1. Advanced Photon Source Upgrade Project:
Univ of Chicago Review, Aug. 30, 2010
Rotating Coil and Wire Measurements for the Advanced Photon Source Upgrade*
Advanced Photon Source Upgrade Project:
The World’s Leading Hard X-ray Light Source
Animesh Jain
Senior Staff Physicist, Argonne National Laboratory
(On behalf of Magnet Group, APS Upgrade Project)
3rd PACMAN Workshop, CERN, March 20-22, 2017
* Work supported by the US Department of Energy under contract DE-AC02-06CH11357

2. Animesh Jain (ANL) - 3rd PACMAN Workshop, CERN, March 20-22, 2017
Introduction
Rotating coils:
Used primarily to measure field quality in accelerator magnets.
Well established technique for precise measurement of field harmonics.
Wire based techniques:
Many options, such as single stretched wire, pulsed wire, and vibrating wire.
Well established for locating the magnetic center relative to magnet fiducials.
Especially powerful for measuring relative alignment between magnets in an assembly of several magnets.
Both rotating coils and wire based techniques are generally applicable to straight magnets and magnet assemblies.
The next generation of light sources based on Multi-bend Achromat (MBA) lattices uses combined function magnets with strong dipole and quadrupole fields. Such magnets may also be curved.
Application of traditional rotating coils and wire based techniques to such curved magnets will be presented in this talk.
Animesh Jain (ANL) - 3rd PACMAN Workshop, CERN, March 20-22, 2017

3. Layman’s guide to rotating coils
Cross-section of a radial coil
Cross-section of a Tangential coil
Rotation of the coil in a magnet causes changes in the flux through the coil, which generates a voltage signal.
The signal varies with angle depending on how the field varies with angle (harmonics).
Fourier analysis of the signal gives the field harmonics.
In practice, multiple coils are used to obtain precise measurements.
Animesh Jain (ANL) - 3rd PACMAN Workshop, CERN, March 20-22, 2017

4. Layman’s guide to wire based measurements
/Data acquisition
Schematic of Vibrating Wire Measurements
AC current is passed through the wire.
Any transverse field seen by the wire causes vibrations at the drive frequency.
High sensitivity is obtained by matching the drive frequency to a resonant mode of the wire.
Vibration amplitude as a function of wire position gives field profile in X-Y plane.
Magnetic center is determined from the measured field profiles.
Sag correction is generally necessary.
Move a stretched wire in a magnet.
Measure change in flux for various types of motion in X and Y.
Use expected field symmetry to locate the magnetic center.
May add rotary stages on both ends to move wire in a precise circle. (Rotating Wire method)
Sag correction is generally necessary.
Animesh Jain (ANL) - 3rd PACMAN Workshop, CERN, March 20-22, 2017

5. Advanced Photon Source Upgrade
2 bending magnets (Double Bend Achromat)
Present
Lattice
7 “forward” bending magnets
Upgrade
Lattice
Multiplet
L-bend
FODO
L-bend
L-bend
6 “reverse” bending magnets
4 longitudinal gradient dipoles (L-bends; Dipole only)
3 transverse gradient dipoles (Q-bends; dipole + quadrupole)
6 reverse bending quadrupoles (Q-bends; dipole + quadrupole)
13 bends total (Multi-bend Achromat)
Animesh Jain (ANL) - 3rd PACMAN Workshop, CERN, March 20-22, 2017

6. Measurement of Field Quality in Q-bends
The curved transverse gradient dipoles have strong dipole and quadrupole fields.
One may use a short rotating coil, moved along the desired trajectory, to measure such magnets.
Needs precision rails tied to magnet fiducials; difficult to know where the rotating coil axis is. Hard to measure magnet “axis” at the level of ~ 10 mm.
One could use Hall probe maps to measure the Q-bends, but:
Time consuming (Point-by-point measurements on a 3-D grid).
Not suitable for accurate harmonics measurements.
Fortunately, the Q-bend magnets are not too long (< 0.8 m), the bend angle is small (< 1.5 degrees), and sagitta is < 2.5 mm
Can one just use a straight rotating coil without much loss of accuracy?
If yes, then how to analyze the measurement data?
Animesh Jain (ANL) - 3rd PACMAN Workshop, CERN, March 20-22, 2017

