c

c

c

Fixed coil in a time-varying field

Coil rotating at angular speed in stationary, uniform field

Coil translating at speed v in stationary field with gradientB




x

y

R2

R1

z2

z1

0 (initial phase of midpoint)

wt

wr

R0

2D ideal rectangular rotating coil geometry

1112

)(

)0(0

n

innref

n

n

nnTt

t coil er

zznLNdtV

C

integration constant: lost with fixed coil measurements,irrelevant (unphysical) for rotating coils

integration boundsset by precise angular encoder rotation speed fluctuations

have negligible effects

Rotating coils

Rotating coils: yield simultaneously field strength, quality (harmonics), direction and center

measured flux depends on both the field

and coil geometry

)()( , FFT 2n N

nnnn

Discrete sampling of flux → Fourier components → field harmonics

2

1n1

n

nref

n Nr

C

n=2, B20

n=1, A10n=1, B10




Rotating coil types

Tangential coils: • higher signal for the same area (on the

boundary of the convergence circle)• blind spot, difficult to align precisely

Radial coils• easier to build and to calibrate• sensitive to all harmonics




Coil sensitivity factors

N radial coil 0=0, =0

tangential coil 0=/2, =0

w=2R0sin/2

tangential coil 0=/2, =0

0 1 A A A

2 AR0 𝑖𝑐𝑜𝑠𝛼2𝐴𝑅0

iAR0

3 𝐴ቆ𝑤212 +𝑅02ቇ −13(1+ 2𝑐𝑜𝑠𝛼)𝐴𝑅02

−𝐴𝑅02

4 𝐴𝑅0ቆ𝑤24 + 𝑅02ቇ −𝑖𝑐𝑜𝑠𝛼𝑐𝑜𝑠𝛼2𝐴𝑅03

−𝑖𝐴𝑅03

5 𝐴ቆ𝑤480 +12𝑤2𝑅02 +𝑅04ቇ 15(1+ 2𝑐𝑜𝑠𝛼+ 2𝑐𝑜𝑠2𝛼)𝐴𝑅04 𝐴𝑅04

6 𝐴𝑅0ቆ𝑤416 + 56𝑤2𝑅02 + 𝑅04ቇ 𝑖3(4𝑐𝑜𝑠2𝛼− 1)𝐴𝑅05 𝑖𝐴𝑅05

• All coefficients can be calculated from coil length L, width w and radius R0

• All coefficients proportional to total coil area Ac=NTLw • All coefficents increase like radius R0

n-1

NB: calibration coefficients can be used at any field level – inherently linear sensorHowever: S/N at calibration gets better at high field


“Magnetic measurements of the Linac4 diagnostic line dipole – first results”/7

MAGNETIC MEASUREMENT LABORATORY cern.ch/mm

Why is it difficult to measure small-aperture magnets ?

• general problem: static and dynamic deformations, vibrations, alignment, temperature drifts are more difficult to control

• Mechanical manufacturing tolerances are fixed=f(tooling) → coil sensitivity coefficient uncertainty 1/r (r=outer rotation radius)

• the number of turns available for coils (→ signal level) r2

• Signal level grow with linked flux variation → rn-1 (e.g. radial coil), rn (stretched wire)(field/gradient strength, rotation/translation speed, length, etc. being equal)

S/N ratio for quadrupole measurement may vary with r3 r4

…. BUT: small magnets are easier to flip around …

nn

rn

r

nnT

n rrnLN

12

e.g.: radial coil, n>1

rrn

n

n )()(



Coil bucking

• The accuracy of higher harmonics measured by individual coils may be affected by geometry errors• Solution = coil bucking (or compensation): suitable linear combinations of coil signals cancel out the

sensitivity to the main (and lower) harmonics robustness to mechanical imperfections• Example: in a perfect quadrupole, average gravity-induced sag on a radial coil flux error including

mainly B1 and B3 components. A four-coil series/anti-series combination cancels out B2 sensitivity error-free harmonic measurement

1 2 3 4 5 6

A

B

C

D

ideal geometry(no sag)

sag-inducedvertical eccentricity

flux error()

(zoomed)

()

Sensitivity coefficient Coil 1 Coil 2 Coil 3 Coil 4 Coil 5

(spare)

Bucked coil: Linear combination

1-2-3+4

1 A A A A A 0

2 -2Aw -Aw 0 Aw 2Aw 0

3 4912𝐴𝑤2

1312𝐴𝑤2 112𝐴𝑤2

1312𝐴𝑤2 4912𝐴𝑤2 𝟒𝑨𝒘𝟐

B

C

D

A

Y

X z1 R0

w

z2

Coil 1 2 3 4 5

• Arbitrary static coil imperfections cause no concern (effective sensitivities can be calibrated)• Position- or time-dependent transversal imperfections errors harmonic n=main order• Position- or time-dependent torsional imperfections errors harmonic n=main order -1• Coil design objective: main=main-1=0, maximize |n| with n>main order• Additional benefit: common mode rejection, improved S/N (requires separate amplification)




