Motivation: why to do magnetic · PDF fileTutorial: “ Overview of magnetic measurements ” IMMW20, Diamond, UK, 04- 09 June 2017 Page 1/42 [email protected] MAGNETIC MEASUREMENT

Tutorial: “Overview of magnetic measurements”IMMW20, Diamond, UK, 04-09 June 2017

Page 1/[email protected]

MAGNETIC MEASUREMENT LABORATORY cern.ch/mm

Mot ivat ion: why to do magnet ic measurements ?

Instrument types and how to choose them

Dynamic effects (eddy currents)Non-linear ef fects (saturation and hysteresis)

mailto:[email protected]








When t o measure magnet s ?

dif f erent t rade-of f s bet ween accuracy and resources at dif f erent t imes

design phase: test material samples for permeabilit y, coercivit y etc…test prototypes or models (scaled down versions) to validate computer simulat ionsand specif ic design choices (e.g. chamfers, shims, many other details …)

prot ot ypes/ pre-series: test f ield qualit y to verify the respect of mechanical tolerances (inverse problem),give feedback to designer and manufacturing f irms. Carry out a fully detailed magnet ic characterizat ion (of ten the t ime to do so will not be available during series tests)

accept ance t est s: monitor product ion qualit y,t rap errors, tooling wear …

as early as possible to steer manufacturing.Build up stat ist ics to reduce tests and minimize

total cost . Get all data required for f iducializat ion (installat ion) and beam opt ics.

NB: internal acceptance criteria might be elast ic, but legal acceptance is binary

(and may be even obligatory !)

t hroughout l if et ime: characterize magnets af ter repairs,or to allow use in dif ferent ways than originally intended


http://www.google.fr/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&ved=0ahUKEwiLoLDS3pXUAhVEPRoKHW6DDKwQjRwIBw&url=http://www.scienceforkidsclub.com/earths-magnetism.html&psig=AFQjCNEDLiuT6I7G7nJti3JJ4ulS83U82w&ust=1496169159624768

http://www.google.fr/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&ved=0ahUKEwizv9SF6JXUAhUCPRoKHTdKBKYQjRwIBw&url=http://www.bloggen.be/gw23vanveen&psig=AFQjCNHpkxgXeID2FyH2iV5csbllNPLJQg&ust=1496171667984133




Mat hemat ical modelsAdvant ages• predict behaviour wit hout having t he physical object (!!!)• f ast and inexpensive for relat ively simple cases; allow parameter space searches, opt imizat ion• virtually unl imit ed resolut ion and precision

Limit at ions• part ial physical model: including all couplings (thermal, mechanical) and phenomena

(magnetost rict ion, magnetoresist ivit y …) that may be relevant is extremely expensive• numerical errors: e.g. singularities in re-entrant corners, boundary location of open regions; these

may spoil results. Special techniques (special corner elements, BEM) require skill and time• high cost of detailed 3D models ∝ ∆x2~3, ∆t-1 (2D simulations not always suff icient …)





Impact of model uncert aint ies

10 µm/100 mm gap error→ 10-4 f ield error at high f ield5% µr error → 5⋅10-3 f ield error at low f ield (typical values)

Analytical 1D model (assume no leakage, constant sross-section),typical accuracy 10-1∼10-2

leak

𝐵𝐵 =𝜇𝜇0𝑁𝑁𝑡𝑡𝐼𝐼

𝑔𝑔 1𝜇𝜇𝑟𝑟ℓ𝑔𝑔 + 1

𝑔𝑔𝐵𝐵𝜕𝜕𝐵𝐵𝜕𝜕𝑔𝑔

= −1

1𝜇𝜇𝑟𝑟ℓ𝑔𝑔 + 1

impact of geometrical uncertainty (mechanical tolerances, assembly errors)

5 10 50 100 500 1000Aspect ratio

g0.005

0.010

0.0500.100

0.5001.000 µr= 10000

µr= 1000

µr= 100

µr= 10

µr= 1

impact of material property uncertainties

𝜇𝜇𝑟𝑟𝐵𝐵𝜕𝜕𝐵𝐵𝜕𝜕𝜇𝜇𝑟𝑟

=1

1 + 𝜇𝜇𝑟𝑟𝑔𝑔ℓ

5 10 50 100 500 1000Aspect ratio

g0.001

0.01

0.1

1 µr= 10000µr= 1000µr= 100µr= 10µr= 1





FE/ MM comparison (1/ 2): CER PS Boost er Dipole

2D FE with nominal B(H)(tweaking the curve does not work !)

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

H [A/m] 10 4

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

B [T

]

steel plates to be reinforced toequalize the rings at high f ield

(+110% @ 2 GeV w.r.t. design value !)

