1. WP2 ESR 2.2 WP2 ESR2.2 Giordana Severino PACMAN WORKSHOP - CERN PCB technology for small diameter field sensing

2. WP2 ESR 2.2 OUTLINE  PACMAN INNOVATIVE DOCTORAL PROGRAM FOR CLIC  FIELD QUALITY IN ACCELERATOR MAGNETS  ROTATING COILS FOR SMALL DIMENSIONS APERTURES Coil production error  COIL CALIBRATION In situ calibration  COIL ROTATION CENTER and MAGNET GEOMETRICAL CENTER Metrology measurements Polygonal and cylindrical reference magnet Coil sag evaluation  FUTURE STUDIES AND DEVELOPMENTS

3. WP2 ESR 2.2 INNOVATIVE DOCTORAL PROGRAMME FOR CLIC The GOAL of the PACMAN program is to develop very high accuracy metrology and alignment tools and integrate them in a single automatic test stand The Compact Linear Collider (CLIC) is a study to implement the future electron-positron Linear Collider for Physics up to the multi-TeV Help of leader companies

4. WP2 ESR 2.2 FIELD QUALITY IN ACCELERATOR MAGNETS “The field quality in accelerator magnets is conveniently described by a set of Fourier coefficients known as field harmonics or multipoles coefficients” 1 How to measure Multipoles coefficients? Oscillating wireRotating coil 1: S.Russenschuck, "Field Computation for Accelerator Magnets: Analytical and Numerical Methods for Electromagnetic Design and Optimization", Wiley (2011) “All the undesired magnetic field harmonic components in a magnet”

5. WP2 ESR 2.2 ROTATING COILS FOR SMALL DIMENSIONS APERTURES Upgrade of LHC (Linear Accelerator 4) Future accelerators (Compact Linear Collider) Existing large accelerators (Large Hadron Collider ) Ø 50 mmØ 20 mm Ø 8 mm Now 2014 2020 2.5 x

6. WP2 ESR 2.2 MULTI-WIRE VS PCB COIL MULTI-WIRE COIL PCB COIL PCB layer misalignment Coil deformation More expensive Limited stiffness ADVANTAGES DISADVANTAGES Stiffness cheap Used for aperture above Ø 19mm: Possibility to use an inclinometer (bubble level) ADVANTAGES DISADVANTAGES Hand made connections are difficult: Both with multifilar wire colour coded (MWS) and LIZ wire Limited downsizing Imperfect coil section Good downsizing Fast to produce Connection on PCB

7. WP2 ESR 2.2 USEFUL BACKGROUND INFORMATION

8. WP2 ESR 2.2 COIL SENSITIVITY COEFFICIENTS Single filament approximation: the crossing section is reduced to a single filament correction factor k n are the complex coil sensitivity coefficients to the harmonic n

9. WP2 ESR 2.2 COIL CALIBRATION Design Parameters Calibration Real Parameters Parameters to calibrate: R 0 : Coil Center radius A: coil magnetic surface Θ: coil tilt K n sensitivity factor Computation of K n sensitivity factors, used for the computation of Multipole field harmonics In-situ calibration 1 :Procedure for calibrating equivalent magnetic area and rotation radius of coil 1 In-situ calibration of rotating coil magnetic measurement systems: a case study on Linac4 magnets at CERN Pasquale Arpaia, Marco Buzio, Giancarlo Golluccio, Fernando Mateo 17th Symposium IMEKO TC

10. WP2 ESR 2.2 IN-SITU CALIBRATION 1 Radius calibration Formula to calculate Radius and area in case of zero initial phase, pure delta x displacement on x axis and no coil tilt Procedure for calibrating equivalent magnetic area and rotation radius with a mechanical displacement inside reference quadrupole magnet In particular focusing on the radius calibration it is possible to determine it from the dipole and quadrupole FFT coefficients of flux STUDY THE EFFECT OF ONE SINGLE HIGHER HARMONICS ON THE CALIBRATION 1: In-situ calibration of rotating coil magnetic measurement systems: a case study on Linac4 magnets at CERN Pasqual Arpaia, Marco Buzio, Giancarlo Golluccio, Fernando Mateo 17 th Symposium IMEKO TC4 2014

