1. S. Russenschuck, CLIC-Workshop, WP2-Pacman, 4.02.2014 1 R&D projects on rotating coil probe and stretched wire techniques for CLIC / PACMAN Stephan Russenschuck for the CERN magnet (measurement) -team CLIC workshop 4.02.2014 1

2. S. Russenschuck, CLIC-Workshop, WP2-Pacman, 4.02.2014 Rotating Coil Measurements Tangential coil Radial flux Radial coil Tangential flux

3. S. Russenschuck, CLIC-Workshop, WP2-Pacman, 4.02.2014 Series Measurements of the LHC Magnets

4. S. Russenschuck, CLIC-Workshop, WP2-Pacman, 4.02.2014 Standardized Equipment – Motor Drive Unit Drive unit for measurements in horizontal (rt) and vertical (cryogenic temp.) position

5. S. Russenschuck, CLIC-Workshop, WP2-Pacman, 4.02.2014 Standardized Equipment – Rotating Coil Shafts Shaft for measurements in a vertical cryostat Shaft R=45 mm, coil length: 130 mm Shaft R=30 mm, coil length: 1200 mm

6. S. Russenschuck, CLIC-Workshop, WP2-Pacman, 4.02.2014 Flexible Framework for Magnetic Measurements

7. S. Russenschuck, CLIC-Workshop, WP2-Pacman, 4.02.2014 Rotating Coil Measurements

8. S. Russenschuck, CLIC-Workshop, WP2-Pacman, 4.02.2014 The Riemann Lebesque Lemma 8 The Fourier coefficients tend to zero as n goes to infinity (Riemann Lebesque) and they must scale according to the Cauchy theorem for bounded functions Simulations !

9. S. Russenschuck, CLIC-Workshop, WP2-Pacman, 4.02.2014 Spread and Noise Floor in Measurements Compensated Noncompensated Radial axes displacement Torsional deformations Blind eye?

10. S. Russenschuck, CLIC-Workshop, WP2-Pacman, 4.02.2014  Challenges – Sensitivity and tolerances on small shafts – Bucking ratio – Vibrations and noise – Calibration – Connection  PACMAN R&D efforts – PCB technology for coils – Rapid prototyping for shaft – Micro-connectors – MRU-II (smaller, smoother) – In-situ calibration – “Intelligent” post-processing

11. S. Russenschuck, CLIC-Workshop, WP2-Pacman, 4.02.2014 Architecture Stretched Wire Experimental Setup

12. S. Russenschuck, CLIC-Workshop, WP2-Pacman, 4.02.2014 The Single Stretched Wire Method

13. S. Russenschuck, CLIC-Workshop, WP2-Pacman, 4.02.2014 Measurement system design Oscillating wireVibrating wire Map of Second Wire Resonance Wire Excitation Frequencies Stretched wire

14. S. Russenschuck, CLIC-Workshop, WP2-Pacman, 4.02.2014 Solenoid Center and Axis Force distribution requires vibration at the second resonance

15. S. Russenschuck, CLIC-Workshop, WP2-Pacman, 4.02.2014 Solenoid Center and Axis: Transversal Field Profiles Left: Perfectly aligned. Right: With swing Therefore: Switch to first resonance, and align (move) the magnet, not the stages

16. S. Russenschuck, CLIC-Workshop, WP2-Pacman, 4.02.2014 Solenoid Center: Oscillation Amplitudes Modulus At x sensor At y sensor For small displacements from the center, the B y component is a linear function in x

17. S. Russenschuck, CLIC-Workshop, WP2-Pacman, 4.02.2014 Linear Regression in the Line Search Procedure

18. S. Russenschuck, CLIC-Workshop, WP2-Pacman, 4.02.2014 Vibrating wire for magnetic axis Solenoid magnet Map of Second Wire Resonance Before alignmentAfter alignment

19. S. Russenschuck, CLIC-Workshop, WP2-Pacman, 4.02.2014 Vibrating wire for magnetic axis Solenoid magnet Map of Second Wire Resonance (on 2 mm radius)

20. S. Russenschuck, CLIC-Workshop, WP2-Pacman, 4.02.2014 Solving Boundary Value Problems I 1. Governing equation in the air domain 2. Chose a suitable coordinate system, make a guess, look it up in a book, use the method of separation, that is, find orthogonal and complete eigenfunctions. Coefficients are not know at this stage 3. Incorporate a bit of knowledge, rename, and calculate field components

