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Research on magnetic center measurement of quadrupole and sextupole using vibrating wire alignment technique in HEPS-TF

  • Lei Wu
  • Xiao-long Wang
  • Chun-hua Li
  • Hua-min Qu
  • Zi-hao Wang
  • Min-xian Li
  • Ling-ling Gong
Original Paper
  • 19 Downloads

Abstract

Purpose

In order to meet the extremely low emittance requirement, the magnets in the storage ring of high-energy photon source (HEPS) need to have a stable support and precise positioning. In HEPS-TF, the key and difficult technologies of HEPS should be researched and developed. Vibrating wire alignment technique is one important project of HEPS-TF. It can be used to pre-align the quadrupoles and sextupoles on one girder with high precision. A vibrating wire measurement system was set up and tested to verify the magnetic center measurement precision and the magnet adjustment error.

Methods

There are one sextupole and one quadrupole installed on a multipole girder. Vibrating wire is stretched through mechanical center of the magnet apertures and supported by the test benches on the two sides. A single conducting wire is stretched through the magnet aperture and electrified by alternating current. The wire will vibrate for a period of Lorentz force. By matching the current frequency to one mode of natural frequency of the wire, the vibrating amplitude will be enhanced. And by measuring the vibrating amplitude, the magnetic field at the wire position can be got. Moving the wire across the magnet aperture in the transversal or vertical direction, the distribution of magnetic field and magnetic center position can be measured. According to the magnetic center position error to adjust the magnet. Measure the magnetic center of all magnets installed on the multipole girder one by one, and adjust their magnetic center to a line.

Results

The magnetic center measurement precision is better than ±3 μm, and the magnet adjustment error is less than 6 μm.

Conclusion

The vibrating wire system design and a series of magnetic center measurement experiments have gained good achievements. It has been proved the vibrating wire system is designed reasonable and using the vibrating wire to align the magnets installed on a multipole girder is feasible and can reach a high precision.

Keywords

Vibrating wire Magnetic center Measurement precision Magnet adjustment 

PACS

29.20.db 

Introduction

High Energy Photon Source (HEPS) is a synchrotron facility proposed by Institute of High Energy Physics which will be built at northeast of Beijing in China. It will be a 6 GeV, approximately 1300 m circumference new-generation synchrotron radiation facility. Vibrating wire alignment technique is aimed to align quadrupoles and sextupoles on a girder about 3–5 m long with high precision to meet the extremely low-emittance requirement (better than 60 pm rad) [1]. Figure 1 shows one of the typical magnets and girder assembly. There are several quadrupoles and sextupoles installed on this girder. The alignment tolerance of magnets on this multipole girder should be better than ± 30 μm in transversal and vertical direction. In HEPS-TF, a vibrating wire measurement system was set up to research the precision of measuring the magnetic center and the alignment of this technique. According to the designed specifications, the magnetic center measurement precision should be better than ± 10 μm and the magnet adjustment error should be less than 15 μm.
Fig. 1

One of the typical magnets and girder assembly in HEPS

The fundamental principle of vibrating wire technique is based on Lorentz force. A single conducting wire is stretched through the magnet aperture and electrified by alternating current. The wire will vibrate for period Lorentz force. By matching the current frequency to one mode of natural frequency of the wire, the vibrating amplitude will be enhanced. And by measuring the vibrating amplitude, the magnetic field at the wire position can be obtained. By moving the wire across the magnet aperture in transversal or vertical direction, the distribution of magnetic field and magnetic center position can be measured. According to the magnetic center position to adjust the magnet, measure the magnetic center of all magnets installed on the multipole girder one by one and adjust their magnetic center to a line. The more detailed theory can be found in Refs. [2, 3, 4, 5].

Vibrating wire measurement system

The vibrating wire measurement system was installed in a laboratory with temperature stability of ± 1 °C before May 2017 (Fig. 2). The wire length was about 3 m for small installation space. Using this 3-m wire, the method of magnetic center measurement has been researched and mastered. But the measurement precision did not achieve an ideal result. The system was removed to a laboratory with temperature stability of ± 0.1 °C in May. The vibrating wire measurement system in thermostatic laboratory is shown in Fig. 3. The magnetic center measurement and magnet adjusting test were carried out systematically.
Fig. 2

3-m vibrating wire measurement system

Fig. 3

5.5-m vibrating wire measurement system

There are one sextupole and one quadrupole installed on a multipole girder. Both the magnets are borrowed from BEPCII, because there are no magnets of HEPS that can be used yet. Vibrating wire is stretched through mechanical center of the magnet apertures and supported by the test benches on the two sides. The wire material is alloy of beryllium copper. Its diameter is 0.125 mm. The length of the wire is about 5.5 m, and the wire is protected by a Plexiglas tube.

