REAL-TIME MEASUREMENT IN SLOW DISPLACEMENT OF THE
TUNNEL FLOOR DUE TO DYNAMIC GROUND MOTION AT THE KEKBINJECTOR LINAC
T. Suwada∗ , Y. Enomoto, K. Kakihara, K. Mikawa, T. Higo, KEK, Tsukuba, Japan
Abstract
A new remote-controllable sensing system in a laserbased alignment system is in progress to evaluate slow dynamic displacement of the tunnel floor in real time at the
KEKB injector linac. Based on the recent real-time measurements over six months, we have found that the transverse displacements of the tunnel floor are not negligibly small in comparison with the required alignment tolerance. The cross-correlation analysis shows the positive
correlation among the measurement positions on averageover the entire linac, except for the two at both ends, while
the cross-correlation function varies irregularly during theshort term. In this report, the measurement and analysis
results are in detail described in slow displacement of thetunnel floor of the KEKB injector linac with a laser-basedalignment system.

INTRODUCTION
The Super KEK B-Factory (SKEKB) project [1] is anext-generation B-factory under construction at KEK after the KEK B-Factory (KEKB) project [2]. The SKEKB
is an asymmetric electron-positron collider comprising 4GeV positron (LER) and 7-GeV electron (HER) rings.
The target luminosity of the SKEKB will be 40 times ofthe peak luminosity of the KEKB. The motivation of theSKEKB is the urgent need to perform high-energy flavor
particle physics experiments concerning the CP violationin B mesons [3]. Because the SKEKB is a factory machine,
well-controlled operation and high-precision alignment for
the accelerator complex are indispensable for maintaining
the injection efficiency, stability of the beam collision, andpeak luminosity at the maximum.
A laser-based alignment technique is one of the prominent alignment techniques developed for long-distance accelerator complexes. This alignment technique is advantageous as it can not only be applied to initial alignment measurements for long linacs but can also be utilized for regular monitoring of the straightness of the beam line along
the entire linac without any interruption during the linac
operation. Based on these benefits, dynamic spatial displacements of the tunnel floor along the entire length of thelinac due to ground motion can be measured in real time.
Our method is a conventional laser-based alignment
technique in which transverse spatial displacements of theaccelerator components from a laser-based fiducial line canbe measured with quadrant silicon photodiodes (QPDs),
where the laser-based fiducial is directly made as a laser∗ tsuyoshi.suwada@kek.jp

axis by connecting two (or three) fiducial points. A QPD is
mounted at a target point, which should be aligned in an accelerator unit, and it is directly irradiated by the laser-based
fiducial with a relatively narrow beam width. The central
positions at the target can be estimated by measuring the intensity centroid of the laser-based fiducial in the transverse
directions on the QPD. Based on this alignment technique,the accelerator units of the linac can be precisely aligned
along the laser axis by measuring the transverse displacements from the laser fiducial.
For the purpose in the real-time measurements of the dynamic displacements, two remote-controllable QPDs were
installed at the head and middle of the injector linac insummer shutdown of 2014, and seven remote-controllable
QPDs were additionally installed in summer shutdown of2015 at multiple locations near expansion joints of the linac
building (see Table 1). After the setup procedure, the realtime measurements of the long-term displacements of thetunnel floor has been started to take data on 7 January 2016.
The tunnel floor is located 5.65 m below the earth’s surface
in which the klystron gallery is situated.
In this report, the consecutively measurement resultswith a laser-based alignment system are in detail described.
Here, the new remote-sensing system and its performance
will be reported elsewhere [4].