Outer rings (higher saturation)2% mismatch FE/MM

Inner rings(high f ield, little saturation)

0.3% mismatch FE/MM

Courtesy A. Newborough, R Chritin

Integralf lux loops

4-ring main bending dipoleof CERN PS Booster





FE/ MM comparison (2/ 2): MedAust ron Bending Dipole• modelling issues more complex for dynamic phenomena (eddy currents)• medical hadrontherapy machine requirements: fast energy changes, high accuracy and stabilit y • set t ling t ime: measured 200 ± 20 ms, computed 150 ms

G. Golluccio, A. Beaumont et al., Overview of the magnetic measurements status for the MedAustron project, IMMW18T. Zickler et al., Design and Optimization of the MedAustron Synchrotron Main Dipoles, IPAC11

Integral PCB f luxmeterMeasured eddy current

decay transient

~ 2M elements, 80 h running time









Induct ion sensors

Fixed coil in a t ime-changing f ield(f luxgate, AC st retched wire)

see J. Di Marco IMMW19−𝑉𝑉𝑐𝑐 =

𝜕𝜕Φ𝜕𝜕𝜕𝜕

=𝑑𝑑𝑑𝑑𝜕𝜕𝒜𝒜𝑩𝑩 𝒏𝒏 𝑑𝑑𝑑𝑑 =

𝒜𝒜

𝜕𝜕𝑩𝑩𝜕𝜕𝜕𝜕

𝒏𝒏 𝑑𝑑𝑑𝑑 + 𝜕𝜕𝒜𝒜𝒗𝒗 × 𝑩𝑩 𝑑𝑑ℓ

𝑑𝑑𝑐𝑐𝜕𝜕𝐵𝐵𝜕𝜕𝜕𝜕

𝑑𝑑𝑐𝑐𝐵𝐵𝜕𝜕𝜕𝜕𝜕𝜕𝜕𝜕

𝑑𝑑𝑐𝑐𝜕𝜕𝐵𝐵𝜕𝜕𝜕𝜕

𝜕𝜕𝜕𝜕𝜕𝜕𝜕𝜕

𝑙𝑙𝑤𝑤𝐵𝐵𝜕𝜕𝜕𝜕𝜕𝜕𝜕𝜕

Wire translating in a DC f ield(classical DC stretched wire)

Coil rotating in a DC f ield

Coil translating in a DC f ield

• Sensitive to the f lux rather than the f ield

• Intrinsically l inear t ransducer(some nonlinearity indirectly due to acquisition electronics e.g. f inite input impedance → small currents circulate in the coil)

• Volt age int egrat ion generally required, with attendant advantages (noise abatement proportional to frequency) and drawbacks (drift, results depend on integration time)

• Direct post-processing of the voltage also possible(relies on accurate speed control and measurement)

see G. CaiafaIMMW20

see Z. WolfIMMW19





Lorent z f orce-based sensors

see Prof . Popovic, M. CalviIMMW20

see Z. Wolf , IMMW19

𝑭𝑭𝑞𝑞

= 𝑬𝑬 + 𝑩𝑩 × 𝒗𝒗

𝜕𝜕𝑭𝑭𝜕𝜕𝑙𝑙

= 𝑩𝑩 × 𝑰𝑰

𝑉𝑉𝐻𝐻 = 𝑘𝑘𝐻𝐻𝐵𝐵 𝐼𝐼

∆𝜌𝜌𝜌𝜌

= 𝑘𝑘𝐵𝐵2

Vibrating wire

Hall ef fect sensor

Magneto-resistive sensor(hardly used in our f ield)

• Sensitive to a single f ield component (with higher order correction terms)

• Mechanical/solid state phenomena → stronger non linearity → more dif f icul t cal ibrat ion





Magnet ic resonance sensors

𝑩𝑩 =𝟐𝟐𝝅𝝅𝜸𝜸𝒇𝒇

see P. Keller, IMMW19G. Boero, IMMW20

• Resonant absorpt ion/re-emission of RF waves in a sample within a uniform f ield (f ield gradient spreads the resonance, impact depends on sample size and shape)

• Transducer sensit ive to the f ield vect or norm(some impact of temperature, orientat ion of t ransducer, chemical nature of sample: < 10-6 for NMR, much st ronger for EPR)

• Gyromagnet ic rat io depends on fundamental constants → met rological golden st andard

𝛾𝛾 = 𝑔𝑔𝑞𝑞

4𝜋𝜋𝑚𝑚= H+(proton) 42.577

free electron 28 015.737𝑀𝑀𝑀𝑀𝑀𝑀 𝑇𝑇−1

NMR (Nuclear Magnetic Resonance)γ constant known to better than 1 ppm

EPR/ESR (Electron Paramagnetic/Spin Resonance), FMR (FerriMagnetic Resonance)actual value in materials depends on: chemical composition, temperature, direction …

r

µ (magnetic moment)

angular velocity ω=2πfangular momentum l

charge qmass m

precession velocity Ω

field Bmagnetic torqueT=µB=γl

Gyromagnetic ratio

Zeeman (quantum)correction factor





Magnet ic measurement dat af low

Physical principle

Met hod Rawdat a

Int ermediat eresult

Fieldrepresent at ion

Finalresult s

Induct ion

𝑉𝑉𝑐𝑐 =𝜕𝜕Φ𝜕𝜕𝜕𝜕

f ixed coil𝑉𝑉𝑐𝑐 = 𝑑𝑑𝑐𝑐𝐵

𝑉𝑉𝑐𝑐(𝜕𝜕) Δ𝛷𝛷(𝜕𝜕)

long. field integral vs. time, transv. pos.

