PCB Coil and stretched wire systems for high-precision quadrupole alignment

J. DiMarco16April2015

Abstract –In the measurement of magnetic fields of accelerator magnets, induction-type probes are

among the predominant devices relied on for stable and accurate determination of field quality and alignment parameters. There are many advantages in using these systems, though fundamentally they are limited by the precision of conductor localization and the sizes of the signals generated. Here we give an overview of the Single Stretched Wire and Printed Circuit Board techniques: how these address the limitations of induction probes and are useful in obtaining high-precision results in demanding applications. We focus particularly on alignment of quadrupole magnets.

Induction or ‘fluxmeter’ method.

Fluxmeter technique:

Definition of magnetic flux

If flux through S changes (i.e. if B changes and/or surface area vector changes), then generate a Voltage according to

Faraday’s Law

Measure flux change from integrated coil voltage during motion (or field change) does not depend on path, only start and stop of measurement.

From , along with coil & motion information, find B

path independent, but have to get the probe to move to correct, or at least known, motion positions

Have to know the geometric parameters

Integrator or ADC

A note on historical legacy:

Use of flux-meter type probe was first made by Wilhelm Weber in 1853 (pre-dating Maxwell’s equations themselves!)

Weber’s got started in magnetic measurements when he had been recruited by Carl Friedrich Gauss in 1831 to work on geomagnetism and the first magnetic survey of the earth.

In order to make simultaneous magnetic observations at both the Physical Laboratory and Astronomical Observatory at Göttingen Weber and Gauss designed the first electromagnetic telegraph used for regular communication in 1833. This telegraph was a battery operated line 3000 metres long!

A note on historical legacy:

Use of flux-meter type probe was first made by Wilhelm Weber in 1853 (pre-dating Maxwell’s equations themselves!)

Weber had been recruited by Carl Friedrich Gauss in 1831 to work on geomagnetism and magnetic survey of the earth.

In order to make simultaneous magnetic observations at both the Physical Laboratory and Astronomical Observatory at Göttingen Weber and Gauss designed the first electromagnetic telegraph used for regular communication in 1833. This telegraph was a battery operated line 3000 metres long!

SOAlthough High Energy Physics can rightly be proud that efforts in their field led to the beginning of the World Wide Web by researchers at CERN,

A note on historical legacy:

Use of flux-meter type probe was first made by Wilhelm Weber in 1853 (pre-dating Maxwell’s equations themselves!)

Weber had been recruited by Carl Friedrich Gauss in 1831 to work on geomagnetism and magnetic survey of the earth.

In order to make simultaneous magnetic observations at both the Physical Laboratory and Astronomical Observatory at Göttingen Weber and Gauss designed the first electromagnetic telegraph used for regular communication in 1833. This telegraph was a battery operated line 3000 metres long!

SOAlthough High Energy Physics can rightly be proud that efforts in their field led to the beginning of the World Wide Web by researchers at CERN,

Remember that it was in fact the quest to perform quality

Magnetic Measurements that started the electronic communications revolution in the first place!!

Idea is to use a Single Stretched Wire (SSW) as a simple fluxmeter probe(J. DiMarco et al., Field alignment of quadrupole magnets for the LHC interaction regions, IEEE Trans. Appl. Supercond., vol. 10-1, p. 127, March 2000)

• Stretched between precision XY motion stages with 1 micron positioning accuracy

• Simple geometry • Can be ‘arbitrarily long’• Large or small apertures

Advantage of SSW is that one can know ‘geometric parameters’ of coilas well as ‘motion positions’to very high absolute accuracy(no additional calibration needed)

Can obtain high accuracy determination of axis position

(Return wire of SSW loop lies on the test bench (or in the magnet) but does move. Any flux change stems from the moving wire.)

Balancing accurate flux measurements for precise +/- motions determines the quad center.

SSW for alignment of quads

For actual magnetic axis need to:• Account for wire sag (about 3.5mm for an 18m wire)• Angles (yaw, pitch, roll) as well as average X,Y center

Stages are equipped with tensioning motor at one end and tension gauge at the other.