11. WP2 ESR 2.2 Single Higher Harmonics effect on radius computation Feed-down of a quadrupole with sextupolar multipole field error Purely horizontal translation  no skew field harmonics excited Substituting the sensitivity coefficient for an ideal radial coil with zero initial phase, we get:

12. WP2 ESR 2.2 ROXIE SIMULATION A sextupole current shell is nested within the quadrupole. NEXT STEP TEST ON REAL MEASURAMENTS To simulate flux measurement: Perform a parametric analysis by rotating the coil 360 degrees in N steps Move the coil rotation center Set the desired coil radius 2D simulation is sufficient by assuming longitudinal homogeneity both in the magnet and the sensing coil

13. WP2 ESR 2.2 IN-SITU CALIBRATION Radius calibration Radius calibration independent from alignment error Linear stages for precise displacement Δz stage movement C k harmonic coefficient R coil rotation radius The quadrupole is not affected by feed-down

14. WP2 ESR 2.2 COIL ROTATION CENTER and MECHANICAL CENTER The magnet geometric axis G and the coil rotation axis C are coincident The magnet is rotated by successive angular steps until a complete rotation is performed… The coil rotation axis C is not coincident with the magnet geometric axis

15. WP2 ESR 2.2 METROLOGY MEASURAMENT d represents the distance between the coil rotation axis and geometrical magnet axis If with metrology measurements the distance d between the magnet geometric center and the coil rotation center is evaluated precisely, the distance obtained from the magnet rotation should be the same.  If there is a difference between these values … MORE GENERAL CASE: COIL FRAME AND MAGNET FRAME ARE NOT COINCIDENT THERE IS A COIL INITIAL PHASE

16. WP2 ESR 2.2 POLYGONAL AND CYLINDRICAL REFERENCE MAGNET Polygonal shape magnet Cylindrical shape magnet  Less machining error  More precise  Impossible to calibrate the initial phase  More machining error  Less precise  It is possible to calibrate the initial phase

17. WP2 ESR 2.2 COIL SAG EVALUATION CHECK DEFORMATION (COIL BEND: In particular in case of absence of an external rigid shaft) EVALUTION OF COIL SAG WITH A THIN MAGNET OF SMALL APERTURE The effect of sag can be corrected in calculation of harmonics Each coil subsection rotates about its local geometric center It is a problem for magnetic axis measurements. 1 2: CAS Accelerator school “Measurement and alignment of accelerator and detector magnets”.11-17 April 1997

18. WP2 ESR 2.2 FUTURE STUDIES AND DEVELOPMENT Bearings to reduce torsion AIR BEARINGS FOR REALLY SMALL SHAFT Ø8 mm Ruby and sapphire can attain very high surface finish. The finish can be routinely maintained at 2 micro-inch and under RING JEWEL BEARINGS Study on extra-small shaft To improve stiffness CARBON FIBER SHAFT ? Comparison of different shafts to find best performance on small dimension Study on fiducialization to be optimized for small aperture test-bench Fiducialization with small shaft is complex

19. WP2 ESR 2.2 Study of effects of PCB fabrication error (misalignment of planes..) on the value of sensitivity coefficients Study of new possible pcb coil configuration optimized for small dimensions Studies to improve coil calibration focus on PCB coil FUTURE STUDIES AND DEVELOPMENT

20. WP2 ESR 2.2 WP2 ESR 2.2 Thank you for your attention

21. WP2 ESR 2.2 FLIP COIL METHOD FOR THE EVALUATION OF COIL AREA The coil is flip two times inside a reference dipole with a magnetic field B known precisely Flipping the coil one side of 180 ˚ and after on the opposite side coming back to the same position it is possible to calculate the area if the Dipole field B in known precisely With calibration in situ The dipole magnet should be controlled with a NMR Monitor temperature and current during the measurement The reference value of the focusing strength 1 GdL must be obtained with independent measurement → SSW single stretch wire

