Magnetic Measurements
for PACMAN
Marco Buzio, TE/MSC/MM
Contents
1 – Rotating coils
2 – Stretched wire
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International Master in Hadronteraphy, Pavia, 10 May 2013
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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
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Search coils
• 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)
B
n
VC  
A
A
VC
d
d
B
   B n dA  
n dA   v  B d
dt
dt A

t
A
A
Faraday’s law (total derivative)
NT
 Ac B
 
 Vc 
  Ac B
t 
 Ac Bv
coil rotating, translating
or deforming (wire)
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 gradientB
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fixed-coil,
time-varying field
“Magnetic Measurements for Particle Accelerators”
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Rotating coils
Rotating coils: yield simultaneously field strength, quality (harmonics), direction and center
y


 

t ( )
C
N
L
    0    Vcoil dt    T z 2n  z1n n n1 e in 
t (0)
n 
 rref
 n 1 


n


2D ideal rectangular rotating
wr
coil geometry

z2
wt

R2
R0
z1
R1
0 (initial phase of midpoint)
x
integration constant:
lost with fixed coil
measurements,
irrelevant (unphysical)
for rotating coils
integration bounds
set by precise angular encoder
 rotation speed fluctuations
have negligible effects

measured flux depends
on both the field
and coil geometry
Discrete sampling of flux → Fourier components → field harmonics
n 1
2
r
n 1
ref
n   FFT n  ,  n  (n )  ( 2Nn )  Cn 
N n
n=1, B10
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n=2, B20
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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
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Coil sensitivity factors
N
radial coil
0=0, =0
1
A
2
AR0
3
4
5
6
𝑤2
𝐴
+ 𝑅02
12
𝑤2
𝐴𝑅0
+ 𝑅02
4
𝑤4 1 2 2
𝐴
+ 𝑤 𝑅0 + 𝑅04
80 2
𝑤4 5 2 2
𝐴𝑅0
+ 𝑤 𝑅0 + 𝑅04
16 6
tangential coil
0=/2, =0
w=2R0sin/2
A
𝛼
𝑖𝑐𝑜𝑠 𝐴𝑅0
2
1
− (1 + 2𝑐𝑜𝑠𝛼)𝐴𝑅02
3
𝛼
−𝑖𝑐𝑜𝑠𝛼𝑐𝑜𝑠 𝐴𝑅03
2
tangential coil
0=/2, =0
0
A
1
(1 + 2𝑐𝑜𝑠𝛼 + 2𝑐𝑜𝑠2𝛼)𝐴𝑅04
5
𝑖
(4𝑐𝑜𝑠 2 𝛼 − 1)𝐴𝑅05
3
iAR0
−𝐴𝑅02
−𝑖𝐴𝑅03
𝐴𝑅04
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 R0n-1
NB: calibration coefficients can be used at any field level – inherently linear sensor
However: S/N at calibration gets better at high field
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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)

N L
 n  T r2n  r1n
n

 n n
 n
r
r
 ( n )
 (r )
n
n
r
e.g.: radial coil, n>1
• 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 …
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“Magnetic measurements of the Linac4 diagnostic line dipole – first results”
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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
()
B
C
A
Y
ideal geometry
(no sag)
Coil 1
2
3
4
z1
z2
X
w

A
1
2
3
4
5
6
Sensitivity
coefficient
C
D
•
•
•
•
•
R0
5
flux error
()
(zoomed)
sag-induced
vertical eccentricity
B
D
1
2
3
Coil 1
Coil 2
Coil 3
Coil 4
A
A
A
A
Bucked coil:
Coil 5
Linear combination
(spare)
1-2-3+4
A
-2Aw
-Aw
0
Aw
2Aw
49
13
1
13
49
𝐴𝑤 2
𝐴𝑤 2
𝐴𝑤 2
𝐴𝑤 2
𝐴𝑤 2
12
12
12
12
12
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)
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0
0
𝟒𝑨𝒘𝟐
Effective coil width
  NT 
L
0
Bd

w( s)B( s)ds  B weff L  B L weff

1 L

B

B( s )ds


0
L

L
NT w( s ) B( s )ds


weff  0 L

Bd 

B( s )ds

0

 Aeff  Lweff

Aeff
•
•
•
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:
L


1
L 0
L
1
L 0
•
w( s) B( s)ds
B( s)ds
L
1
L 0

1
w( s)ds
Define: effective width (NT gets lumped in for convenience) = average of width weighted with the field
considerations made here for a dipole field hold true for other components as well
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Linac4 harmonic coil test bench
•
•
•
•
•
Developed for small-aperture Linac4 permanent-magnet and fast-pulsed quads
19 mm, 200~400 mm long quadrupole-bucked coils (difficult measurement: S/N  aperture3 !)
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
0.010
Coil 1
Nt=100
0.005
Coil 3
Nt=64
0.000
- 0.005
Coil 2
Nt=64
- 0.005
0.000
0.005
0.010
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Innovative miniature coils for CLIC quadrupoles
CLIC QD0 prototype
64-layer PCB stack
3-coil dipole- and quadrupole- bucked array
can be chained to measure long magnets at once
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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 8 mm rotating PCB coil shaft: mechanical stiffness of the assembly (materials, geometry, resins …),
alignment and stability of ball bearings, scaling above and below 8 mm (e.g. is it possible 4 mm for CLIC, 20 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
Page 12/7
“Magnetic measurements of the Linac4 diagnostic line dipole – first results”
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Single Stretched Wire
B stage
Reference
quadrupole
Page 13/7
“Magnetic measurements of the Linac4 diagnostic line dipole – first results”
A stage
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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
…)
S0, pitch, yaw
A
C
iterative
axis finding
Page 14/7
B
Gxdy, Gydx
field direction (roll)
“Magnetic measurements of the Linac4 diagnostic line dipole – first results”
field harmonics
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Shape of stretched wire with / without magnetic forces
Magnetic Field
A stage
Y position
B stage
Mag
Force
Sag  
f 
Mag
Force
wg 2
l wire
8T
1
2lwire
T
w
Z
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
28.09.2005
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Wire selection
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Integrated Strength (Gdl) (5)
Magnetic properties of the wire
Four different wires have been tested:
 0.1mm CuBe wire from California Fine Wire Co, USA
1.
 0.1mm Mg wire from California Fine Wire Co, USA
2.
3.
4.
SCS-6 Silicon Carbide
CuBe
 0.13mm CuBe wire from Goodfellow Co, UK
Carbon fiber HTA5241
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)
Different type of tested wire
Slopes of strength for different types of wire in [T/s2]
0.76kA
5kA
11.85kA
χ
Wire
Note:
• if strength rises when tension increases, wire is diamagnetic
CuBe 0.1mm
30.4
2000
9480
>0
Mg 0.1mm
6.1
500
4977
>0
CuBe 0.13mm
2.3
50
474
<0
-
-
380
<0
Multi filament Carbon
strand
28.09.2005
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• If strength falls when tension increases, wire is paramagnetic
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Single Stretched Wire
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