KEKB INJECTOR LINAC
Here, we briefly describe the components and operation
scheme only related to a laser-based alignment system of
the injector linac. Figure 1 shows a schematic layout of the
KEKB injector linac [5]. It comprises eight sectors (A–C
and 1–5), which together constitute two long straight sections. One section is 125 m long and is composed of sectors
A and B; the other is 476 m long and is composed of sectors C and 1–5. These two straight sections are connected
to a 180◦ arc section with a circumferential length of 31 m.
Single-bunch electron beams can be generated from a
conventional thermionic electron gun (AT gun) and arepassed through a pre-injector to attain a pulse width of∼10 ps [6]. The electron gun can generate electron beams
at maximum charges of 20 nC/bunch and a maximum repetition rate of 50 Hz for positron production. The primaryelectron beams (∼10 nC/bunch) can be stably accelerated
to 3.3 GeV from the end of the buncher up to a positron
production target installed at the front of unit 1-5.
The positrons are captured with a flux concentrator andaccelerated up to an energy of 120 MeV using largeaperture S-band accelerating structures [7]. The subsequently positioned normal S-band accelerating structures

AB laser fiducial line (132 m)

B-8

B-7

Sector
e. j.

B

B-5

B-3

B-6

B-4

Sector
B-2

B-1

A-4

A
e. j.

A-3

A-2

AT Gun (e-)

to DR

Laser

A-1

RTL
Laser

C-1

C-2

C-3

C-4

e. j.
Sectoro

180 -Arce- 1.5 GeV

C-5

C-6

C-8

C-7

1-2

1-1

3-3

3-4

3-5

3-6

Sector

3

1-6

1-7

1-8

e. j.

2-1

2-2

2-3

2-4

2-7

2-6

e. j.

e+ TargetC

Sector

LTR

2-8

e. j.

1

Sector

2

SY2
PF

e. j.
3-2

1-5

1-3

3-7

3-8

e. j.
4-1

4-2

4-3

4-4

4-5

4-6

4-7

4-8

Sector 4

e. j.
5-1

5-2

5-3

5-4

Sector

5-5

5-6

5

5-7

5-8

e. j.

SY3

SKEKB LER/HER
PF-AR

C5 laser fiducial line (500 m)

Figure 1: Schematic layout of the KEKB injector linac and laser fiducials for two long straight sections. The abbreviation
e.j. indicates an expansion joint between the building blocks of the linac. The two arrows (red) show the laser-based
fiducials for two long straight sections. The solid circles (blue) represent the remote-controllable QPDs fixed at theaccelerator unit and the open circles (blue) represent the reference remote-controllable QPDs fixed at the tunnel floor.

Table 1: Summary table in the locations of the remotecontrollable QPDs and expansion joints (e.j.) along the injector linac from the laser source. Some measurement results, the maximum norm (rm ) of the displacement vector
and the maximum slope (sr ) in the variations in the time
traces of the norm, are also summarized depending on the
QPD locations.
QPD
e.j.
L
rm
sr
[m]
[mm] [µm/day]
REF1UA
1.74
0.19
3.3
C3D
44.31
−
−
11DA
106.11 0.55
5.5
11D
106.72−−
1814DA
177.04 0.65
5.1
1814D 178.39−−
21UA
180.17 0.47
4.2
28G6DA
259.07 0.65
6.6
28G6D 259.64−−
28REFUA
263.32 0.44
4.1
38DA
339.58 0.68
4.1
38G5U 341.60−−
48DA
419.08 0.88
4.6
48G5U 421.11−−
51UA
423.65 0.84
5.1
57G7U 498.01−−
584D
499.94−−accelerate the positrons up to an energy of 1.1 GeV at second beam switchyard (SY2) and the positron beam is injected into a new damping ring (DR) [8] through the linacto-DR transport line (LTR) [9]. The positron beams shallsubsequently be transported back through the DR-to-linac
transport line (RTL) to the SY2, and again accelerated up
to 4.0 GeV in the linac for injection into the SKEKB LER,
while the electron beams can be directly accelerated up
to 7 GeV in the linac for injection into the SKEKB HER
through the 180◦ arc section where the beam energy is