1𝑤𝑤𝑐𝑐ℓ𝑐𝑐

Δ𝐵𝐵 𝜕𝜕, 𝜕𝜕, 𝑠𝑠 𝑑𝑑𝑠𝑠 𝑑𝑑𝜕𝜕

Commonly required results:

• f ield polarit y• integrated/ local f ield st rength

(main harmonic)• f ield direct ion

(phase of main harmonic),• integrated/ local f ield errors

(higher harmonics)• magnet ic axis

(t ransversal posit ion)• magnet ic axis

(pit ch and yaw angles)• magnet ic center

(longitudinal)

vs. t ime, current , excitat ion history, environmental condit ions etc.

rot at ing coil𝑉𝑉𝑐𝑐 = 𝜔𝜔𝑑𝑑𝑐𝑐𝐵𝐵

𝑉𝑉𝑐𝑐(𝜗𝜗) 0

2𝜋𝜋

𝛷𝛷 𝜓𝜓 𝜅𝜅 𝜗𝜗 − 𝜓𝜓 𝑑𝑑𝜓𝜓avg. field expansion coefficients

Cn = Bn + i An

t ranslat ing coil

𝑉𝑉𝑐𝑐 = 𝑠𝑑𝑑𝑐𝑐𝜕𝜕𝐵𝐵𝜕𝜕𝑠𝑠

𝑉𝑉𝑐𝑐(𝑠𝑠) −∞

∞

𝛷𝛷 𝑢𝑢 𝜅𝜅 𝑠𝑠 − 𝑢𝑢 𝑑𝑑𝑢𝑢

long. avg. field profile vs. transv. pos.

1𝑤𝑤𝑐𝑐

𝐵𝐵 𝑠𝑠, 𝜕𝜕 𝑑𝑑𝜕𝜕

moving wire

𝑉𝑉𝑐𝑐 = 𝜕𝑑𝑑𝑐𝑐𝜕𝜕𝐵𝐵𝜕𝜕𝜕𝜕

𝑉𝑉𝑐𝑐(𝜕𝜕) Δ𝛷𝛷 𝜕𝜕

long. avg. field integral

1Δ𝜕𝜕 ℓ𝑤𝑤

Δ𝐵𝐵 𝜕𝜕, 𝑠𝑠 𝑑𝑑𝑠𝑠 𝑑𝑑𝜕𝜕

Lorent z f orce

𝜕𝜕𝜕𝜕𝜕𝜕𝑠𝑠 = 𝐵𝐵 𝑠𝑠 𝐼𝐼(𝜕𝜕)

vibrat ing wire𝛿𝛿𝑥𝑥(𝑠, 𝜕𝜕)𝛿𝛿𝑦𝑦(𝑠, 𝜕𝜕)

eigenmode amplitudes

𝛿𝛿𝑥𝑥𝑥𝑥𝑠𝑠𝑠𝑠𝑠𝑠(2𝜋𝜋𝑠𝑠𝑠𝑠ℓ𝑤𝑤

)

𝛿𝛿𝑦𝑦𝑥𝑥𝑠𝑠𝑠𝑠𝑠𝑠(2𝜋𝜋𝑠𝑠𝑠𝑠ℓ𝑤𝑤

)

1𝛿𝛿𝑦𝑦𝑥𝑥

𝐵𝐵𝑥𝑥𝑥𝑥 𝑠𝑠 𝑠𝑠𝑠𝑠𝑠𝑠(2𝜋𝜋𝑠𝑠𝑠𝑠ℓ𝑤𝑤

)𝑑𝑑𝑠𝑠

1𝛿𝛿𝑥𝑥𝑥𝑥

𝐵𝐵𝑦𝑦𝑥𝑥 𝑠𝑠 𝑠𝑠𝑠𝑠𝑠𝑠(2𝜋𝜋𝑠𝑠𝑠𝑠ℓ𝑤𝑤

)𝑑𝑑𝑠𝑠

Hall ef f ect𝑉𝑉𝐻𝐻 = 𝑘𝑘𝐻𝐻𝐼𝐼𝐻𝐻𝐵𝐵

1D/ 2D/ 3D probes 𝑉𝑉𝐻𝐻(𝜕𝜕) 𝐵𝐵(𝜕𝜕)

Magnet icResonance

𝑓𝑓 = 𝛾𝛾 𝑩𝑩

NMR/ EPRprobes 𝑉𝑉𝑅𝑅𝑅𝑅(𝜕𝜕) 𝑉𝑉𝐿𝐿𝑅𝑅(𝜕𝜕) 𝑩𝑩 =

𝑓𝑓 𝜕𝜕𝑟𝑟𝑟𝑟𝑟𝑟𝛾𝛾

s : longitudinal coordinate; x,y : transversal coordinates. B : magnetic field component normal to the coil, the movement of the wire and to the Hall sensor





Overview of magnet ic inst rument sInst rument B

[T]B.W.[Hz]

𝝈𝝈𝑩𝑩𝑩𝑩

Sensorsize Remarks

Rot at ing-coil f luxmet er >10-4 ~DC 10-4 ∅8-350 mm

30 – 1300 m

• full 2 D f ield information (absolute and relative, integral or local): strength, multipoles, axis and direction

