1. 1 1 Uncertainty analysis of a vibrating-wire system for magnetic axes localization Pasquale Arpaia, Dip. di Ingegneria Elettrica e Tecnologie dell’Informazione, Università di Napoli Federico II, Naples, Italy European Organization for Nuclear Research (CERN), Technology Dept., Geneva, Switzerland. Domenico Caiazza, Dipartimento di Ingegneria, Università degli Studi del Sannio, Benevento, Italy European Technology Dept., Organization for Nuclear Research (CERN), Geneva, Switzerland. Carlo Petrone, Technology Dept., European Organization for Nuclear Research (CERN), Geneva, Switzerland. Stephan Russenschuck, Technology Dept., European Organization for Nuclear Research (CERN), Geneva, Switzerland 1 The 9 th International Conference on Sensing Technology Dec. 8 – Dec. 10, 2015, Auckland, New Zealand

2. 2 2 Domenico Caiazza 9 th International Conference on Sensing Technology ICST’15 Outline Introduction CLIC accelerator magnets and magnetic measurement Wire-based transducers Response surface for vibrating wires Methodology Experiments Conclusions

3. 3 3 Domenico Caiazza 9 th International Conference on Sensing Technology ICST’15 PACMAN (1/2) Particle Accelerator Components’ Metrology and Alignment to the Nanometer scale  «Marie Curie» Action, Program funded by the EU within the Seventh Framework Programme  Goal of the project: training of 10 researchers in beam instrumentation, metrology, micrometric alignment, magnetic measurements, nano-positioning and high precision engineering  A wide academic and industrial network https://pacman.web.cern.ch/

4. 4 4 Domenico Caiazza 9 th International Conference on Sensing Technology ICST’15 PACMAN (2/2) GOAL: An integrated test station for fiducialization and initial alignment of particle accelerator components Quadrupole magnets (Quad) Beam position monitors (BPM) Accelerating structures (AS) Quad BPM AS Stretched-wire systems for the magnetic measurement of small-aperture magnets Quadrupole alignment

5. 5 5 Domenico Caiazza 9 th International Conference on Sensing Technology ICST’15 Beyond Large Hadron Collider: The Clic Study Metrological challenges imposed by CLIC  Small beam size and impact section  submicron range  High-precision in focusing the beam  500 nm horizontal and 5 nm vertical normalized beam emittance  Tight specifications on components’ alignment  17 μm uncertainty budget over 200 m for the quads A two-beam, 50-km, e+/e- collider V. AA., “A Multi-TeV linear collider based on CLIC technology: CLIC Conceptual Design Report”. CERN-2012-007. 2012. QUAD BPM ACCEL. Struct.

6. 6 6 Domenico Caiazza 9 th International Conference on Sensing Technology ICST’15 44,020 magnets for CLIC Two-beam technology: drive and main beams Quadrupole magnets to focus the beams more than 40 000 units in the drive beam 4020 units in the main beam Main beam quad Final focus quad V. AA., “A Multi-TeV linear collider based on CLIC technology: CLIC Conceptual Design Report”. CERN-2012-007. 2012. Drive beam quad Two beams

7. 7 7 Domenico Caiazza 9 th International Conference on Sensing Technology ICST’15 Magnetic measurements for PACMAN Challenges small apertures limited access for traditional magnetic probes Large Hadron Collider (2008) Ø 50 mm Ø 10 mm CLIC main beam quadrupole Methods Printed-circuit board (PCB) rotating coils Single stretched-wire systems Stretched wires PCB rotating coils

8. 8 8 Domenico Caiazza 9 th International Conference on Sensing Technology ICST’15 Wire-based transducers Integrated test system: field strength and direction field quality field profiles magnetic axis

9. 9 9 Domenico Caiazza 9 th International Conference on Sensing Technology ICST’15 Magnetic axis localization Magnetic axis: points locus where the magnetic flux density is zero Goals: provide a reference for magnet installation place the wire on the magnetic axis for fiducialization Quadrupole section S S N N

