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# Rotating Coils

Rotating Coils. PACMAN meeting 14.04.14 Printed Circuit Coils – Future developments. Rotating coils. Rotating coils measurement systems are developed to characterize the magnetic field quality of magnets in accelerators facilities.

## Rotating Coils

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1. Rotating Coils PACMAN meeting 14.04.14 Printed Circuit Coils – Future developments

2. Rotating coils Rotating coils measurement systems are developed to characterize the magnetic field quality of magnets in accelerators facilities. The field harmonics are computed knowing the rotating coil’s precise geometry. The process of bucking allows improving the measurement accuracy.

3. Rotating coilsUseful background information • The systemisbased on Faraday law : U = - A magnetic flux measurement by means of the rotating coils thus requires the integration of the voltage induced on the coil • Magnetic field quality in the aperture of accelerator magnets is commonly described by a set of Fourier coefficients known as field harmonics or multipole coefficients. • The field harmonics (multipoles) are derived using knowledge of the coil geometry. Using an angular encoder w

4. Rotating coilsUseful background information • Radial coil: Harder to build for small dimension, better the tangential coil • A rotating coil (loop of wires) measures the variation of the intercepted magnetic flux • multipole coefficients Bn(ref) and An(ref) are called normal and skew multipole coefficients

5. Tangential coil Horizontal dipole Vertical dipole Quadrupole

6. Tangential coil: Blind eye Rc =coil central radius D = Opening angle

7. Rotating coilsMotion related issues • Vibration motion causes spurious harmonics in the coil signal • Torsion motion Minimize (errors)“Bucking method” Effect Coil system whose sensitivity to the (n -1)- th harmonic is zero Coil system whose sensitivity to the n- th harmonic is zero Torsion Vibration

8. Rotating coilsBucking • Analog bucking: • Digital bucking: The BuckingRatio is the ratio of the harmonic n in the absolute and compensated measurements It is the «quality check» for bucking For a quadrupole it should be tipically 100

9. Rotating coilsExample: How to calculate the gain factor • Example on a tangential coil setup: 3 FFT signals from the 3 coils Considering the sum of the dipole and quadrupole harmonics is zero: • Gain will be applied also to calculate the sensitivity factor Kn of the compensated coil Kn_comp = Kn_coil1 + Kn_coil2* g1 + Kn_coil3 *g2

10. Rotating coilsSensitivity Factor • General: • Tangential: • Radial: • Calibrated parameters (coil central radius, axial tilt, magnetic surface) • a, R2, and R1 • Construction drawings

11. Rotating coilsFabrication problems • Handmade systems: Time of fabrication is long, wiring is a complicated process. • Connectors Manual coil winding facility

12. Printed circuit rotating coils • The PCB coil is based on the same principle as classic rotating coil. • PCB coils are made up by multiples layers boards on which are printed the coil loops traces on both sides.

13. Ideal PCB coil A perfect PCB coil: • accuracy implies high stiffness and straightness of the coils • excellent knowledge of traces (windings) localization. • Coils fabrication should also be easy and low-cost, so that coil parameters (type, length, number of turns, radius, etc.) can be customized to the magnet requiring test.

14. Printed circuit rotating coils • The trace continues in loops of increasing width on the reverse side (dashed line) following the original traces and maintaining the same chirality to complete a winding:

15. Printed circuit rotating coilsDipole and Quadrupole bucking • Quadrupole and Dipole Bucking DQB(1+3) • Also only Dipole bucking DB (1+2+3+4)

16. Printed circuit rotating coilsSensitivity factor • One method to compute it is: • The (-1) j gives the sign of the current flow of each wire and the (xj,yj) are the locations of the wires with respect to the rotation axis. • Multiple layers: The position of traces in not well known…  Hard to calculate with high precision L length of a given wire R reference radius

17. Printed circuit rotating coilsOpening angle • Tangential coils: Determinate the distances between traces according to the opening angle:

18. Printed circuit rotating coilsSensitivity factor • Comparison between tangential coil and pcb tangential coil (one layer) at probe radius of 16mm and 32mm

19. Printed circuit rotating coilsTo sum up: Advantages… • The number of turns can be increased by adding identical layers (PCB stack) • Precise trace positioning (<10 μm) • Sensitivity comparable to traditional designs (with 32 or more layers) • Manufacture large series quickly, reproducibly, cheap • Makes practical high-order compensation schemes (B1=B2=B3=B4=0)

20. Printed circuit rotating coils… and inconvenients • Coil Resistance is High [kW]: consequent instrumentation required • Cost of production when producing few coils • Human error on multiple layers assembly (stack of double layer) • Stiffness of the structure too low, flexible during rotation  much harder to calibrate

21. Printed circuit rotating coils… and inconvenients • Fabrication errors:

22. Some PCB coils-related R&D themes • General improvement of multi-layer PCB coils: track density (currently only ~1/3 of conventional coils) • Optimization of track layout to minimize sensitivity to production errors

23. Some PCB coils-related R&D themes • 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 • Development of a more compact Mini Rotating Unit MRU-II

24. Some PCB coils-related R&D themes • Micro PCB connectors for multi-strand wire coils : • Standard for all number of Brins • Easy to use • Avoid human errors • PCB fluxmeters : • upper limits of current printing • pressing and assembly techniques • new possibilities offered by ELTOS

25. Some PCB coils-related R&D themes • Polyvalent PCB sandwich coil shaft advanced materials (foams, honeycombs etc … for higher stiffness-to-weight ratio) • Software tool to facilitate the design of new PCB coils, bypassing traditional CAD: • from geometry specifications layer design  Gerber format file • Other techniques alternative to PCB: circuits printed on flexible rolls, inkjet circuit printers • Other tasks….

26. Scientific Planning for 2014

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