1.5 GeV.

LASER-BASED ALIGNMENT SYSTEM
Two independent laser-based alignment systems areavailable. One is for the alignment of the AB straight section, and the other is for that of the C5 straight section (seeFig. 1). The lengths of the laser-based fiducial lines are
132 m and 500 m for the AB and C5 straight sections, respectively. Two laser sources with commercially available
1-mW and 10-mW He-Ne lasers are installed along with
the input optical system for the AB and C5 straight sections, respectively. Here, only the alignment system for the
C5 straight section is described because the system is very
similar between the AB and C5 straight sections.
The laser source is 16 m upstream from the upstream
end face of unit C-1. The laser passes through laser pipes
in vacuum while the laser source is installed in an atmospheric environment. The inner surface of the laser pipe iscoated with a black paint composed of acrylic resin in order to prevent any unnecessary reflection and scattering of
the laser light.
The laser pipes are evacuated using two scroll pumps
with a pumping speed of 1000 l/min, which are installed
178 m and 321 m downstream from the input optical system. Two vacuum windows (thickness: 20 mm and 15 mm)
made out of transparent synthetic quartz have been attachedto the end faces of the initial and final (or first and last) laser
pipes of the straight section to maintain vacuum higher inthe laser pipes. A vacuum level of a few Pa can be attained. The propagation and stability characteristics of thelaser fiducial along with the optical system are described indetail elsewhere [10].
A holder is precisely connected to both ends of the accelerator unit through a vacuum flange; a QPD with silicon
semiconductor (diameter: 10 mm) is mounted at the centerof the holder. The fifty accelerator units, with both regularand irregular lengths, are distributed along the C5 straightsection; these units must be aligned with more than one

hundred QPDs in total within the transverse displacementsof 0.1 mm in one standard deviation along the laser-based
fiducial.
There are two fiducial points, which specify the transverse coordinates with respect to the laser axis. They are
the transverse central positions of the initial and last QPDs
(QPD REF1UA and QPD 584D, respectively) installed at
z=6.3 m and z=500 m downstream from the input opticalsystem, respectively. These two fiducial QPDs are rigidly
fixed at the floor of the accelerator tunnel after they havebeen locally aligned with a conventional laser tracker.
The transverse positions of the laser axis at the initial
QPD is manually adjusted by translating the laser beam at
the input optical system with the parallel plate in order tocorrespond to the center of the initial QPD, while the pointing of the laser beam is stabilized at the last QPD by controlling the x and y injection angles at the input opticalsystem based on a feedback control [10].
The initial alignment of the accelerator units was carriedout at the locations of QPDs. Each QPD can be manually(or remotely only one part) inserted into the center of thelaser pipe. The transverse displacements of both the end
surfaces of the accelerator unit can be determined with respect to the laser axis by analyzing the signal readouts fromthe QPD. Such a series of measurements provides an accurate view in the high-precision alignment of long linacs.

REAL-TIME MEASUREMENT ON
DYNAMIC FLOOR MOTION
Long-term variations of the displacement vectors
The x and y ingredients of the displacements of accelerator components in rectangular coordinates are usuallyindependently analyzed in time-series data. It is, however,important in the analyses to directly take into account thedisplacement vector instead of the use of the x (or y) ingredient because no special directivity may be provided in the
direction of the displacement vector due to ground motion.
Fig. 2 shows a typical example in the time series of the displacement vector obtained for QPD 38DA. It can be seenthat the displacement vector has smoothly moved aroundthe laser axis in the time direction. This is the reason why it
is advantageous to the analysis with the displacement vectors in order to evaluate the transverse motion.
Figure 3 shows the time traces of the norm and phasein the displacement vectors measured for the accelerator
units (or tunnel floor) at multiple locations with the remotecontrollable QPDs during a nearly six-month period beginning on 7 January 2016. During the term the end positionsof the laser axis were sufficiently stabilized to the center ofthe last QPD with the feedback control on. Here, it should
be noted that the data are represented as the amount of variation in the displacement vectors, that is, the differentials
from the corresponding initial data.
It can be understood that the norms of the displacement vectors monotonically increase except for that of
QPD REF1UA, which is nearest to the laser source. On

QPD38DA: 3D display of the displacement vector

y [mm]
7.Jan.
4.Feb.
15.Apr.