• coil bucking → higher multipoles at ppm resolution, decreased sensitivity to mechanical imperfections

• time resolution up to ~0.1 s

Fixed-coilf luxmet er >10-4 >10-2 10-4 < 7 m

• natural (and only) option for very fast pulsed magnets• allows easy dynamics studies (eddy current and history-

dependent effects)• integration constant requires separate measurement

Translat ing-coilf luxmet er >10-4 DC 10-4 ~100 mm • adaptable to curved or very long magnets

• longitudinal f ield profile requires deconvolution

St ret ched wire (moving) >10-3 DC 10-4 ∅ 0.1 mm< 20 m

• calibration reference for integral f ield strength, direction and axis (precision of the XY stages)

• equivalent to 1-turn variable-geometry coil• best geometrical f lexibility (long magnets, narrow gaps)

St ret ched wire (vibrat ing) >10-3 DC 10-4 ∅ 0.1 mm< 20 m

• extremely sensitive for axis (at resonance)• only option for harmonics in small gaps• longitudinal resolution possible via FFT (λ>0.1 m)

Hall probe >10-4 <104 ~10-3 <1 mm2 • widespread, vast range of commercial options• high accuracy requires laborious calibration

NMR probe >0.043 <20 10-6 1 cm3• metrological golden standard• works only in highly uniform f ields• limited bandwidth; provides f ield vector norm

Fluxgat e >10-8

<10-3 <102 10-3 1 cm3 • geomagnetic and environmental f ield applications• fringe f ields, residual f ield, safety





Typical t ransversal vs. longit udinal size

1.E-03

1.E-02

1.E-01

1.E+00

1.E+01

1.E+02

1.E+03

1.E-02 1.E-01 1.E+00 1.E+01 1.E+02 1.E+03 1.E+04 1.E+05

Fixed coils

Hallsensor

Rotatingcoils

FMR

Stretched wires

Longitudinal sensor size (mm)

NMR

Traj

sver

sals

enso

r size

(mm

)





Typical accuracy vs. f ield range1.E-07

1.E-06

1.E-05

1.E-04

1.E-03

1.E-02

1.E-011.E-12 1.E-11 1.E-10 1.E-09 1.E-08 1.E-07 1.E-06 1.E-05 1.E-04 1.E-03 1.E-02 1.E-01 1.E+00 1.E+01 1.E+02

Fixed/rotating coils

Hall sensor

FMR

Stretched wires

NMR

Sensor field range [T]

rela

tive

unce

rtai

nty

[-]





Accuracy vs. t est t ime

The st andard uncert aint y of an inst rument is a cert if ied funct ion of the operat ing condit ions (f ield range/ f requency, gradient , temperature etc. … ) can be further improved based on the t ime and ef f ort taken

• Repeat to get rid of random errors: σ 𝜕𝜕 = 𝜎𝜎 𝑥𝑥𝑥𝑥

(diminishing returns for large n)

• Oversample (time/angle) to reduce aliasing(e.g. MHz sample rate for kHz bandwidth → much improved drift correction)

• Flip and repeat to estimate and subtract systematic errorseither the magnet or the instrument, as is more practical

• Reverse polarity to recover ambient or intrinsic offsets(e.g. remanent f ield)

• Redundant takes will give you confidence !

αα1

meas∆α

-α

α2meas

∆α

B

reference axis

⇒

I [A]

x

+I

-I

𝜕𝜕(0) =𝜕𝜕 𝐼𝐼 + 𝜕𝜕(−𝐼𝐼)

2𝑑𝑑𝜕𝜕𝑑𝑑𝜕𝜕

=𝜕𝜕 𝐼𝐼 − 𝜕𝜕(−𝐼𝐼)

2





Inst rument select ion crit er ia

1) Compat ibil it y with f ield level/gradients (could not work at all!)2) Transverse size (it must f it , and should reach as wide as possible)

- local ripple close to the pole may degrade the accuracy of harmonics- ext rapolat ion further f rom the axis can be applied, at a cost

3) Bandwidt h- sensit ivit y may drop above cutof f- addit ional errors e.g. f rom induct ive cable loops

4) Longit udinal size- the integral can be computed by scanning longitudinally (t ime-consuming)- de-convolut ion of longitudinal scans done with a longer probe → low-pass f ilter, noise

5) Accuracy- uncertainty can be reduced by repetition, changing orientation, cross-checks …

6) Result f ormat : harmonics vs. map (1D/2D/3D)- can be translated into one another, with caveats

7) Pract ical considerat ions: cost, measurement time,output signal format, cabling length,commensurate size of sensors and magnet,availability of trained personnel …

“hard” criteria

“soft” criteria









CERN ELENA bending dipole

• Dif f icult case: 60° bending, low-energy pbar ring → low f ield (50 to 420 mT),accelerating & decelerating cycles, 2 min-long long e-cooler plateaux

• 0.5 mm laminations with high dilution 2:1 electrical steel M270-50 A HP/304 L to reduce hysteresis; 13° cut angle for focusing