Figure 4 shows the structure of wire support 1 on one side. The wire support 2 on the other side is similar to that. The wire is fixed on support 1 by welding and stretched by a 1 kg weight through a pulley on support 2. The wire is located by the V notch on the test benches and can move in transversal and vertical direction by the 2D translation stages. X1 and Y1 sensors on support 1 are used to detect the wire vibration in transversal direction and vertical direction separately. And another set of vibration sensor X2 and Y2 installed on support 2 is used to detect wire vibration redundantly and contrast with the test of X1 and Y1. The vibration sensor is a kind of photo-interrupter. The sensor’s output voltage is linear with the wire vibration amplitude [6].
Fig. 4

Structure of wire support 1

Magnetic center measurement

Measurement procedures

At first, using laser tracker to preliminary align the vibrating wire measurement system roughly, it mainly includes the wire supports, magnets and girder. In this alignment procedure, ± 0.05 mm alignment tolerance of wire supports is enough and the magnets alignment tolerance is better than ± 0.1 mm.

Then using vibrating wire to measure the magnetic center, most of the magnetic center measurement procedures are carried out by an automatic program written with LabVIEW. The main procedures are as follows:

(1) Determination of measurement parameters. According to the wire vibration amplitude to set appropriate measurement parameters, parameters mainly consist of the wire measurement direction and measurement position, amplitude and frequency of AC (output voltage of sinusoidal signal generated by signal generator) in the wire. So a roughly measurement should be carried out to make sure the optimized measurement parameters. By roughly measurement, the wire measurement parameters of this quadrupole and sextupole are described in Table 1.
Table 1

Magnetic center measurement parameters

 

Quadrupole

Sextupole

Frequency of AC (Hz)

58.6 ± 1

117.2 ± 1

Transversal

 Wire position (mm)

− 0.5,− 0.3,− 0.1, 0.1, 0.3, 0.5

− 2.2,− 1.8,− 1.4, 1.0, 1.4, 1.8

 Amplitude of AC (V)

1.6, 2.5, 5, 5, 3.7, 1.9

10, 10, 10, 10, 10, 10, 10

Vertical

 Wire position (mm)

− 0.5,− 0.3,− 0.1, 0.1, 0.3, 0.5

− 1.7,− 1.3, 0.9, 1.5, 1.9, 2.3

 Amplitude of AC (V)

1.6, 2.8, 5, 5, 3, 1.8

10, 10, 10, 10, 10, 10, 10

By measurement, the first mode of natural frequency of the wire is about 29.3 Hz. The vibration amplitude should be smaller than the working area of vibration sensors (< 0.1 mm) and keep a good S/N. The frequency of AC is near to the 2nd mode of natural frequency when measuring quadrupole and 4th mode when measuring sextupole. This is because the sensitivity of yaw and pitch between wire and magnetic axis to different mode natural frequency is different. According to Eq. (1), a best mode can be calculated. In this equation, l is the wire length. n is the natural frequency mode. zmag is the magnetic position along the wire. lmag is the magnet length. β is the angle of yaw or pitch. ∆α is the magnetic center measurement error produced by yaw or pitch.
$$ \Delta \alpha = \left( {\frac{l}{n\pi }} \right)\cot \left( {\frac{{n\pi z_{\text{mag}} }}{l}} \right)\left[ {1 - \left( {\frac{{n\pi z_{\text{mag}} }}{l}} \right)\cot \left( {\frac{{n\pi l_{\text{mag}} }}{2l}} \right)} \right]\beta $$
(1)

The magnetic field gradient of quadrupole is much stronger, the amplitude of output voltage of signal generator can be smaller, and the biggest one reached 5 V, but the voltage should be much higher when measuring the sextupole for the low magnetic field gradient. The output voltage is 10 V.