10. 10 Domenico Caiazza 9 th International Conference on Sensing Technology ICST’15 Vibrating-wire method A. Temnykh. “Vibrating wire field-measuring technique”. Nuclear Instruments and Methods in Physics Research, 1997. Feeding the wire by alternating current (Lorentz Force) Wire in magnetic field Measure wire vibrations (X and Y components) Relate motion to magnetic field Procedure MBQ optical detectors ~ current source δ σ

11. 11 Domenico Caiazza 9 th International Conference on Sensing Technology ICST’15 Locating the axis 11 MBQ AVERAGE CENTER TILT The wire is sensitive to the distance from the average center when the first eigenmode is excited The wire is sensitive to the tilt when the second eigenmode is excited

12. 12 Domenico Caiazza 9 th International Conference on Sensing Technology ICST’15 Vibrating-wire zero method Example

13. 13 Domenico Caiazza 9 th International Conference on Sensing Technology ICST’15 Environment and configuration 13 MBQ ~ Excitation current source δ Wind speed Magnet length L m Wire length L Wire tension T Vibration amplitude δ Phototransistor’s working voltage V W Current excitation frequency f exc Stage misalignment θ s Wind speed s w V W : phototransistor’ s working point ?

14. 14 Domenico Caiazza 9 th International Conference on Sensing Technology ICST’15 Performance 14 Performance Repeatability (σ c ) Sensitivity (S) Nonlinearity (σ NL ) VW system Configuration parameters L/L m, T, δ, WP, f exc s w, ϑ s Noise parameters Vibration amplitude with phase change σ c : 1- σ standard deviation of x c and y c S: the slope of the regression line σ NL : variance of the linear regression error (residuals) Output: Combined performance index

15. 15 Domenico Caiazza 9 th International Conference on Sensing Technology ICST’15 Hp: orthogonality of the parameters (no interactions) The additive statistical model describes the relation between performance and parameters 15 Response surface methodology Mean performance Parameter effects Model error

16. 16 Domenico Caiazza 9 th International Conference on Sensing Technology ICST’15 Space of experiments Mapping the performance on the configuration space Parameter ranges are discretized on three levels Taguchi’s array: only a subset is mapped (L18 array) 16 ParameterSymbolLevelsUnit 123 Wire length / magnet lengthL/L m 5.3010.1420.40- Wire tensionT6009001100g Vibration amplitudeδ0.10.71.5V Working voltageVWVW 5.76.16.5V Distance from resonance∆f exc -0.50.0Hz Air speedswsw 0.150.300.70m/s Stage angleϑsϑs -10-50mrad From 3 7 to 18 experiments!

17. 17 Domenico Caiazza 9 th International Conference on Sensing Technology ICST’15 Main effects : factor effects and ∆: variability range Predominance of the vibration amplitude Other effects: wire length, excitation frequency, air speed 17 ParameterLevels∆ 123 L/L m -5.422.632.808.22 T-0.37-0.190.560.93 δ-12.493.668.8321.32 VWVW -0.651.31-0.661.97 ∆f exc 2.701.73-4.437.13 swsw 6.070.36-6.4412.51 ϑsϑs 0.320.22-0.550.87 ParameterLevels∆ 123 L/L m -4.40-0.034.438.83 T-3.481.302.185.66 δ-11.953.168.7920.75 VWVW 3.48-2.78-0.706.25 ∆f exc 5.601.16-6.7612.36 swsw 4.39-1.26-3.147.53 ϑsϑs -2.57-0.901.694.26

18. 18 Domenico Caiazza 9 th International Conference on Sensing Technology ICST’15 ANOVA (1/2) Sum of Squares (SS), Degrees of Freedom (DF), Mean Squares (MS), F ratio (F) contribution to overall variance importance in changing the value of the mean 18 ParameterSSDFMSF L/L m 264.902132.453.94 T2.9121.460.04 δ1484.502742.2722.07 VWVW 15.5527.780.23 ∆f exc 179.43289.712.67 swsw 471.022235.517.00 ϑsϑs 2.7321.3630.04 Error100.88333.63 Total2522.0117 ParameterSSDFMSF L/L m 233.882116.949.53 T111.11255.584.53 δ1381.342690.6756.27 VWVW 121.75260.874.96 ∆f exc 470.492235.4519.17 swsw 184.37292.187.51 ϑsϑs 116.73258.364.76 Error36.82312.27 Total2656.4817

