1. 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. 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

3. 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)
April 15, 2017
1-st PACMAN Workshop, CERN Feb 2-4, 2015

4. 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)

5. 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

6. 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

7. 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 = mm
Vertical vibration mode amplitudes
Reconstructed horizontal magnetic field, Bx(z)
Q0W
Q0E
Y = mm
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

8. 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 = mm
2) I(Q1W) = 466A
x = mm
1) I(Q1E) = 231A
y = mm
2) I(Q1E) = 466A
y = mm
Q1E, vertical
x = mm
x = mm
Q1E, horizontal
1) I(Q1W) = 243A
Y = mm
2) I(Q1W) = 465A
Y = mm
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

9. Application / CESR Final Focus Quadrupole magnets alignment
CESR final focusing quadrupole survey data,
Jan
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

10. 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
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, February 2008
April 15, 2017
1-st PACMAN Workshop, CERN Feb 2-4, 2015

11. 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, 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

12. Application / LCLS quadrupole magnets fiducialization
Fixed wire, movable quad stage
Wire Length m, 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

13. 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 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

14. 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

15. 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

16. 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

17. 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

18. 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

19. 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