7. Q-bend measurements using a straight rotating coil
Hard Edge model;
Dipole and quadrupole fields are assumed constant along the curved magnetic axis, and zero outside the magnet.
Curved and straight path lengths are the same within ~20 ppm
Quadrupole term is not affected by small offsets (< 1 mm), as long as the sextupole and other higher order terms are small.
Integrated quadrupole field can be obtained with sufficient accuracy, limited mainly by the absolute calibration.
Dipole and other harmonic terms are affected by offsets Dx(z).
Animesh Jain (ANL) - 3rd PACMAN Workshop, CERN, March 20-22, 2017

8. Q-bend measurements: The dipole term
Hard Edge model;
Harmonics assumed constant along the curved magnetic axis
Measured dipole field =
[to first order in Dx(z)]
If the data are centered (by post-processing) such that the dipole to quadrupole ratio is x as per design, then the average offset of rotating coil is zero. => Dipole term is not really measured here, it is enforced.
(Nothing new here, it is standard practice for regular quadrupoles!)
Animesh Jain (ANL) - 3rd PACMAN Workshop, CERN, March 20-22, 2017

9. Q-bend measurements: Higher harmonics
Hard Edge model;
Harmonics assumed constant along the curved magnetic axis
Measured Normal (Bn) and Skew (An) Harmonics:
(n = 0 is dipole)
[to first order in Dx(z)]
If the data are centered such that the dipole to quadrupole ratio is as per design, then the average offset, , is zero. Measured harmonics should be OK.
The curvature may limit the radius of rotating coil that can be used.
Animesh Jain (ANL) - 3rd PACMAN Workshop, CERN, March 20-22, 2017

10. Real Q-bend magnets: will a rotating coil work?
The analysis assumes a hard edge model, with constant harmonics along the beam trajectory.
In real life, the field falls off gradually at the ends, and there are strong end harmonics. These features may invalidate the simple data analysis presented so far.
How to know if the proposed scheme will really work?
Detailed Opera-3D simulations of Q-bends exists (M. Jaski)
Use field harmonics from Opera-3D simulations to compute the true integral on the curved path, and also to compute the measured integral on a straight path.
Apply the analysis described earlier to the measured integral and see if the results are close to the true integral.
Results of simulations for a M4 magnet are presented here.
Animesh Jain (ANL) - 3rd PACMAN Workshop, CERN, March 20-22, 2017

11. Simulation of rotating coil measurement in M4
Animesh Jain (ANL) - 3rd PACMAN Workshop, CERN, March 20-22, 2017

12. Axial distribution of sextupole term in M4
End harmonics are localized around s = ±0.3 m
Other higher harmonics show similar profiles
Based on data from M. Jaski, APS
Animesh Jain (ANL) - 3rd PACMAN Workshop, CERN, March 20-22, 2017

13. How to improve the measurement accuracy?
The simple averaging of offsets does not work because the field harmonics are not constant along the curve.
There is a central region of ~0.5 m with nearly constant harmonics. The method should work if applied to integral over the central 0.5 m only.
Since the end harmonics are highly localized, their contribution can be measured correctly if the rotating coil is placed at the trajectory position where the end harmonics have a peak.
Measure central 0.5 m region at one transverse position
Measure the two ends at another transverse position, suitably offset from the first position.
Animesh Jain (ANL) - 3rd PACMAN Workshop, CERN, March 20-22, 2017

14. Selecting the ideal locations for measurement
Central Coil (0.5 m) X = mm
End Coil 1 (0.25 m) X = mm
End Coil 2 (0.25 m) X = mm
Ends should be measured with an offset of mm from the central coil
(for this particular design of the M4 type Q-bend magnet)
Animesh Jain (ANL) - 3rd PACMAN Workshop, CERN, March 20-22, 2017

15. Simulation of 3-part rotating coil measurement in M4
Animesh Jain (ANL) - 3rd PACMAN Workshop, CERN, March 20-22, 2017