Wire sag can be compensated for by measuring at increasing tensions (frequency) and extrapolating to infinite tension.

average center

Measure vertical offset vs 1/ compensation of sag at the level of ~0.5% (20 microns with 18m wire)

Co-directional motion

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Counter-directional motion

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Co-directional motion

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Counter-directional motion

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Get angles by additional wire motions…

• Roll angle by measuring X-offset as a function of vertical position the slope yields –

• Yaw and Pitch angles by making ‘counter-directional’ motions with the wire (stages moving opposite directions) and accounting for geometry between magnet and stages

Roll Angle Measurement

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where the geometric parameters are:

Aligned to 0.5mm

Offset resolution ~ <0.5 microns

Measuring strength at high fields, the small BeCu wire magnetic susceptibility can cause significant wire motion – strength error can be significant if not compensated.

Susceptibility effects removed with 1/ measurements

Transfer function consistent @ 100.83+/- 0.03 T/kA

Lmag = 5.501m

The +/- wire motions also yield an absolute value of integrated magnetic strength (at the level of flux and motion error) – useful as a standard against which to calibrate other probes

Again measure as a function of wire vibration frequency – extrapolate back to ‘infinite tension’ on the wire (1/ =0)

2DdLg

Magnetic Strength

For measurements where signals are weak, can apply AC current to magnets and make a series of measurements at various wire positions.

stems from rather than from

‘locking-in’ fixed frequency improves signal to noise by ~100x over DC powering AC technique rejects any background field (earth’s field, test stand, etc.)

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0 5 10 15 20

FFT Order

Flu

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AC magnet current

Of course can also find center using the vibrating wire technique

XY optical detectors

SSW alignment of correctors with a rotating wire• Correctors include e.g. skew and normal dipole, quad, sextupole, octupole

and 12-pole• The usual mode of the SSW - horizontal and vertical motions - could not

be used to align these high order correctors. • Also signal size was very small, and sometimes the correctors are at the

ends of larger magnets, making the geometry difficult

Use ‘Rotating SSW’ measuring at set of discrete angles with AC current on the corrector magnets (or DC current if the signal size is high enough)

Have essentially a rotating coil measurement where position of probe is very well known.

Use ‘feed-down effect’* to determine offset.

*When a rotating probe axis is off-center with respect to the magnet axis, it causes the main field to ‘feed-down’ and create spurious (unallowed) harmonic(s) of lower order. For example, being off-center in a quadrupole creates dipole field. Measurement of the apparent dipole then allows the centering offset to be calculated.

MCSTX Cor. Pkg.

MCSOX Cor. Pkg.

MQSX

Example of a measurement on 12-pole corrector (MCTX)

Note that this also obtains a measurement of strength and harmonics.

Also can make a rotating wire measurement ‘counter-directionally’ to find the true (not just average) axis

Can also get center (as well as harmonics and field strength) from continuously rotating wire system.

Chuck Doose at Argonne uses rotary stages (shown here)(C. Doose, M. Kasa, Multipole Magnetic Measurement using a Lock-in Amplifier Technique, Proceedings of Particle Accelerator Conference, 2013)

Photo by Chuck Doose

Photo by Chuck Doose

In principle, with the quality of motion control technology available today, continuous synchronized rotary motion with low vibrations can also be achieved with XY systems.

After placing the wire on the magnetic axis (at the level of microns), its position must be transferred to fiducials which reside on the magnet so that those can be referenced when the magnet is installed.

To accomplish this, the position of the wire (which rests between a pair of 1mm dia. ball bearings at each end) is first transferred to laser tracker targets on the stage. This can be done at the level of a few microns with a measuring microscope.

Typically a laser tracker then measures magnet and stage targets and encodes the axis found by the wire onto the magnet fiducials. This process has an error of about 50-100um – usually dominating the total axis determination error.

Stage laser tracker targetsWire

supports

Transfer

Have discussed finding magnet center with a rotating wire acting as a rotating coil – now discuss rotating Printed Circuit Board (PCB) probes.

Why PCB rotating coils?

Flux-meter based approaches are usually limited by:• Precision of conductor localization and knowledge of motion positions• Sizes of the signals generated

SSW overcome the first limit, though it can have difficulty with the second (using AC current on the magnet or wire are ways that try to overcome those).

The advantage of PCB probes over hand-wound coils is that they also (like SSW) maintain precise conductor localization (i.e. at least within a plane) while increasing the signal to noise ratio (multiple turns).