• Measured with Litz-wire f luxmeter (see O. Dunkel, IMMW19), with 2% coil area uncertainty originally intended as a backup for higher quality PCB unit





Mult i-ref erence cross-cal ibrat ion

(1) 2D Hall probe mapon the mid-plane

Courtesy of Lucio Fiscarelli

(2) Cent ral NMR for high-f ield calibrat ion

(3) Integral calculated along st raight linesmatched to St retched Wire

(5) Integral of B’ interpolated on a curvedpath to match f luxmeter coil

𝑤𝑤𝑟𝑟𝑒𝑒𝑒𝑒 =Φ0 + ∫0

𝑡𝑡 𝑉𝑉𝑐𝑐𝑑𝑑𝜕𝜕

∫−∞+∞𝐵𝐵′(𝑠𝑠)𝑑𝑑𝑠𝑠

(4) Hall probe gain and offset calibration

𝐵𝐵′ = ∆𝐵𝐵 + 1 + 𝜀𝜀 𝐵𝐵

independentremanent f ieldmeasurement

pulsed-modefluxmeter coilmeasurement

f inal result(3× 9-coil f luxmeters)





Is measuring along a curve t ruly necessary ?

• Simplest example: hard-edge dipole field distribution, uniform along s

• Let bn be the transversal harmonic expansionof the integral along straight lines

• Let βn be the transversal harmonic expansionof the integral along arcs of radius R(approximated by parabolas with negligible loss of accuracy)

• bn and βn are connected by a feed-down-like linear relation:

𝑏𝑏1𝑏𝑏2𝑏𝑏3𝑏𝑏4𝑏𝑏5𝑏𝑏3

=

1𝛼𝛼

12𝛼𝛼2

80𝛼𝛼3

448𝛼𝛼4

2304𝛼𝛼5

11264

0 1𝛼𝛼6

3𝛼𝛼2

80𝛼𝛼3

1125𝛼𝛼4

2304

0 0 1𝛼𝛼6

3𝛼𝛼2

405𝛼𝛼3

224

0 0 0 1𝛼𝛼3

𝛼𝛼2

8

0 0 0 0 15𝛼𝛼12

0 0 0 0 0 1

𝛽𝛽1𝛽𝛽2𝛽𝛽3𝛽𝛽4𝛽𝛽5𝛽𝛽3

𝐵𝐵 𝜕𝜕, 𝑠𝑠 𝑑𝑑𝑠𝑠 = 𝐵𝐵0 1 + 𝑏𝑏2𝜕𝜕𝑎𝑎

+ 𝑏𝑏3𝜕𝜕2

𝑎𝑎2+ …

𝜕𝜕 field integrals along straight and curved pathscontain the same amount of information

𝐵𝐵 𝜕𝜕, 𝜁𝜁 𝑑𝑑𝜁𝜁 = 𝐵𝐵0 1 + 𝛽𝛽2𝜕𝜕𝑎𝑎

+ 𝛽𝛽3𝜕𝜕2

𝑎𝑎2+ …

𝜕𝜕𝜁𝜁

𝑠𝑠

𝐿𝐿

2𝑎𝑎

𝑅𝑅 =𝐿𝐿2

8𝛼𝛼𝑎𝑎

𝜕𝜕𝑎𝑎≈ 𝛼𝛼

2𝑠𝑠𝐿𝐿

2









Measurement of eddy current ef f ect s• Method: current plateaux of durat ion >>

expected τ

• High-speed acquisition of integral coil voltage →detailed prof ile of I*-Im

• The relative amplitude a/Im(t s) and logarithmic decay ratio τ of the exponential starting at the end of the ramp = eddy current effect

• Scaling law for the time constant:τ = 𝐿𝐿𝑒𝑒

𝑅𝑅𝑒𝑒∝ ℓ

ℓ ℓ2= ℓ2

5000

4500

4000

3500

3000

2500

2000

1500

1000

-500

0

500

1000

1500

2000

2500

3000

3500

4000

4500

5000

2 3 4 5 6 7 8 9 10 11 12time (s)

-2.50

-2.25

-2.00

-1.75

-1.50

-1.25

-1.00

-0.75

-0.50

-0.25

0.00

0.25

0.50

0.75

1.00

1.25

1.50

1.75

2.00

2.25

2.50

I[A]

Vcoil[V]

-500

0

500

1000

1500

2000

2500

3000

2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0time (s)

I (A)

B scaled (A)

-20

-10

0

10

20

30

3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 7.5 8.0time (s)

2996.0

2996.2

2996.4

2996.6

2996.8

2997.0

2997.2

Im(t)

Vcoil(t)

Im(t)

apparent advance / lagdue to saturation

exponential decay

I*(t)-Im(t)

τ

a

I*(t)

ts

𝐼𝐼∗ 𝜕𝜕 =𝑑𝑑𝑐𝑐𝐿𝐿𝑐𝑐𝑐𝑐

𝐵𝐵 𝜕𝜕 =𝐼𝐼𝑐𝑐 𝜕𝜕𝑟𝑟𝐵𝐵 𝜕𝜕𝑟𝑟

𝐵𝐵 𝜕𝜕





Eddy current -cancel ing overshoot

3 τ to complete stabilization

1.5 τ to complete stabilization(theoretical …)

end oframp-up

0 5 10 15

Time (s)