Effective coil width

• The flux corresponding to a given coil position can be obtained in various ways (flipping or rotating the coil, pulsing the field from zero)

• L can be considered as known from mechanical measurements• General case: unless B(s) or w(s) are constant and can be taken out of the integral sign, the flux cannot

be obtained from average width and average field:

• Define: effective width (NT gets lumped in for convenience) = average of width weighted with the field

eff

Bd

A

eff

L

T wLBLwBdssBswNeff

)()(0

1)()(

)()(

01

01

01

L

L

L

L

L

L

dsswdssB

dssBsw

Bd)(

)()(

)(1

0

0

0

effeff

L

L

Teff

L

wLA

dssB

dssBswNw

dssBL

B

considerations made here for a dipole field hold true for other components as well




Linac4 harmonic coil test bench

• Developed for small-aperture Linac4 permanent-magnet and fast-pulsed quads• Æ19 mm, 200~400 mm long quadrupole-bucked coils (difficult measurement: S/N Æaperture

3 !)• Harmonic measurements in DC (continuously rotating coil) or fast-pulsed (stepwise rotating) mode. • small size flipping the magnet around allows elimination of many systematic errors• in-situ calibration technique to improve accuracy despite geometrical coil imperfections

- 0 .005 0 .000 0 . 005 0 .010

- 0 .005

0 .000

0 .005

0 .010

Coil 1 Nt=100

Coil 3 Nt=64

Coil 2 Nt=64




Innovative miniature coils for CLIC quadrupoles

CLIC QD0 prototype 64-layer PCB stack

3-coil dipole- and quadrupole- bucked arraycan be chained to measure long magnets at once




PCB coil-related R&D themes

1. general improvement of multi-layer PCB coils: track density (currently only ~1/3 of conventional coils), layer referencing and alignment (currently ~0.1 mm)

2. optimization of track layout to minimize sensitivity to production errors

3. improvement of the existing Æ8 mm rotating PCB coil shaft: mechanical stiffness of the assembly (materials, geometry, resins …), alignment and stability of ball bearings, scaling above and below Æ8 mm (e.g. is it possible Æ4 mm for CLIC, Æ20 mm for Linac magnets, or even more ?)

4. development (as suggested by Stephan) of a more compact Mini Rotating Unit MRU-II, i.e. about 10-12 contacts instead of the current 76, better adapted to small coils, with less angular vibrations

5. PCB-based quench antennas (with compensation)

6. micro PCB connectors for multi-strand wire coils (as suggested by Olaf, to replace the existing micro-soldered connectors that only Lucette knows how to make)

7. large scale PCB fluxmeters: upper limits of current printing, pressing and assembly techniques + new possibilities offered by ELTOS; alternative architectures e.g. multiple mass-produced short boards + suitable inter-board connections

8. quality assurance of PCB fluxmeters: AC measurement of coil width, R/L measurement, calibration of magnetic equivalent coil area and coil distance inside reference magnets

9. micron-level precision coils for high order analog bucking (e.g. integrated circuit - scale fluxmeters)

10. Joe di Marco-style, polyvalent PCB sandwich coil shaft (flexible design, may be very practical for very large diameter rotating systems). Advanced materials (foams, honeycombs etc … for higher stiffness-to-weight ratio)

11. electronic acquisition systems: correction of side effects of high resistance load coils (input impedances, automatic resistance measurement and off-line correction, noise and offsets)

12. software tool to facilitate the design of new PCB coils, bypassing traditional CAD: from geometry specifications (e.g. straight/arc/straight or more realistic continuously varying curve) layer design Gerber format file

13. other techniques alternative to PCB: circuits printed on flexible rolls, inkjet circuit printers



Single Stretched Wire

B stage

Reference quadrupole

A stage



Classical Single Stretched Wire

• DC operation: nominal field level• AC operation : enhanced sensitivity at very low

field levels (e.g. 1 A in LHC cryomagnets),elimination of DC offset (stray fields, remanent …)

A B C

iterativeaxis finding

Gxdy, Gydxfield direction (roll)

field harmonics

S0, pitch, yaw



1528.09.2005

2

8 wirelTwg

Sag

As tension measurement is affected by friction problems and gauge accuracy, the SSW system measures the fundamental frequency of the wire, which depends uponh its mechanical properties

wT

lf

wire21

Shape of stretched wire with / without magnetic forces

Z

Y po

sitio

nMagnetic Field

Mag Force

Mag Force

B stageA stage




Wire selection



IMMW14 1728.09.2005

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

Four different wires have been tested:

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

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

3. Æ 0.13mm CuBe wire from Goodfellow Co, UK4. Carbon fiber strand from Toho Tenaz Europe gmbh, type HTA5241

(5). (Æ 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




Single Stretched Wire

Contents 1 – Rotating coils 2 – Stretched wire

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Transcript of Contents 1 – Rotating coils 2 – Stretched wire