Date

6.Junex [mm]
24.July.2016

Figure 2: Variations in the time trace of the displacement
vector obtained for the accelerator units (QPD 38DA) withthe feedback control on.
the other hand, it can be seen that there are some incomprehensible fine structures in each time trace. The variationsin the maximum norm (rm ) of the displacement vector ineach time trace as a function of the QPD location are shownin Table 1. The maximum norms are spread over a rangeof 0.19–0.88 mm depending on the QPD location, and theaverage maximum norm (⟨rm ⟩) is 0.65 mm except for thatof QPD REF1UA. The variations in the maximum growth
rates (sr ) in the time traces as a function of the QPD location are shown in Table 1. The maximum growth ratesof the norms are spread over a range of 3.3–6.6 µm/day
depending on the QPD location, and the average maximum growth rate (⟨sr ⟩) is 4.9 µm/day except for that of
QPD REF1UA.
It can also be found that the variations in the phase angle of the displacement vector in each time trace approachalmost constant value since the middle of May 2016, while
it can be seen that there are some steep variations until theend of March depending on the QPD location. Here, it
should be noted that stepwise variations of the phase in thetime traces normally arise in the phase region of 0 over 2π
because the phase is defined by an angular range of 0-2π.
However, it can be clearly seen that relatively large stepwise jump arises on 28 January 2016 in the time traces ofthe phase for QPD 1814DA and QPD 28REFUA. It takes
about four days in the rise time of the jump, and on theother hand, in the variations in the norms of the displacement vector during the corresponding term are less than
0.2 mm. It could be understood that during the corresponding term the displacement vector of the accelerator unit
has rotated rather than increased in the transverse plane.
Based on such vector representation in the displacement
vector in polar coordinates, for the first time, complex anddynamic behavior of the tunnel floor could be seen much
more clearly than the previous analysis.
The 500-m-long linac building comprises two floors,which together constitute the klystron gallery and tunnel
in ground and underground floor, respectively. The linac

Figure 3: Time traces in (a) the norm and (b) phase angle of the displacement vector for the accelerator units (or tunnel
floor) measured by the remote-controllable QPDs.
building comprises eight building blocks which are joined
to be linearly aligned with seven expansion joints, which
can absorb certain amount of elastic deformation due toexpansion or contraction of the building blocks. However,
the residual stress may induce some elastic deformation forthe building blocks themselves. This mechanism may also
contribute to the displacement of the accelerator units along
the tunnel.
Last but not least, it should be noted that the two fiducial points to define the laser axis could also move dynamically. Thus, the laser axis itself could not become an entirely fixed and stable fiducial axis as an absolute fiducial
line.

Cross-correlation analysis among the displacement vectors
It is generally valid to apply cross-correlation analyses inorder to capture features in their mutual relations between
different multivariate vector variables [11]. Based on the
cross-correlation analyses in time traces of the displacement vectors, the variations in a cross-correlation function
can be obtained in real time. This is one of powerful analysis methods to understand not only localized displacementsof the accelerator units but also structural deformation of
the building blocks along the entire length of the linac tunnel.
A cross-correlation function (R̂k (i, j)) between the n-th

displacement vectors (d⃗n (i) and d⃗n (j)) obtained for the ith and j-th QPDs, respectively, in time series with time lagof k is defined by
⟨⃗
µ(i)⟩

=

1 ∑ ⃗
dn (i),N n=1

Ĉk (i, j)

=

N
1 ∑ ⃗
(dn (i) − ⟨⃗µ(i)⟩) ·
N

N

(1)

n=k+1

(d⃗n−k (j) − ⟨⃗µ(j)⟩), (2)R̂k (i, j)=

Ĉk (i, j)√.
Ĉ0 (i, i)Ĉ0 (j, j)(3)Here, the dot in eq. (2) indicates the inner product for the
displacement vectors, and ⟨⃗µ(i)⟩ is the average of the i-th
displacement vector in time series with a maximum data
length of N , and Ĉk (i, j) is the cross-covariance function,
which is similarly defined to the cross-correlation function. It should be noted that R̂k (i, j) is normalized by using the cross-covariance functions, Ĉ0 (i, i) and Ĉ0 (j, j) for
the i-th and j-th QPDs, respectively, without any time lag,
k=0. Thus, R̂k (i, j)=1 (−1) shows strong positive (negative) correlation, and R̂k (i, j)=0 shows no correlation, andR̂k (i, j) at k=0 (k̸=0) stands for the cross-correlation function at present (past) time.
Figure 4 shows the time traces in the cross-correlation