21. S. Russenschuck, CLIC-Workshop, WP2-Pacman, 4.02.2014 Solving Boundary Value Problems II 4. Measure or calculate the field (flux) on a reference radius and perform a discrete Fourier analysis (develop into the eigenfunctions). Coefficients are known here. 5: Compare the known and unknown coefficients 6. Put this into the original solution for the entire air domain

22. S. Russenschuck, CLIC-Workshop, WP2-Pacman, 4.02.2014 Solving the Boundary Value Problem Take any 2  periodic function and develop according to For the oscillating wire technique: Use the oscillating amplitudes measured at one position longitudinally as we move the wire such that they become the generators of a cylinder inside the magnet aperture

23. S. Russenschuck, CLIC-Workshop, WP2-Pacman, 4.02.2014 Optical sensors Phototransistor Sharp GP1S094HCZ0F Response of the Phototransistors

24. S. Russenschuck, CLIC-Workshop, WP2-Pacman, 4.02.2014 Use Wire Displacements Proposition: We are done if:

25. S. Russenschuck, CLIC-Workshop, WP2-Pacman, 4.02.2014 Solution of the Wave Equation (Assumptions)

26. S. Russenschuck, CLIC-Workshop, WP2-Pacman, 4.02.2014 Use Wire Displacements

27. S. Russenschuck, CLIC-Workshop, WP2-Pacman, 4.02.2014 Solution of the Wave Equation (Steady State)

28. S. Russenschuck, CLIC-Workshop, WP2-Pacman, 4.02.2014 Check 2: Numerical simulation (FDTD) and the Steady State Solution

29. S. Russenschuck, CLIC-Workshop, WP2-Pacman, 4.02.2014 Solution of the Wave Equation III Check: Known longitudinal field or oscillation profiles Ideas welcome on how to measure the longitudinal profile of the oscillation wire (30 phototransistors, inductive, capacitive)

30. S. Russenschuck, CLIC-Workshop, WP2-Pacman, 4.02.2014 Solution of the Wave Equation IV The slackline The hard-edge (model) magnet

31. S. Russenschuck, CLIC-Workshop, WP2-Pacman, 4.02.2014 Test Cases Air coil: Academic worst case LEP-IL-QS The “blue” magnet

32. S. Russenschuck, CLIC-Workshop, WP2-Pacman, 4.02.2014 The Air Coil Longitudinal field distribution Longitudinal shape of the wire oscillation

33. S. Russenschuck, CLIC-Workshop, WP2-Pacman, 4.02.2014 Convergence of the Modal Amplitude Functions

34. S. Russenschuck, CLIC-Workshop, WP2-Pacman, 4.02.2014 Results for the Air Coil

35. S. Russenschuck, CLIC-Workshop, WP2-Pacman, 4.02.2014 Results for the Blue Magnet

36. S. Russenschuck, CLIC-Workshop, WP2-Pacman, 4.02.2014 Conclusion on the Wire Techniques  The classical stretched wire technique is routinely used for axis and gradient measurements  There is still a lot of potential in the oscillating wire technique  Because we measure the oscillation amplitude only at one point, we make in intrinsic error caused by the varying end fields as we move along the circular trajectory – The method is exact for the hard-edge (model) magnet and consequently for small-aperture magnets excited by rare-earth material – There is an intrinsic error because we measure only one amplitude. This error can be estimated when the numerical model is available – Effects from stage misalignment are much larger than the intrinsic error – We would be exact if it was possible to measure the shape of the wire oscillation

37. S. Russenschuck, CLIC-Workshop, WP2-Pacman, 4.02.2014 Solution of the Wave Equation (Recall)

38. S. Russenschuck, CLIC-Workshop, WP2-Pacman, 4.02.2014 Longitudinal field Profiles Behavior around resonance frequencies

39. S. Russenschuck, CLIC-Workshop, WP2-Pacman, 4.02.2014  Challenges – Bandwidth of the system – Intrinsic error – Noise at 1 kHz – Nonlinearities in the physical model – Tilt and swing alignment of the quadrupole  PACMAN R&D efforts – Measurement of oscillation profiles – New stages and wire tensioning systems – Fiducilization – Software framework (data and task manager) – “Intelligent” postprocessing (tension, multipoles) – String of magnets