IBIC2023, Saskatoon, Canada
JACoW Publishing
ISSN: 2 6 7 3 - 5 3 5 0
d o i : 1 0 . 1 8 4 2 9 / J A C o W - I B I C 2 0 2 3 - W E P 0 1 1

A PRELIMINARY DESIGN OF BUNCH-BY-BUNCH
3D POSITIONS MEASUREMENT
Ruizhe Wu, Yunkun Zhao, Dongyu Wang, Ping Lu, Leilei Tang, Baogen Sun∗
University of Science and Technology of China (USTC),
No. 96, JinZhai Road Baohe District, Hefei, Anhui, China
Abstract
The decrease of beam emittance in the 4𝑡ℎ generation
light source greatly increases the electron density, thus thewakefields and beam impedance in the storage ring are significantly enhanced, resulting in various beam instabilities.
Therefore, it is necessary to observe the transient state ofbeams using the bunch-by-bunch technique, so as to dig into
these instabilities. Here a three-dimensional (3D) positions
measurement instrument is designed based on data synchronization module (DSM) to acquire the transverse positions
and longitudinal phases of beams in real-time.

INTRODUCTION
Compared with the 3𝑡ℎ generation light sources, the 4𝑡ℎgeneration light sources are generally built with compact
MBA structures, so that the horizontal emittance of the beamis reduced by 1 to 2 orders, close to the X-ray diffraction
limit. Consequently, the strong nonlinear elements in theMBA structures make the dynamic aperture significantly
smaller, causing the beam dynamics to be extremely sensitive to the effects of instabilities, and even affecting themaximum beam current during operation time. Hence, itis essential to observe the beam characteristics on fine timescales using bunch-by-bunch technique, figuring out the instabilities induced by wakefields, and even eliminating theseinstabilities.
Generally, bunch-by-bunch technique covers bunch length,
longitudinal phase, bunch charge, transverse positions andbunch profiles [1–5]. However, it is obvious that these measurements are limited by the number of sampling channels
on a single acquisition board, and only one single beam parameter can be obtained, rather than multiple parameterssimultaneously. In order to break through the limitation of
the number of sampling channels, a bunch-by-bunch 3D positions measurement instrument is designed with DSM [6],as shown in Fig. 1.
The instrument is mainly composed of microwave components and digital logic components, in which the microwave
components are divided into signal part and timing part. For
the signal part, it duplicates the four-channel signal sensed
from the BPM in the storage ring and sends the two duplicated four-channel signals to data acquisition boards. For
the timing part, the synchronous signal generated from thestorage ring timing system is frequency quadrupled and thendivided into two channels to data acquisition boards, between
which there is a certain phase difference due to the delay

Figure 1: The layout of bunch-by-bunch 3D positions measurement instrument.
line. As for the digital logic components, two four-channel
signals are digitized by the acquisition boards, then these
digitized signals are synchronized by the DSM in FPGA,
and finally the 3D positions of each bunch are calculated.
Since these microwave components are at the factory, anevaluation system based on oscilloscope is set up to researchthe 3D positions measurement processes in the designed
instrument.

EVALUATION SYSTEM SETUP
In order to determine the measurement performance in the3D positions, an oscilloscope-based performance evaluation
system was constructed, as shown in Fig. 2. With the helpof the low-pass filter, the bandwidth of the oscilloscope isequivalent to that of the acquisition board, so that the dataobtained by the oscilloscope and the data acquisition board
are consistent. After the acquisition, these data will be sent
to the computer for processing, and finally obtain the signalsof each bunch during the bunch interval [7]. Finally, thecorresponding measurement performance can be obtainedby analyzing the signals in the bunch interval.

Figure 2: Evaluation system based on oscilloscope.

∗ bgsun@ustc.edu.cn

WEP011
09 Data Acquisition and Processing Platforms

347

Content from this work may be used under the terms of the CC-BY-4.0 licence (© 2023). Any distribution of this work must maintain attribution to the author(s), title of the work, publisher, and DOI

12th Int. Beam Instrum. Conf.
ISBN: 9 7 8 - 3 - 9 5 4 5 0 - 2 3 6 - 3

12th Int. Beam Instrum. Conf.
ISBN: 9 7 8 - 3 - 9 5 4 5 0 - 2 3 6 - 3IBIC2023, Saskatoon, Canada
JACoW Publishing
ISSN: 2 6 7 3 - 5 3 5 0
d o i : 1 0 . 1 8 4 2 9 / J A C o W - I B I C 2 0 2 3 - W E P 0 1 1Content from this work may be used under the terms of the CC-BY-4.0 licence (© 2023). Any distribution of this work must maintain attribution to the author(s), title of the work, publisher, and DOI