0

0.1

0.2

0.3

0.4

0.5

0.6

Bdl (T

m)

Bdl (Tm)

1 2 3 4 5 6

20

40

60

80

100Im

∆t h

1.8 2.0 2.2 2.4 2.6 2.8 3.0

20

15

10

5

0

I*-Im

• Eddy currents can be part ially, totally or over-canceled by a t riangular current overshoot at the end of ramp-up• Example: stable f lat -top reached at the t ime cost of ∼1.5τ (to be compared with exponent ial decay t ime ∼3τ)• Caveats: - power converter needs high dV/dt ;

- the maximum working point may increase considerably, at the risk of saturat ion- hysteresis → f inal f ield level changes (new limit cycle, st ill OK if stable)





Fast -cycled quads

-10 0 10 20 30 40 50 60 70-0.5

0

0.5

1

1.5

2

-10 0 10 20 30 40 50 60 70-0.04

-0.03

-0.02

-0.01

0

0.01

0.02

0.03

• Example: fast capacit ive discharge powering of Linac4 inter-tank EMQs

• current spikes lead to minor hysteresis loops →f ield reproducibility degradation

• oscillations at the end of the ramp-down may provide a beneficial “f ree” degaussing, if symmetrical

• the overshoot at the end of the ramp-up may give a more stable f lat-top, but makes it less reproducible

I (A)

I (A)

GdL [T] – Hysteresis cycle

GdL [T]

Hysteresis cycle (linear part removed)

A

B

0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04-10

0

10

20

30

40

50

60

70

2.9 3 3.1 3.2 3.3 3.4 3.5

x 10-3

-0.5

0

0.5

1

1.5

2

2.5

3

3.5

6 6.5 7 7.5 8

x 10-3

65.8

66

66.2

66.4

66.6

66.8

67

67.2

67.4

67.6

t (s)

I (A)

A

B

AB

(uncont rol led) f lat -bot t om oscil lat ions

initial state (0,0)

remanent GdL = 0.002 T

Courtesy Samira Kasaei```





Ot her dynamic ef f ect s• Magnet ic af t er-ef f ect (magnet ic viscosit y): class of

relaxat ion phenomena linked to the magnetoelast icinteract ion between ferromagnet ic domain walls and crystal lat t ice leading to a lag between H and M

• Logarithmic time-dependence is a function of relaxation times distribution and is valid at intermediate time scales

• All ferromagnetic metals are affected• does not depend on the geometry (unlike eddy currents)• weakly correlated with f ield level and initial ramp rate• strongly dependent upon temperature• In soft steels: small effect, large time constant → can

usually be ignored

• Disaccommodat ion: after-effect on the initial permeability

• Magnet ic ageing: irreversible phenomena affecting the metallurgical nature of the steel (precipitation, dif fusion, crystal phase transition) on long time scales

∆𝑀𝑀 ∝ 𝑘𝑘𝐵𝐵𝑇𝑇 log 𝜕𝜕

H(t)





Non-l inear f eat ures in iron-dominat ed magnet s (1/ 2)

Courtesy Anthony Beaumont, Giancarlo Golluccio

large fluctuations due to history-dependent residual fieldreproducibility degrades at low field

saturation tends to erase previous magnetic history→ better reproducibility at high field

ℓ𝑐𝑐(𝐼𝐼) =1

𝐵𝐵0(𝐼𝐼)−∞

∞𝐵𝐵 𝐼𝐼, 𝑠𝑠 𝑑𝑑𝑠𝑠

eddy current decay (τ=0.2 s)

m drops due to saturation in the ends

m diverges due toBr at center << integral

central coil replaced by NMR (DC cross-check)

time

I(t)

I stand-by (112 A)

I extraction proton (1072 A)

I extraction ion (2800 A)

linear range(up branch only!)

MedAustron main bending





Non-l inear f eat ures in iron-dominat ed magnet s (2/ 2)

• Transfer line bending in the ISOLDE heavy isotope test facilit y

• Minor loops span the whole width of the major hysteresis cycle

• Open loop cont rol: « random » cycling → 0.7% errors

• Missing linear range ?!

Courtesy Guy Deferne, Giancarlo Golluccio





Increasing dB/ dt

Hyst eresis + eddy current s

• Aim: ext rapolate dynamic measurements to DC to predict behavior at arbit rary dB/dt• Eddy currents ∝ dB/dt → both f ield lag and dissipation (hysteresis loop area) ∝ dB/dt• Measurement result not so ideal … loops cross each other, more drift on slower cycles• hysteresis/drift ef fects need to be corrected by absolute measurements on the plateaux

ramp-up duration

fixed-coilmeasurement

ELENAbending dipole





Non-l inear f eat ures in superconduct ing magnet s (1/ 2)

0.705

0.7075

0.71

0.7125

0.715

0 5000 10000Current (A)

Tran

sfer

func

tion

(T/k

A)

MBP2N1

Superconduct ing f ilament magnet izat ion (persist ent eddy current s)• large hysteresis with relat ive errors of the order of 10-3 at low f ield (inject ion)• hysteresis depends on temperature, current and current history (negligible at high f ield)• main f ield and mult ipoles af fected in dif ferent ways