22. WP2 ESR 2.2 Single Higher Harmonics effect on radius computation of in- situ calibration ROXIE simulation: quadrupole with a sextupole harmonic error The magnet is modelled by means of current shells of an ideal distribution that generates a pure multipole field of order n A sextupole current shell is nested within the quadrupole. 2D simulation is sufficient by assuming longitudinal homogeneity both in the magnet and the sensing coil SOME OF CALIBRATION CASE STUDIES IDEAL QUADRUPOLE QUADRUPOLE WITH A SEXTUPOLE HARMONIC ERROR NEXT STEP TEST ON REAL MEASURAMENTS

23. WP2 ESR 2.2 Calibration method with sextupole harmonic 20th IMEKO TC4 International Symposium – Benevento (Italy)23 Proposed calibration in a quadrupole with sextupole error harmonic

24. WP2 ESR 2.2 Calibration method with sextupole harmonic 20th IMEKO TC4 International Symposium – Benevento (Italy)24 Substituting the sensitivity coefficient for an ideal radial coil with zero initial phase. Ac calibrated area L coil lenght W coil width

25. WP2 ESR 2.2 Calibration method with one higher multiple harmonic The same procedure can be applied with an octupole error harmonic and a negligible sextupole : One should keep the coil positions as close as possible to the magnet center, as the sextupole harmonic is not negligible otherwise:

26. WP2 ESR 2.2 2D simulation with ROXIE 20th IMEKO TC4 International Symposium – Benevento (Italy)26 2D simulation is sufficient by assuming longitudinal homogeneity both in the magnet and the sensing coil CALIBRATION CASE STUDIES IDEAL QUADRUPOLE QUADRUPOLE WITH A SEXTUPOLE HARMONIC ERROR QUADRUPOLE WITH AN OCTUPOLE HARMONIC ERROR

27. WP2 ESR 2.2 Roxie simulation 20th IMEKO TC4 International Symposium – Benevento (Italy)27 For the numerical simulation the CERN field computation program ROXIE was used One of the innovative aspect of ROXIE is that it allows to simulate a rotating coil both hand wound and PCB.

28. WP2 ESR 2.2 ROXIE SIMULATION: QUADRUPOLE WITH A SEXTUPOLE HARMONIC ERROR 20th IMEKO TC4 International Symposium – Benevento (Italy)28 A sextupole current shell is nested within the quadrupole. To simulate flux measurement: Perform a parametric analysis by rotating the coil 360 degrees in N steps Move the coil rotation center Set the desired coil radius The magnet is modelled by means of current shells of an ideal distribution that generates a pure multipole field of order n

29. WP2 ESR 2.2 ROXIE SIMULATION: QUADRUPOLE WITH A SEXTUPOLE HARMONIC ERROR 20th IMEKO TC4 International Symposium – Benevento (Italy)29

30. WP2 ESR 2.2 COIL SAG EVALUATION CHECK DEFORMATION (COIL BEND: In particular in case of absence of an external rigid shaft) Check the coil profile along the z axis in four position (one every rotation of 90 ˚) EVALUTION OF COIL SAG WITH A THIN MAGNET OF SMALL APERTURE The sag of a measuring coil due to its own weight changes along the coil the distance between the mechanical center and the rotation axis. It could be interesting to check the distance in three position of the coil The effect of sag can be corrected in calculation of harmonics Each coil subsection rotates about its local geometric center It is a problem for magnetic axis measurements. Difficult to distinguish between true offset of magnetic axis and apparent due to sag 2 2: CAS Accelerator school “Measurement and alignment of accelerator and detector magnets”.11-17 April 1997