3D POSITIONS MEASUREMENT
For longitudinal phases of bunches, its measurement formula is shown as Eq. (1) [7]:𝐿 = 𝐾 ⋅ 𝑉𝑂𝑆𝑀(1)Where coefficient 𝐾 represents the linearity of the BPM
sum signal, which is determined by the amount of charge
and the length of the bunch, and 𝑉𝑂𝑆𝑀 is the BPM sum
signal at one sampling point during the bunch interval.
However, this measurement method of longitudinal phases
is susceptible to the jitters of the synchronous signals, so that
the 𝑉𝑂𝑆𝑀 obtained has a certain deviation from the actual,
for whose detailed information please refer to Ref. [7]. To
eliminate the influence of the clock jitters on longitudinal
phases, it is necessary to adopt a two-point sampling method
as shown in Fig. 3.
Figure 4: Relations between (𝑉𝐴 , 𝑉𝐵 ) and 𝑉𝑂𝑆𝑀 .
of clock jitters. Moreover, it is worth noting that the datarelations (𝑉𝐴 , 𝑉𝐵 ) − 𝐿 can be directly constructed, then thecorresponding longitudinal phase 𝐿 of the bunch can bedirectly calculated through Eq. (3), as depicted in Fig. 5.
Here the red line shows the actual longitudinal phase of thebunch, while the blue line is the longitudinal phase of thebunch obtained through the data relations (𝑉𝐴 , 𝑉𝐵 ) − 𝐿.
Figure 3: Sampling with two points in the bunch interval.
In the two-point sampling method, 𝑇𝑔 is determined by
the length of the delay line in the instrument, and the amplitude of the two sampling points 𝑉𝐴 and 𝑉𝐵 are completelydetermined by the BPM sum signals collected by the acquisition board A and B. Hence, the factor 𝐾 in Eq. (1) can becompletely determined, as Eq. (2):𝐾 = (𝑉𝐵 − 𝑉𝐴 ) /𝑇𝑔(2)

While the value of 𝑉𝑂𝑆𝑀 in Eq. (1) can also be determinedby 𝑉𝐴 and 𝑉𝐵 , although the two sampling points corresponding to 𝑉𝐴 and 𝑉𝐵 have certain clock jitters. For one bunch ina specific filling pattern, the data relations (𝑉𝐴 , 𝑉𝐵 ) − 𝑉𝑂𝑆𝑀
can be constructed according to the bunch-by-bunch datacollected by the oscilloscope-based evaluation system, as
shown in Fig. 4.
In this way, with the data relations (𝑉𝐴 , 𝑉𝐵 ) − 𝑉𝑂𝑆𝑀 , thevector 𝑉𝑀 (𝑉𝐴 , 𝑉𝐵 ) collected by the instrument in real-time
is carried out with multiple vectors 𝑉𝐷 (𝑉𝐴 , 𝑉𝐵 ) in the data
relations as shown in Eq. (3), and the corresponding data
𝑉𝑂𝑆𝑀 is selected as the actual 𝑉𝑂𝑆𝑀 when the matchingcoefficient 𝑀 is the highest one.
𝑀 = (𝑉𝑀 ⋅ 𝑉𝐷 ) / (∣𝑉𝑀 ∣ ⋅ ∣𝑉𝐷 ∣)(3)

Thus, the longitudinal phases 𝐿 of each bunch can beobtained by two sampling points (𝑉𝐴 , 𝑉𝐵 ) without the effects

Figure 5: The actual longitudinal phases and the longitudinal
phases calculated with relations.
As for the transverse positions of bunches, they are calculated with the Δ − Σ method, but using the four-channel
signal whose BPM sum signal is larger between 𝑉𝐴 and 𝑉𝐵
to ensure the signal-to-noise ratio. The related equations areas follows:
1⎧{ 𝑇𝑥/𝑦 = 𝐾𝑥/𝑦 ⋅ (𝑉1 − 𝑉2/4 − 𝑉3 + 𝑉4/2 ) ⋅ ∑4 𝑉𝑖=1 𝑖⎨{𝑉𝑖 = 𝑉𝐴𝑖 if 𝑉𝐴 > 𝑉𝐵 else 𝑉𝐵𝑖⎩(4)

Wherein: 𝑥/𝑦 is the transverse position of x-direction ory-direction, 𝐾𝑥⁄𝑦 is a constant with unit “mm” dependingon the geometry of button BPM, 𝑉𝑖 are the digitized fourchannel signals from BPM, and the subscript 𝑖 indicates

WEP011348

09 Data Acquisition and Processing Platforms

IBIC2023, Saskatoon, CanadaJACoW Publishing
ISSN: 2 6 7 3 - 5 3 5 0d o i : 1 0 . 1 8 4 2 9 / J A C o W - I B I C 2 0 2 3 - W E P 0 1 1

the identifier of the four channels. Besides, 𝑉𝐴𝑖 and 𝑉𝐵𝑖
represent the four-channel signals on sampling points 𝐴 and𝐵 respectively.

• Construct the formula for (𝑉𝐴 , 𝑉𝐵 ) − 𝑉𝑂𝑆𝑀 .