Figure 4: Time traces in the cross-correlation function of the displacement vectors between the reference QPD(QPD REF28DA) and other QPDs.
function (k=0) of the displacement vectors for other
QPDs to the reference QPD (QPD REF28DA). Here,QPD REF28DA is located almost at the middle locationin the injector linac.
It can be seen that each cross-correlation function varies
irregularly in the corresponding time trace, and however, the averages in the time traces decrease in therange of R̂0 =0.67 to 0.48 in accordance with the distancefrom the reference QPD except for QPD REF1UA whereR̂0 =0.06. This means that the relatively strong positive
cross-correlations show averagely high coherency in dynamic displacements of the accelerator units along the entire length of the linac tunnel except for QPD REF1UA. In
other words, the results show that the floor level even at the
expansion joints in each building block moves coherently
on average with each other.
It should be noted that the time trace in the crosscorrelation function for QPD REF1UA is markedly different from those in the other cross-correlation functions.
It may come from that the floor for the laser source isstructurally separated from the tunnel floor of the building
block [10]. It seems for QPD REF1UA to stand alone fromthe other building blocks.
The cross-correlation functions for all the QPDs obtained at two different instantaneous dates are shown in
Fig. 5. Here, those on a straight line tilted at 45 degree passing through the axis origin are the self-correlation function,and it becomes R̂0 =1 by definition. Figure 5 (a) showsthat the intensity distribution pattern obtained on 15 February 2016 at 0:00 am shows strong coherency, while Fig. 5(b) obtained on 27 February 2016 at 8:00 am shows lesscoherency. It should be noted that the cross-correlation
function to QPD REF1UA (z=1.74 m) show much less coherency because of the isolated behavior of QPD REF1UA.
Though the analysis of the displacement vectors using the cross-correlation technique shows complicated features, some important features can be seen and it will beeffective for the further analysis to understand the floor
movement along the linac as a whole.

CONCLUSIONS
A new remote-controllable sensing system in a laserbased alignment system has been developed to measureslow dynamic displacements of the tunnel floor of the
KEKB injector linac in real time. Based on the real-timemeasurements with the new system, we have observed nonnegligible floor displacements due to dynamic ground motion during a nearly six-month period beginning on 7 January 2016.
The cross-correlation analysis on the floor displacements
over the entire length of the linac tunnel was performed
with the same data. Based on the analyses in the time tracesof the displacement vectors, it can be seen that the crosscorrelation functions vary irregularly in the correspondingtime traces. However, the transverse positions of the floor
measured at the remote-controllable QPDs moves coherently on average with each other. Such real-time measurements in dynamic motion of the tunnel floor along the entire length of the linac could help realize the stable operation of the injector linac.

(b)QPD Location [m]QPD Location [m](a)QPD Location [m]QPD Location [m]Figure 5: Intensity distributions of the cross-correlation function among all the QPDs in the displacement vector measurements along the C5 straight section obtained on (a) 15 February 2016 at 0:00 am and (b) 27 February 2016 at 8:00
am. The intensity distribution pattern is linearly encoded by the color scale, where bright yellow (dark blue) represents
R̂0 maximum (minimum) value.

ACKNOWLEDGMENT
The authors would like to thank Prof. K. Furukawa of
Accelerator Laboratory of KEK for his continuous supports on this work. They also thank Mrs. T. Kudou and
Y. Mizukawa of Mitsubishi Electric System & Service Co.,
Ltd., who helped to conduct this work.

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