(2) Measure the total magnetic field of the six measurement positions when the magnet at working current. In this procedure, the magnetic field produced by not only the test magnet but also the background field, such as the remnant field of the other magnets installed on the same girder and ground field. The total magnetic field and background field measurement will be introduced in "Magnetic field distribution" section.

(3) Measure the magnetic field of the six measurement positions when the test magnet without current. In this procedure, the magnetic field was produced by background field. The influence of the remnant field of other magnet has a great influence on the magnetic field measurement.

(4) Use the total field, subtract the background field to obtain the real magnetic field of the test magnet, and analyze the distribution of the field to obtain the magnet center position.

It should be paid attention that when measuring the vertical magnetic center, the sag correction should be considered. Sag correction will be introduced in "Magnet adjustment experiment" section.

Magnetic field distribution

Magnetic field distribution of quadrupole

As given in Eq. (2), the magnetic field varies linearly with the offsets from the center in quadrupole. G is the quadrupole gradient. (x0, y0) is the magnetic center location, and (x,y) is the wire location in transverse and vertical direction. Bx and By are the magnetic field component in transverse and vertical direction. The magnetic center in transversal direction is located where the magnetic field By is zero and vertical magnetic center is located where Bx is zero. X1 and X2 sensors detect the wire vibration caused by By. Y1 and Y2 sensors detect the wire vibration caused by Bx [7, 8, 9].
$$ B_{y} = G(x - x_{0} );\quad B_{x} = G(y - y_{0} ) $$
(2)
Figures 5 and 6 show one transversal and one vertical magnetic field distribution and magnetic center measurement results of quadrupole measured by Y1 and X1 sensor. The measurement results measured by Y2 and X2 are similar to that. The total magnetic field intensity varies linearly with the wire position, and the fitting line has a larger slope. The background field intensity is rather small, and the slope of the fitting line is near 0. After doing background field correction, the vibrating wire is only affected by the magnetic field of quadrupole. The magnetic center after background correction is located at (0.054, 0.027) mm in the vibrating wire coordinate system. The influence of background field is about 20 μm in transversal direction and 10 μm in vertical direction in this measurement.
Fig. 5

Magnetic field of quadrupole in transversal direction

Fig. 6

Magnetic field of quadrupole in vertical direction

Magnetic field distribution of sextupole

As in Eq. (3), the magnetic field of sextupole varies quadratic with the offsets from the center, and the magnetic center is the extreme point of parabola. B3 is the sextupole field at a reference radius Rref. Transversal and vertical magnetic center measurements are all using By measured by X1 and X2 sensors. That is a difference between sextupole and quadrupole.
$$ B_{y} = B_{3} \left[ {\frac{{(x - x_{0} )^{2} - (y - y_{0} )^{2} }}{{R^{2}_{\text{ref}} }}} \right] $$
(3)
Figures 7 and 8 show one transversal and one vertical magnetic field measurement result of sextupole. The distribution of total magnetic field is parabolic, and the background field is linear. After doing background field correction, the distribution of sextupole magnetic field is still parabolic. The magnetic center after background correction is located at (0.028, 0.175) mm in the vibrating wire coordinate system. The transversal magnetic center is affected a lot by background field for it has a larger slope. The difference reaches to 176 μm with and without background field correction. The background field with small slope has little effect on vertical magnetic center. The difference is about 5 μm with and without background field correction.
Fig. 7

Magnetic field of sextupole in transversal direction

Fig. 8

Magnetic field of sextupole in vertical direction

The influence of background field

As above, background field has different influences on quadrupole and sextupole. This is because the most of the background field is the remnant field of other magnet. So in this measurement, the background field mainly concludes the remnant field of sextupole when measuring quadrupole. And it mainly concludes the remnant field of quadrupole when measuring sextupole.

The measurement position is from − 0.5 to 0.5 mm when measuring quadrupole, and the sextupole remnant field is small and has little difference near the vertex of the parabola. So the background field has small effect on measuring the magnetic center of quadrupole.

When measuring sextupole, By is the measurement magnetic field both transversal and vertical direction. But quadrupole remnant field By only effect the transversal direction as Eq. (2) shows for By only relate to x and has no effect on vertical direction for By has no relationship with x. So the quadrupole remnant field is linear and has a great slope in transversal direction and has a small slope in vertical direction.