(𝑉𝐴 , 𝑉𝐵 ) − 𝐿, in which the machine learning is needed todetermine the vector matching parameters of each bunch in
the filling pattern. Therefore, it is necessary to collect mass
data with the oscilloscope-based evaluation system and thenbuild its corresponding relations before building this bunchby-bunch 3D positions measurement instrument, otherwise
the measurement results will have a deviation. As revealedin Fig. 5, part of the reason why the longitudinal phasesof the bunch calculated by vector matching module deviate
from the actual longitudinal phases is owe to the insufficientamount of data relations (𝑉𝐴 , 𝑉𝐵 ) − 𝐿. But it is not ruled outthat these deviations are also caused by inconsistencies ofthe movements of the bunches in the specific filling modes.
Anyway, the two reasons need to be verified later throughbuilding sufficient data relations.

• Utilize data dimensional reduction methods.

CONCLUSIONDISCUSSION
Using the two-sampling method, the evaluation for theresolution of the transverse positions makes no difference
from our previous work [7]. While for the resolution of
the longitudinal phases, the error transfer formula is hard toobtain precise results due to the non-formulaic form of thedata relations (𝑉𝐴 , 𝑉𝐵 ) − 𝑉𝑂𝑆𝑀 . In view of this, there are
two ways to acquire the actual resolution of the longitudinal
phases:For the first way, its essence is still the error transfer formula, but the construction is difficult. As for the second way,
the longitudinal phases of the bunches obtained through datarelations (𝑉𝐴 , 𝑉𝐵 ) − 𝑉𝑂𝑆𝑀 are processed for dimensional reduction, and the data variance before and after dimensional
reduction is taken as the resolution assessment. However, it
has subjective judgment factors in the dimensionality reduction.
Moreover, the data processing flows for 3D positions measurement can be basically determined, as shown in Fig. 6.
After these digitized BPM signals are synchronized by themodule DSM, the BPM sum signals (𝑉𝐴 , 𝑉𝐵 ) at two sampling positions in the bunch interval will be sent to the vector
matching module to complete the calculation of Eq. (3) tofind the most matched data relation (𝑉𝐴 , 𝑉𝐵 ) − 𝐿, and thematched 𝐿 is taken as the longitudinal phase of the bunch.
At the same time, the sampling selection module will selectthe four-channel signal whose BPM sum signal is lager as
the input of the Δ − Σ module, which outputs the transverse
positions of the bunch.

To design the instrument for observing the 3D positions ofbunches in the storage ring, one oscilloscope-based evaluation system is set up to determine the data dealing processesof the 3D positions, and the framework of the logic blocks
inside FPGA. However, there is some deviations between
the longitudinal phases obtained with the vector matching
and the actual longitudinal phases, which is due to the insufficiency of the data relations, or the inconsistency of themovement laws of the bunches in the specific filling mode.
More research work is need to verify the two possibles.

REFERENCES[1] J. Lee, M. H. Chun, G.-J. Kim, D.-C. Shin, D.-T. Kim, and S.
Shin, “Bunch-by-bunch position measurement and analysis atPLS-II”, J. Synchrotron Radiat., vol. 24, no. 1, pp. 163–167,
2017. doi:10.1107/S1600577516018154[2] Y.-M. Zhou, et al., “Bunch-by-bunch longitudinal phase monitor at SSRF”, Nucl. Sci. Tech. vol. 29, no. 113, 2018.
doi:10.1007/s41365-018-0445-6[3] F.-Z. Chen et al., “Touschek lifetime study based on the precise bunch-by-bunch BCM system at SSRF”, Nucl. Sci. Tech.,vol. 30, no. 144, pp. 1–8, 2019.
doi:10.1007/s41365-019-0655-6[4] A. Drago, et al., “Bunch-by-bunch profile diagnostics in storage rings by infrared array detection”, Meas. Sci. Technol.,vol. 26, no. 9, pp. 094003, 2015.
doi:10.1088/0957-0233/26/9/094003[5] L.-W. Duan, Y.-B. Leng, R.-X. Yuan, Z.-C. Chen, “Injection
transient study using a two-frequency bunch length measurement system at the SSRF”, Nucl. Sci. Tech., vol. 28, no. 7, p. 93,
2017. doi:10.1007/s41365-017-0247-2

Figure 6: Data processing flows inside the 3D positions
measurement device.
It should be noted that the construction of the vector
matching module requires a large number of data relations[6] R. Wu, Y. Zhao, S. Jin, L. Tang, P. Lu, and B. Sun, “Data synchronization module for multi-dimensional bunch-by-bunchmeasurement in a storage ring” Rev. Sci. Instrum., vol. 93,
no. 12, pp. 123301, 2022. doi:10.1063/5.0115976[7] R. Wu, Y. Zhao, S. Jin, L. Tang, P. Lu, and B. Sun, “A one-timesampling method for the real-time measurement of bunch-bybunch three-dimensional positions in storage rings”, J. Instrum., vol. 17, no. 11, pp. P11001, 2022.
doi:10.1088/1748-0221/17/11/P11001

WEP011
09 Data Acquisition and Processing Platforms

349

Content from this work may be used under the terms of the CC-BY-4.0 licence (© 2023). Any distribution of this work must maintain attribution to the author(s), title of the work, publisher, and DOI

12th Int. Beam Instrum. Conf.
ISBN: 9 7 8 - 3 - 9 5 4 5 0 - 2 3 6 - 3