Iron sat urat ion• af fects only small area in the collar (B>2T)• relat ive errors ∼ 1% at high f ield• additional multipoles generated

Linear regime (geomet ric cont r ibut ion)• f ield is proportional to the current(can be computed with B iot-Savart’s law)• the T.F. depends only on the coil geometry

injection





Non-l inear f eat ures in superconduct ing magnet s (2/ 2)

Normal sextupole during ramps

-3

-2

-1

0

1

2

0 2 4 6 8 10field (T)

B3 -B

3 geo

met

ric (G

auss

@ 1

0 m

m)

35 A/s50 A/s

10 A/s20 A/s

MTP1N2

0

1

2

3

4

5

0 500 1000 1500time from beginning of injection (s)

b3 (u

nits

@ 1

7 m

m)

500

700

900

1100

1300

1500

dipo

le c

urre

nt (A

)

Coupl ing current s• f inite inter-f ilament and inter-st rand

resistance (RC) gives rise to loops linked with changing f lux

• mult ipole errors ∝ Ḃ, R C-1

• hysteresis depends upon f ield level, temperature and powering history

Decay and snap-back• superconductor magnetization and coupling

currents interact in a complex way → long-term logarithmic time dependence effects (f ield decay)

• hysteresis branch switching at the end of decay → sudden current redistribution and additional multipole errors (snap-back)





Sat urat ion model l ing

• Qualitat ive example: anhysteret ic t ransfer funct ion• Simple analyt ical interpolat ion, too coarse for open-loop f ield cont rol

but adequate for inner-loop power converter cont rol

Magnetization curve of PSB main dipole (current configuration)

Outer rings: k = 0.3465 Tm/kA , n=4, I0 = 12000Inner rings: k = 0.3463 Tm/kA, n=7, I0 = 11500

∫𝐵𝐵𝑑𝑑ℓ𝐼𝐼

= 𝑘𝑘 1 −𝐼𝐼𝐼𝐼𝑜𝑜

𝑥𝑥𝐿𝐿 =

Φ𝐼𝐼

= 𝑁𝑁𝑡𝑡 𝑤𝑤𝑝𝑝∫𝐵𝐵𝑑𝑑ℓ𝐼𝐼

= 𝐿𝐿0 1 −𝐼𝐼𝐼𝐼𝑜𝑜

𝑥𝑥

Regos

PSB main dipole





0.002

0.004

0.006

0.008

0.010

0.012

0 1000 2000 3000 4000 5000

L (

H)

I (A)

Inductance L(I) of SPS reference dipole MBB 004

Ld=(V-RI)/IdotL=Φ/ILwLgap

-0.5

-0.4

-0.3

-0.2

-0.1

0.0

0.1

0

2

4

6

8

10

12

0 1000 2000 3000 4000 5000

BdL (

Tm)

I (A)

Magnetization of SPS MBB 004 (reference dipole)

Induct ance model ing

𝑉𝑉 = 𝑅𝑅𝐼𝐼 +𝑑𝑑Φ𝑑𝑑𝜕𝜕

= RI + 𝐿𝐿𝑑𝑑𝑑𝑑𝐼𝐼𝑑𝑑𝜕𝜕 𝐿𝐿𝑑𝑑 = 𝐿𝐿 + 𝐼𝐼

𝑑𝑑𝐿𝐿𝑑𝑑𝐼𝐼

= 𝐿𝐿0 1 − (1 + 𝑠𝑠)𝐼𝐼𝐼𝐼∗

𝑥𝑥

• A large drop of the dif ferent ial inductance at saturat ion is to be expected even for mildly saturated magnets.E.g. SPSmain dipoles: f ield saturat ion 3.4% dif ferent ial inductance saturat ion of 40%.

• Measurement of the inductance curves can be easily done in parallel with standard magnet ic tests.• If this is not possible, the drop of dif ferential inductance may be estimated from the model of f ield saturation





Rapid Cycl ing Synchrot ron bending prot ot ype • Dipole prototype opt imized for a possible future RCS with 100 ms cycle t ime

• 0.3 mm Si-steel laminat ions

• ideal testbed to decouple hysteresis f rom dynamics

integral f ixed coilcent ral Hall probeto compute magnet ic lengthand est imate integrator drif t





Bipolar repeat abil it y on RCS

0.21320.21330.21340.21350.21360.21370.21380.2139

-1 0 1 2 3 4 5 6

|BdL

| [Tm

]

Cycle index

Stabilization of integrated field @ ±1.4 GeV

+1.4 → -1.4

+2.0 → -1.4

+2.0 → +1.4

0.2718

0.2719

0.2720

0.2721

0.2722

0.2723

0.2724

-1 0 1 2 3 4 5 6

|BdL

| [Tm

]

Cycle index

Stabilization of integrated field @ ±2.0 GeV

+1.4 → +2.0

+2.0 → -2.0

+1.4 → -2.0

1.07921.07941.07961.07981.08001.08021.08041.08061.0808

-1 0 1 2 3 4 5 6

B0 [T

]