Alignment with Rotating Coils

• Main advantage is that can have much higher sensitivity:multiple (hundreds or even thousands of) turns

• Main disadvantage is in transferring the offset to the magnet fiducials.

If want to transfer, usually have to physically contact the probe shaft extending out of the magnet for the survey measurements.• Have to work hard to ensure that probe is mechanically stable and moves repeatably. • Even then, don’t know how it really relates to coil portion within the magnet.• Have to find some way to calibrate the survey measurements of the shaft with the coil –

usually this involves measuring with a magnet that can be inverted and swapped end-for-end and combining measurements to understand the offset.

• Have to verify that calibrated offset is stable.

If use rotating probe for relative measurements (e.g. examining center stability vs. current), more straightforward - basically just need to make stable mechanical system for probe (and magnet).

Note that for measuring stability, pcb probes do not have a particular advantage…

Rotating coils

“A Rotating Coil Apparatus with Sub-micrometer Magnetic Center Measurement Stability”, Zack Wolf, et al., 2005

Non-pcb rotating probe center stability measurement at SLAC

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Fixed Probe Flux ChangeDuring Changes in Magnetic Field

Flux in dipole and quad windings L= probe length

D= distance from center of wires on probe

Dg= change in gradient from ramping

d= initial probe offset

Dd = change in probe offset

Calculating offset from fluxes

Some rough values ( assume 10 steps of 5T/m each to check stability )

So for 1000 turns, 1 micron change yields 60mVs

If takes 6s to ramp the 5T/m,

then see about 10uV signal (even w/o amp). Should be achievable.

Centering changes with stationary probes

700mm x 47 mm29 layers (24 for dipole)1152 turns (48 dipole/layer)Dipole sensitivity 22 sq. m(dipole windings buck quad)

For ILC studies, tried to check if quad center changed for change in strength using B

Probe was used to check stray field in (shielded) cavity test facility – lots of sensitivity!

But studies were limited by poor power supply performance…

Harmonics measurements with PCB probes in small magnets

Splice region

Periodic variation from cable twist pitch ~10cm

‘Printed Circuit Board’ probes - housed in parts made on a 3D printer (Fused Deposition Modeling) joined with carbon fiber rods.

26 mm long probe

130 mm long probe

• Both probes have analog bucking with ratios 500-1000*

• Also, circuitry for on-board amplifiers• Fabrication time 2weeks

DipoleTF

26mm pcb

B3 TF26mm

pcb

Probe diameter 28mm

* Removing the main fields suppresses spurious harmonics caused by vibrations during measurements

(sample)

Since bucking factors high, can ‘self-calibrate’ pcb radius and vertical offset.

What is the smallest PCB probe that could buck dipole and quad fields?

Traces drawn here are separated by 1mm, but basically the 7 positions (including the space) can be scaled by the trace density – e.g. if space density is 0.1mm, the extent of the coil is from -0.2 to +0.4mm.

Can have quite small pcb coils

Current CLIC probe design

Example of radial DQBuck (not really optimized)

Can try to compare sensitivity of radial designs to current probe

Effects of misalignment of layers

Small if r/r is ‘small’

Cn/Cn = n r/r

linear wrt order so that if find ‘average radius’ e.g. from self-calibration, then harmonic errors would cancel when averaged.

This seems to be the case at the level of 0.1mm errors, even for probe r=3.75But needs to be studied more (simulating random positioning errors and evaluating Kn)

Effect on harmonics of relatively large ends in pcb probes

• Probe in body field – no effect, Kn factors include the known changing lengths of the loops

• Entire probe exposed to (same) z-gradients – no effect (the missing effects at one end cancel the extra ones at the other)

• End of probe in z-gradients, rest of probe in body field – worst case –

e.g. 4mm end for 12 turns

probe body length 20mm 100 100

field z-gradient percent/mm

1 1 0.5

Appx. percent field error (all harmonics)

0.25 0.055 0.028

Note these effects are for ‘end in z-grad’ positions – if trying to get integral, the effects would be diluted by positions that have no such effects.

However, (as Stephan pointed out) besides these effects, the local measurements will also have some effects owing to the 3D nature of the field as these positions.

Thanks for your attention!!