Alexander Temnykh Cornell University, Ithaca NY, USA Theory and applications of the vibrating stretched wire technique for high-precision quadrupole alignment Alexander Temnykh Cornell University, Ithaca NY, USA 1st PACMAN Workshop, CERN Feb 2-4 2015

1-st PACMAN Workshop, CERN Feb 2-4, 2015 Outline Theory of vibrating wire (VW) magnetic field measurement technique High-precision quadrupole alignment CESR super-conducting quadrupole fiducialization at room temperature CESR final focusing quadrupoles in-situ alignment NSLS-II (BNL) quadrupole and sextupole magnets alignment on girders LCLS (SLAC) quadrupole fiducialization SwissFEL quadrupole fiducialization Small aperture quadrupole magnets characterization at CERN Other applications Solenoid magnets magnetic axis finding CHESS G-line PM wiggler field integrals tuning LCLS undulator field integrals characterization Conclusion April 15, 2017 1-st PACMAN Workshop, CERN Feb 2-4, 2015

Theory Motion equation Setup with boundary condition: General solution Taut wire free motion Damping Gravity Lorenz forces between magnetic field and driving current with boundary condition: General solution Gravity Wire motion induced by Lorentz forces Gravity term with minimum (sag) at and can be represented in the similar way: ; ; Wire vibrating mode amplitude Term in the magnetic field Fourier sine series expansion A. Temnykh, Vibrating wire field-measuring technique, NIMA 399 (1997) 185-194 April 15, 2017 1-st PACMAN Workshop, CERN Feb 2-4, 2015

Demonstration experiments Theory Demonstration experiments Dipole magnet field reconstruction Quadrupole magnet alignment Test Quadrupole location Test dipole magnet at x = 45cm position. Wire length ~1.15 m, for the field reconstruction 13 vibrating modes are used . Wire length ~3.15 m, for the field reconstruction 30 vibrating modes are used A. Temnykh, Vibrating wire field-measuring technique, NIMA 399 (1997) 185-194

Application / CESR SC quads fiducialization at room temperature Setup 7.92 × 10−2 T/m at room temperature A. Temnykh, The Use of Vibrating Wire Technique for Precise Positioning of CESR Phase III Super- Conducting Quadrupoles at Room Temperature, PAC2001 April 15, 2017 1-st PACMAN Workshop, CERN Feb 2-4, 2015

Application / CESR Final Focus Quadrupole magnets alignment CESR interaction region assembly view Setup Q0E/W – permanent quadrupole magnets Q1E/W and Q2E/W super-conducting quadrupole magnets in cryostats (1) – 7.536m long 0.1mm copper-beryllium wire (2) – precise movable stages with optical targets. (3) – constant tension mechanism. (4) – wire motion sensors Challenges: Long wire Mix of PM and SC quads 1T longitudinal CLEO solenoid field A. Temnykh and S. Chapman, Alignment of the CESR interaction region qudrupole magnets using vibrating wire technique, IMMW 14 (2005) April 15, 2017 1-st PACMAN Workshop, CERN Feb 2-4, 2015

Application / CESR Final Focus Quadrupole magnets alignment PM quadrupoles survey/alignment we used with 30 vibration modes Wire vertical position at Q0E,W Differential effect dy = - 0.1mm Y = 0.039mm Vertical vibration mode amplitudes Reconstructed horizontal magnetic field, Bx(z) Q0W Q0E Y = -0.061mm A. Temnykh and S. Chapman, Alignment of the CESR interaction region qudrupole magnets using vibrating wire technique, IMMW 14 (2005) April 15, 2017 1-st PACMAN Workshop, CERN Feb 2-4, 2015