Cycle index

Stabilization of central field @ ±1.4 GeV

+1.4 → -1.4

+2.0 → -1.4

+2.0 → +1.4

1.39981.40001.40021.40041.40061.40081.40101.40121.40141.4016

-1 0 1 2 3 4 5 6

B0 [T

]

Cycle index

Stabilization of central field @ ±2.0 GeV

+1.4 → +2.0

+2.0 → -2.0

+1.4 → -2.0

0.19730.19740.19750.19760.19770.19780.19790.19800.1981

-1 0 1 2 3 4 5 6

Lm [m

]

Cycle index

Stabilization of magnetic length @ ±1.4 GeV

+1.4 → -1.4

+2.0 → -1.4

+2.0 → +1.4

0.19390.19400.19410.19420.19430.19440.19450.1946

-1 0 1 2 3 4 5 6Lm

[m]

Cycle index

Stabilization of magnetic length @ ±2.0 GeV

+1.4 → +2.0

+2.0 → -2.0

+1.4 → -2.0

• cycles simulat ing all possible t ransit ions between ±1.4 and ±2.0 GeV beams in the new PSB extraction switch• f ield errors up to 2⋅10-3 just after a transition• f ield errors down t o 4⋅10-5 af t er t wo repeat ed cycles





Bipolar reproducibil it y

• Example: bipolar operat ion of ELENA bending dipole• An addit ional intermediate degaussing cycles improves repeatabilit y by a factor 2

(but const rains and delays operat ion !)

Degaussing, Cycle 1, Cycle 2

Degaussing, Cycle 1, Degaussing, Cycle 2 (not complete)

Repeatabilit y: 2.2⋅10-4

Dif ference at ±Imax: 11.3⋅10-4

Difference at ±Imax: 5.4⋅10-4

asymmetry between asymptotedepends on remanent field only!

hyperbolic asymptote due to B(0)≠0(eddy currents + remanent field)

Integral transfer function in ELENA bending dipole: ∫ 𝑩𝑩𝑩𝑩ℓ𝑰𝑰





Magnet ic st abil izat ion • Reproducibilit y of magnet ic f ield improves by reset t ing the magnet ic state with current pre-cycles• The operat ing mode of the magnet should be respected:

Bipolar magnets- steerers- correctors- switching dipoles- experimental magnets

→ degaussing

Unipolar magnets- main ring bending/quads

→ pre-cycles

• Random cycling → minor cycles → unpredictable errors within the envelope of the limit cycle• Enforce monotonic cycling for critical magnets (at the cost of more time spent ramping)• Stay as high as possible above zero to improve reproducibility

Imin Imax

B [T]

O

A

I [A]

F

E

DB

C

-0.80

-0.60

-0.40

-0.20

0.00

0.20

0.40

0.60

0.80

-400 -300 -200 -100 0 100 200 300 400

H (A/m)

B (

T)

5 10 15 20 25 30time s

40

20

20

40

60

IA𝐼𝐼𝑘𝑘+1𝐼𝐼𝑘𝑘

= −23

maximum current injected

power supplyresolution

NB: “real” demagnetization requires T≥Tcurie ≈ 948 °C !!

10 20 30 40 50 60times20

40

60

80

100

120

IAmaximum current in operation

minimum current in operation









Summary

• we must measure because mathemat ical predict ion at the level of precision we need is in many cases more expensive or impossible

• measuring under reproducibil it y condit ions allows est imat ion and correct ion of systemat ic errors → convince your management to take more data points

• there is no universal method ! combine complement ary t oolsto optimize resources

• commercial choices increasing but still limited – in-house or (better) col laborat ive R&D often necessary





Ref erences

List of CERN Accelerator School proceedings and other resources covering the fundamentals:

ht t ps:/ / t e-msc-mm.web.cern.ch/

An extensive bibliography by one of our founding fathers, including links to the whole IMMW series: ht t p:/ / henrichsen.ch/ magnet / def ault .ht m


http://https/te-msc-mm.web.cern.ch/

http://henrichsen.ch/magnet/default.htm




Thanks f or your at t ent ion

… and good luck wit h new

discoveries !





Acknowledgement

Inst ruments and measurements discussed are based on the collect ive work of the TE/MSC/MM team at CERN:

P Arpaia, A Beaumont , J L Bardanca Iglesias, R Belt ron Mercadillo, N Brut i, G Caiafa,M E Cervera, D Caiazza, R Chrit in, M Colciago, G Deferne, O Dunkel, P Evangelakos,L Fiscarelli, F N Galli, J Garcia Perez, D Giloteaux, G Golluccio, X Gontero, C Grech,

P La Marca, R Mart inez Estebanez, I D Ould-Saada, A Parrella, C Pet rone,M A Roda, G Severino, E Tournaki, J Weick, T Zickler

Special thanks to present and former team leaders that taught me many of the techniques described:

L Bot tura, D Cornuet , S Russenschuck, L Walckiers


Documents

Motivation: why to do magnetic · PDF fileTutorial: “ Overview of magnetic measurements ” IMMW20, Diamond, UK, 04- 09 June 2017 Page 1/42 [email protected] MAGNETIC MEASUREMENT