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Magnetic Measurements
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Magnetic Measurements for PACMAN Marco Buzio, TE/MSC/MM. Contents 1 – Rotating coils 2 – Stretched wire. Main PACMAN WP 2.2 goal

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Contents 1 – Rotating coils 2 – Stretched wire

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Contents 1 rotating coils 2 stretched wire

Magnetic Measurementsfor PACMAN

Marco Buzio, TE/MSC/MM


1 – Rotating coils

2 –Stretched wire

Contents 1 rotating coils 2 stretched wire

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

Contents 1 rotating coils 2 stretched wire

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

fixed-coil,time-varying field

coil rotating, translatingor deforming (wire)

Faraday’s law (total derivative)

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

Contents 1 rotating coils 2 stretched wire

Rotating coils

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

2D ideal rectangular rotating coil geometry

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

integration boundsset by precise angular encoder rotation speed fluctuationshave negligible effects

measured flux depends on both the fieldand coil geometry

Discrete sampling of flux → Fourier components → field harmonics

Contents 1 rotating coils 2 stretched wire

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

Contents 1 rotating coils 2 stretched wire

Coil sensitivity factors

  • 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

Contents 1 rotating coils 2 stretched wire

Why is it difficult to measure small-aperture magnets ?

e.g.: radial coil, n>1

  • 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 …

Contents 1 rotating coils 2 stretched wire

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







ideal geometry(no sag)



  • 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)

flux error()(zoomed)

sag-inducedvertical eccentricity



Contents 1 rotating coils 2 stretched wire

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

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

Contents 1 rotating coils 2 stretched wire

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 µÆaperture3 !)

  • 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

Contents 1 rotating coils 2 stretched wire

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

Contents 1 rotating coils 2 stretched wire

PCB coil-related R&D themes

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

  • optimization of track layout to minimize sensitivity to production errors

  • 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 ?)

  • 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

  • PCB-based quench antennas (with compensation)

  • 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)

  • 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

  • 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

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

  • 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)

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

  • 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

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

Contents 1 rotating coils 2 stretched wire

Single Stretched Wire

B stage

A stage

Reference quadrupole

Contents 1 rotating coils 2 stretched wire

Classical Single Stretched Wire

  • DC operation: nominal fieldlevel

  • 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

iterativeaxis finding

field harmonics

Gxdy, Gydxfield direction (roll)

Contents 1 rotating coils 2 stretched wire

A stage

B stage

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

Contents 1 rotating coils 2 stretched wire

Wire selection

Integrated strength gdl 5

Magnetic properties of the wire

Integrated Strength (Gdl) (5)

  • Four different wires have been tested:

  •  0.1mm CuBe wire from California Fine Wire Co, USA

  •  0.1mm Mg wire from California Fine Wire Co, USA

  •  0.13mm CuBe wire from Goodfellow Co, UK

  • Carbon fiber strand from TohoTenaz 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)

SCS-6 Silicon Carbide


Carbon fiber HTA5241

Different type of tested wire

Slopes of strength for different types of wire in [T/s2]

  • Note:

  • if strength rises when tension increases, wire is diamagnetic

  • If strength falls when tension increases, wire is paramagnetic


Contents 1 rotating coils 2 stretched wire

Single Stretched Wire

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