Application / CESR Final Focus Quadrupole magnets alignment Surveyed magnets Application / CESR Final Focus Quadrupole magnets alignment For Q1E,W SC quadrupoles survey used 4-th order field vibration mode 1) I(Q1W) = 233A x = -0.019 +- 0.001mm 2) I(Q1W) = 466A x = -0.022 +- 0.002mm 1) I(Q1E) = 231A y = 0.142 +- 0.007mm 2) I(Q1E) = 466A y = 0.141 +- 0.010mm Q1E, vertical x = -0.010 +- 0.004mm x = -0.002 +- 0.001mm Q1E, horizontal 1) I(Q1W) = 243A Y = -0.159 +- 0.013mm 2) I(Q1W) = 465A Y = -0.169 +- 0.018mm Q1W, horizontal Q1W, vertical survey A. Temnykh and S. Chapman, Alignment of the CESR interaction region qudrupole magnets using vibrating wire technique, IMMW 14 (2005) April 15, 2017 1-st PACMAN Workshop, CERN Feb 2-4, 2015

Application / CESR Final Focus Quadrupole magnets alignment CESR final focusing quadrupole survey data, Jan 26 2003 Magnet Gradient [T/m] Length [m] Horizontal position [mm] Vertical position [mm] Q2E - SC 8.28 0.661 -0.004 0.114 Q1E - SC 12.48 -0.006 0.142 Q0E - PM 28.8 0.182 -0.140 -0.200 Q0W - PM 0.110 Q1W - SC -0.020 -0.164 Q2W - SC -0.031 0.004 Electron beam orbit measurement confirmed the data A. Temnykh and S. Chapman, Alignment of the CESR interaction region qudrupole magnets using vibrating wire technique, IMMW 14 (2005) April 15, 2017 1-st PACMAN Workshop, CERN Feb 2-4, 2015

Application / NSLS-II magnet system alignment NSLS-II girder with magnets Girder length ~ 5 m Alignment Specifications: 30 µm magnet-to-magnet; ±0.2 mrad magnet roll; 100 µm girder-to-girder; Because it was difficult to achieve the required accuracy using magnet fiducialization, coupled with optical survey, Vibrating Wire technique was adopted. Quadrupoles Sextupoles Steering magnets 7.3m long wire Movable wire stages, two sets of vertical and horizontal wire vibration sensors 550-600 µm wire sag Various types of magnets (sextupoles and quads) Mass production A. Jain, VIBRATING WIRE R&D FOR ALIGNMENT OF MULTIPOLE MAGNETS IN NSLS-II, The 10th International Workshop on Accelerator Alignment, KEK, Tsukuba, 11-15 February 2008 April 15, 2017 1-st PACMAN Workshop, CERN Feb 2-4, 2015

Application / NSLS-II magnet system alignment Quadrupole magnets alignment (1) Sextupole magnets axis finding (2) (1) A. Jain, VIBRATING WIRE R&D FOR ALIGNMENT OF MULTIPOLE MAGNETS IN NSLS-II, The 10th International Workshop on Accelerator Alignment, KEK, Tsukuba, 11-15 February 2008 (2) A. Temnykh and A. Jain, Determination of Magnetic Axis in a Sextupole magnet using Vibrating Wire Technique, 15th IMMW, FNAL, 2007 April 15, 2017 1-st PACMAN Workshop, CERN Feb 2-4, 2015

Application / LCLS quadrupole magnets fiducialization Fixed wire, movable quad stage Wire Length 1.477m, fundamental frequency 115Hz, driving current ~7mA, sag ~23 microns The second vibrating mode not sensitive to uniform Earth magnetic field was used for alignment . The driving AC current frequency was maintained on resonance all time. Tooling balls served as references. FARO arm Coordinate Measurement Machine was used to find magnet tool balls position relative to wire position detector. Wire to quadrupole axis alignment precision was better than 1 micron. Tool ball on quads to quad magnetic center precision ~15 micron Mass production ! Z. Wolf et. al. , A Vibrating Wire System For Quadrupole Fiducialization , presentation on IMMW 14 (2005) Z. Wolf, A Vibrating Wire System For Quadrupole Fiducialization, LCLS-TN-05-11 M. Levashov and Z. Wolf, Set Up and Test Results for a Vibrating Wire System for Quadrupole Fiducialization , LCLS-TN-06-14 April 15, 2017 1-st PACMAN Workshop, CERN Feb 2-4, 2015