19. 19 Domenico Caiazza 9 th International Conference on Sensing Technology ICST’15 ANOVA (2/2) Most influential: vibration amplitude + sensitivity, (-) repeatability Wire tension + More significant on the vertical coordinate search Phototransistors working voltage Changes for each specific device Excitation frequency + if 1 Hz lower than resonance to stabilize vibration amplitude Wire length + with longer wire 19

20. 20 Domenico Caiazza 9 th International Conference on Sensing Technology ICST’15 Verification experiment (1/2) Optimum prediction Selecting the optimum level for each factor Using the additive model Experiment with optimum configuration With each factor at the optimum level Adequacy of the additive model The prediction error lies in the confidence interval 20 xym.u. Predicted performance38.5942.06dB Observed performance37.5241.63dB Prediction error variance20.177.64dB Confidence interval (2σ)±8.98±5.53dB

21. 21 Domenico Caiazza 9 th International Conference on Sensing Technology ICST’15 Verification experiment (2/2) Optimum configuration vs shorter wire Envelope curves of vibration amplitude 21 Repeatability σ c xym.u. Short wire2.64.6µm Long wire0.91.1µm Long wire Short wire

22. 22 Domenico Caiazza 9 th International Conference on Sensing Technology ICST’15 Conclusions Uncertainties reduction for the vibrating wire Vibration amplitude for sensitivity Excitation frequency lower than resonance for more stability Long wire and high tension for improving repeatability Phototransistor working voltage to set adequately Outlook Incorporate systematic uncertainties

23. 23 Domenico Caiazza 9 th International Conference on Sensing Technology ICST’15 Thanks for your attention

24. 24 Domenico Caiazza 9 th International Conference on Sensing Technology ICST’15 Spares

25. 25 Domenico Caiazza 9 th International Conference on Sensing Technology ICST’15 PACMAN: the team WP4 Beam Instrumentation M. Wendt WP3 Precision mech. & stabilization M. Modena WP2 Magnetic Measurements S. Russenschuck WP1 Metrology & Alignment H. Mainaud Durand Domenico Claude Solomon Vasileios Giordana Iordan Peter David Silvia Natalia “Stretched-wire systems for the magnetic measurement of small-aperture magnets” https://pacman.web.cern.ch/

26. 26 Domenico Caiazza 9 th International Conference on Sensing Technology ICST’15 Architecture Sensors: phototransistor Sharp TM GP1S094HCZ0F Current generator: Keithley® 6351 Common marble support for magnets and stages System architecture P. Arpaia, M. Buzio, J. G. Perez, C. Petrone, S. Russenschuck, L. Walckiers. “Measuring field multipoles in accelerator magnets with small-apertures by an oscillating wire moved on a circular trajectory”, IOP JINST - Journal of Instrumentation, 2012.

27. 27 Domenico Caiazza 9 th International Conference on Sensing Technology ICST’15 Vibrating-wire axis measurement o P. Arpaia, C. Petrone, S. Russenschuck, L. Walckiers, “Vibrating-wire measurement method for centering and alignment of solenoids”, IOP Journal of Instrumentation, Vol. 8, Nov., 2013. o Z. Wolf. “A Vibrating Wire System For Quadrupole Fiducialization ”, Tech. rep. LCLS-TN-05-1. SLAC, Menlo Park, California, USA, 2005. A zero-finding problem Vibration amplitude nulling method QUAD A B Procedure 1)Center finding (horizontal and vertical)  First resonance  Co-directional wire movement 2)Tilt finding (pitch and yaw)  Second resonance  Counter-directional wire movement QUAD A B

28. 28 Domenico Caiazza 9 th International Conference on Sensing Technology ICST’15 Vibrating wire: Mathematical model Hp: Plane motion Uniform and constant tension Small deflections Constant length Uniform mass distribution ~ current source