The repeatability of magnetic center measurement

In order to verify the magnetic center measurement precision, repetitive measurement is essential. Ten consecutive transversal and vertical magnetic center measurements are shown in Figs. 9 and 10. The total variation, standard deviation and the agreement of magnetic center measured by X1 sensor and X2 sensor of these 10 measurements can be seen in these figures. The biggest total variation is smaller than 4 μm, the standard variation is about 1 μm, and the agreement between two sets of sensors is smaller than 4 μm.
Fig. 9

Ten consecutive transversal measurements of quadrupole

Fig. 10

Ten consecutive vertical measurements of quadrupole

To further verify the precision of the magnetic center measurement, transversal and vertical magnetic center was been tested several days. The magnetic center position is shown in Figs. 11 and 12. The magnetic center positions change little in different days. The biggest total variation is smaller than 4.3 μm, the standard variation is about 1.6 μm, and the agreement between two sets of sensors is smaller than 1 μm.
Fig. 11

Quadrupole transversal center measured in several days

Fig. 12

Quadrupole vertical center measured in several days

So no matter measuring the magnetic center consecutively or testing in several days, the quadrupole magnetic center measurement precision is better than ± 1.6 μm (1σ confidence interval).

Ten consecutive transversal and vertical magnetic center measurements of sextupole are shown in Figs. 13 and 14, and the measurements in several days are shown in Figs. 15 and 16. The sextupole magnetic center measurement precision is better than ± 2.8 μm.
Fig. 13

Ten consecutive transversal measurements of sextupole

Fig. 14

Ten consecutive vertical measurements of sextupole

Fig. 15

Sextupole transversal center measured in several days

Fig. 16

Sextupole vertical center measured in several days

According to the magnetic center measurement above, a summary about measurement precision is shown in Table 2. The measurement precision is pretty good in both consecutive measurements and measured in different days. The quadrupole field distribution is linear, and the vibration signals around the center are better than sextupole, so it is more easy to obtain a high precision than sextupole. Considering all the data in Table 2, the magnetic center measurement precision is better than ± 3 μm.
Table 2

Magnetic center measurement repeatability of 5.5-m vibrating wire in laboratory with temperature stability of ± 0.1 °C

Precision (μm)

Quadrupole

Sextupole

10 times

5 days

10 times

5 days

Transversal

± 0.3

± 0.7

± 2.4

± 2.3

Vertical

± 1.0

± 1.6

± 1.8

± 2.8

Temperature stability is very important for magnetic center measurement repeatability. Table 3 shows the measurement precision of 3-m vibrating wire measurement system in the laboratory with temperature stability of ± 1 °C. Contrast with the precision measured in the thermostatic laboratory shown in Table 2, the precision is worse, especially in different days.
Table 3

Magnetic center measurement repeatability of 3-m vibrating wire in laboratory with temperature stability of ± 1 °C

Precision (μm)

Quadrupole

Sextupole

10 times

5 days

10 times

5 days

Transversal

± 1.0

± 4.8

± 3.0

± 3.0

Vertical

± 2.7

± 9.0

± 4.0

± 4.5

An effective method to increase the precision is improving AC signal intensity properly to improve S/N. Reducing the interruption of human activities is also necessary for the long wire and is sensitive to airflow disturbance and ground vibration. Installing a Plexiglas tube outside the wire is effective in signal stability enhancement, especially in the condition of weak magnetic field.

Each magnet measurement will take about 50 min, and the measurement efficiency is a bit low.

Sag correction

Because of the gravity, 5.5-m-long wire can generate a quite large of sag about 350 μm, the wire sag shaped like Fig. 17. So when measuring the vertical magnetic center, sag correction should be considered. According to Eq. (4), sag is only related to acceleration of gravity and the wire fundamental natural frequency. So sag correction can be based on the measurement of wire fundamental natural frequency f1. And the sag correction s at the magnet position zmag can be calculated according to Eq. (5).
Fig. 17