Application / Swiss FEL quadrupole magnets fiducialization Setup PLL OFF Magnet Wire vibration sensor PLL ON Fixed quad, movable wire stages Wire Length 1.2 m, fundamental frequency ~101 Hz, driving current ~ 75mA The second vibrating mode was used for alignment . FARO arm Coordinate Measurement Machine was employed to measure magnet references position relative to wire pins. The driving current frequency was maintained on resonance all time using lock-in-amplifier with Phase Lock Loop (PLL) function. With PLL function ON, demonstrated resolution is ~ 0.2 micrometer. For 0.36T quadrupole (0.17m long, 2.1 T/m gradient) 0.2 micron resolution implies 0.072 G-cm field integral sensitivity! C. Wouters et. al., Vibrating Wire Technique and Phase Lock Loop for Finding the Magnetic Axis of Quadrupoles, IEEE TRANSACTIONS ON APPLIED SUPERCONDUCTIVITY, VOL. 22, NO. 3, JUNE 2012 V. Vrankovic et. al., A Method for the Submicrometer Accuracy Determination of Quadrupole Magnetic Axis, IEEE TRANSACTIONS ON APPLIED SUPERCONDUCTIVITY, VOL. 24, NO. 3, JUNE 2014 April 15, 2017 1-st PACMAN Workshop, CERN Feb 2-4, 2015

Application / CERN – characterization of a small aperture quadrupole Wire locations in the course of measurements (on circle) Setup Quadrupole Wire vibration sensor Fixed quad, movable wire stages Wire Length ~1.0 m, off resonance operation, Vibration amplitude (displacement) is proportional to magnetic field at wire location sextupole octupole quadrupole etc. P. Arpaia et. al., Magnetic field measurements on small magnets by vibrating wire systems, IEEE Instrumentation and Measurement Technology Conference 01/2011 April 15, 2017 1-st PACMAN Workshop, CERN Feb 2-4, 2015

Application / Solenoid alignment Solenoid alignment technique has been used for Cornell ERL injector focusing solenoids fiducialization. A. Temnykh, Application of the VW technique for the solenoid magnet magnetic center finding, IMMW 14 (2005) April 15, 2017 1-st PACMAN Workshop, CERN Feb 2-4, 2015

Application / Solenoid alignment A. Temnykh, Application of the VW technique for the solenoid magnet magnetic center finding, IMMW 14 (2005) April 15, 2017 1-st PACMAN Workshop, CERN Feb 2-4, 2015

Application / G-line wiggler tuning First and second field integrals tuning CHESS G-line Wiggler (PM) Period [cm] 12 Number of poles 50 Peak field [T] 0.78 T Length [m] 3 m MULTIPOLE FIELD ERRORS CORRECTION (the source location was found with vibrating wire) A. Temnykh, THE CHESS G-LINE WIGGLER TUNING, PAC2001 April 15, 2017 1-st PACMAN Workshop, CERN Feb 2-4, 2015

Application / LCLS undulator characterization Horizontal beam trajectory Vertical beam trajectory Beam trajectories calculated for Hall probe and Vibrating Wire measured field. Single shim effect. The field change was measured and reconstructed using 25 vibrating modes A. Temnykh, Y. Levashov and Z. Wolf, A study of undulator magnets characterization using the vibrating wire technique, NIMA 622 (2010) 650–656 April 15, 2017 1-st PACMAN Workshop, CERN Feb 2-4, 2015

1-st PACMAN Workshop, CERN Feb 2-4, 2015 Conclusion After it was developed in 1997, Vibrating Wire technique has been used in many occasions and became a standard tool. For several big projects VW technique was critical. More applications can be expected. April 15, 2017 1-st PACMAN Workshop, CERN Feb 2-4, 2015