16. Wire based measurements of the axis of Q-bends
For the APS-U Q-bend magnets, 0.1 mm alignment error will consume about 20% of the total bending correction available.
Need to align much better than 0.1 mm in X.
Tolerance: 30 mm rms.
Defines “axis”
Known Parameters: R, x, qbend
Integration path is assumed parallel to tangent at xc (Analysis of general case shows up to 20 mr misalignment is acceptable; < 5 mr should be easily achievable.)
Goal is to locate the point xc relative to magnet fiducials. This information can then be used to align the magnet.
Animesh Jain (ANL) - 3rd PACMAN Workshop, CERN, March 20-22, 2017

17. Center of Q-bend based on Integral along a line
Knowing Integrated field Vs. X , the “center” can be determined using other known constants.
Absolute measurement is not needed: any wire based method should work.
Animesh Jain (ANL) - 3rd PACMAN Workshop, CERN, March 20-22, 2017

18. Trajectory in X-Z plane
Bend angle from end slopes = – mr
Matches design requirement of – mr
Based on data from M. Jaski, APS
Animesh Jain (ANL) - 3rd PACMAN Workshop, CERN, March 20-22, 2017

19. Test of Q-bend axis measurement principle
Gives xc = – mm xvertex = – mm
(+6 mm off from actual)
Must use slope in the region of interest. xc
Animesh Jain (ANL) - 3rd PACMAN Workshop, CERN, March 20-22, 2017

20. Use of rotating wire for axis measurements
Well known wire based techniques, such as single stretched wire, or vibrating wire, are capable of measuring alignment between magnets in an assembly with a resolution of ~ 5 microns.
Unfortunately, the measurement time is too long to do good measurements (~15 min. or more per magnet).
In order to minimize the measurement time, a rotating wire technique will be used for the APS upgrade.
In this technique, a single-turn loop of wire is rotated from both ends, and is used like a rotating coil (radius ~ 10 mm)
Measurement time is comparable to rotation period (1 second).
Insensitive to higher harmonics and applicable to all magnet types.
R&D is underway to study error sources.
Animesh Jain (ANL) - 3rd PACMAN Workshop, CERN, March 20-22, 2017

21. Rotating wire setup at APS
Multiplet bench
Single magnet bench
Animesh Jain (ANL) - 3rd PACMAN Workshop, CERN, March 20-22, 2017

22. Measuring the curved multiplet section
Total (reverse) bend angle = deg. (3.189 mr)
Q4 mechanical center is offset ~2 mm; Q5 mechanical center is offset ~5 mm. (Straight magnets)
Vacuum chamber may be offset by up to ~ 0.5 mm from the nominal beam axis.
Animesh Jain (ANL) - 3rd PACMAN Workshop, CERN, March 20-22, 2017

23. Measuring curved multiplet section
With the wire aligned to the Q3-S1 axis, it is offset by ~ 4 mm in the Q6 magnet.
Rotation radius of the wire may be limited to only ~5-6 mm, but the magnetic centers of all magnets can be measured, even with the vacuum chamber installed.
Animesh Jain (ANL) - 3rd PACMAN Workshop, CERN, March 20-22, 2017

24. Measuring curved FODO section
With the wire aligned to the axis of Q7 at one end, it is offset by ~ 168 mm in the Q7 at other end, which is well into the yoke of the magnet.
A very long wire (~8 m) is needed, and only ~2-3 mm motion is possible. Vibrating wire method is best suited for the geometry, but many difficulties in applying to combined function magnets.
Wire stages with long (~300 mm) travel and precise motion with almost no X-Y coupling will be needed.
In the case of FODO, it will be more convenient to fiducialize individual magnets, and then install by survey.
Animesh Jain (ANL) - 3rd PACMAN Workshop, CERN, March 20-22, 2017

25. Animesh Jain (ANL) - 3rd PACMAN Workshop, CERN, March 20-22, 2017
Summary
Use of rotating coils and wire based methods is well established in the field of magnetic measurements.
The next generation of light sources require combined function magnets with strong dipole and quadrupole components. These magnets may also be curved.
Curved combined function magnets pose significant challenges to measurement of the field quality and precise alignment of such magnets.
Schemes are developed to measure field quality and magnetic center in such magnets using conventional rotating coils and wire based techniques, by applying appropriate analysis of the data.
These schemes were simulated using field maps from Opera-3D calculations, with promising results.
Tests in prototype magnets will be carried out in the near future.
Animesh Jain (ANL) - 3rd PACMAN Workshop, CERN, March 20-22, 2017