Model of wire sag correction

$$ {\text{sag}} = \frac{g}{{32f_{1}^{2} }} $$
(4)
$$ s = - \frac{{4{\text{sag}}}}{{l^{2} }}z_{\text{mag}}^{2} + \frac{{4{\text{sag}}}}{l}z_{\text{mag}} $$
(5)
In the process of measuring magnetic center, the wire vibrations are acquired in time domain. A function about F(ω) is established to transfer the vibration time domain signal to frequency domain signal using Fourier transform. By measuring a series of F(ω) and through nonlinear fitting, the wire natural frequency can be obtained. Figure 18 shows one F(ω) fitting picture of the wire 4th natural frequency f4. So the fundamental natural frequency f1 is 29.2 Hz.
Fig. 18

F(ω) fitting to measure f1

In order to know the effectiveness of the wire sag correction method, an experiment was carried out to test. Table 4 shows three times vertical magnetic center measurement results. In this measurement, the wire fundamental natural frequencies were different because the wire was stretched by different weights. So the sag correction value s and the magnetic centers before sag correction are all different. But after sag correction, the magnetic centers are consistent. That is a good proof of the validity of sag correction.
Table 4

Magnetic center measurement before and after sag correction

Weights (kg)

f1 (Hz)

s (mm)

Magnetic center (mm)

Before correction

After correction

1

28.95

0.247

0.031

− 0.216

1.1

29.3

0.241

0.026

− 0.215

1.15

30.1

0.228

0.013

− 0.215

Magnet adjustment experiment

In order to make sure the correctness of this vibrating wire measurement system and the effectiveness and feasibility of alignment using vibrating wire, the magnet adjustment experiment has been done. Firstly, use vibrating wire to measure the current magnetic center of the magnet (x0, y0). Secondly, adjust the magnet in transversal and vertical direction according to position offset of the current magnetic center to (0, 0). The adjustment amount is known at the monitor of the magnet position displacement sensor. Thirdly, use vibrating wire to measure magnetic center position again to see whether the magnetic center has close to the origin of the coordinate system of vibrating wire.

There are eight magnet position displacement sensors with 1 μm accuracy installed under the magnet. Four of them are used to monitor the magnet vertical direction, two for transversal direction and two for beam direction. Some of the sensors are shown in Fig. 19. The adjustment displacement can be read directly by a LabVIEW program.
Fig. 19

F(ω) fitting to measure f1

Table 5 shows several times of alignment adjustment experiment results. Before adjustment, the magnetic center is located in different quadrant spaces. Each adjustment offsets and direction are different, as small as a few microns and as large as hundreds of micrometers. After adjustment, the magnetic center position offsets are all smaller than 6 μm. That is a pretty good result. It is better than the aim of 15 μm.
Table 5

Magnet center before and after adjustment

Magnet

Magnetic center (x0, y0) (mm)

Before adjustment

After adjustment

Quadrupole

(0.070, 0.009)

(0.003, 0.005)

(− 0.048, − 0.043)

(0.004, 0.002)

(0.057, 0.052)

(− 0.002, 0)

Sextupole

(− 0.144, 0.089)

(0.006, − 0.001)

(0.055, − 0.051)

(− 0.002, − 0.002)

Conclusions

The vibrating wire system design and a series of magnetic center measurement experiments have gained good achievements. It has been proved that the vibrating wire system designed reasonable and using vibrating wire to align the magnets installed on a multipole girder is feasible and can reach a high precision. The magnetic field distribution of quadrupole is more simple. It will be more easily to obtain a higher precision than the measurement of sextupole. A good environment with temperature stable is important for vibrating wire measurement.

The magnetic center measurement precision is better than ± 3 μm, and the magnet adjustment error is less than ± 6 μm. That is better than the aim of the task. Using vibrating wire technique to align the magnets installed on multipole girder in HEPS is feasible. When the magnets of HEPS are available, a formal measurement and alignment will be carried out.

Notes

Acknowledgements

This work was supported by High Energy Photon Source Test Facility (HEPS-TF). We sincerely thank the help of Professor Jain Animesh from Brookhaven National Laboratory.

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Copyright information

© Institute of High Energy Physics, Chinese Academy of Sciences; Nuclear Electronics and Nuclear Detection Society and Springer Nature Singapore Pte Ltd. 2018

Authors and Affiliations

  1. 1.Institute of High Energy PhysicsChinese Academy of SciencesBeijingChina
  2. 2.Dongguan Institute of Neutron SciencesDongguanChina
  3. 3.University of Chinese Academy of SciencesBeijingChina

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