REFINEMENT OF ARC ALIGNMENT BETWEEN TWO STRAIGHTSECTIONS FOR INJECTOR LINAC OF SUPERKEKB
M. Tanaka∗ , T. Kamitani, K. Kakihara, and T. Higo, KEK, Tsukuba, JapanK. Kimura, K. Suzuki, N. Toyotomi, and S. Ushimoto,
Mitsubishi Electric System & Service CO., LTD, Tsukuba, Japan
Abstract
The beam line of the KEKB injector linac is under realignment as the restoration after the big Earthquake in2011, but with the refinement for the SuperKEKB in mind.
The linac consists of two straight sections connected by a180 degree ARC. Precise alignment of the ARC magnets is
one of the key issues for the emittance preservation of theelectron beam. The ARC beam line was defined by measuring these two straight lines. Then, the misalignment of theARC magnets were reduced from 3 mm maximum down
to 0.1mm in the errors perpendicular to the beam direction.
This paper describes how we defined the ARC beam lineand performed the alignment. The connection method of
the laser tracker data needed for the definition of the ARC
was also studied and described.

INTRODUCTION
The injector linac of KEKB is a 600-m-long linear accelerator consisting of 8 sectors[1]. As shown in Figure1,it comprises of the upstream 1.5 GeV linac with a lengthof 100 m (A, B sector) followed by the downstream 5.5
GeV linac with a length of 500 m (C, 1-5 sector) connected
through a 180 degree ARC with a radius of 7.5 m.
Each sector is about 80 m and comprised of 8 accelerator
units. In each unit the hard wares such as the accelerator
tubes are set on a rigid girder of 9 m in length. The axis 420
mm down from and parallel to the beam axis is used for thealignment and defined by a laser beam whose position ismeasured by the segmented photo-diode (PD) detector[2]attached to the reference point located at each end of thegirder.
For the emittance preservation in the injector linac ofSuperKEKB[4], the local misalignment at the straight section is required to be within 0.1 mm in sigma, while global
one with 0.3 mm in sigma[5]. On the other hand, the ARC
magnets are set on the independent support structures andaligned independently. In order to suppress the emittance
growth due to the perturbation given from the ARC misalignment, the magnet alignment is required to be within
0.1 mm. Since the misalignment of the ARC became up to3 mm in maximum after the big Earthquake, the realignment is needed. The ARC configuration can be the same as
KEKB but the refinement of the alignment is required[3].
We decided to re-define the ARC orbit design to minimize
the hardware movement by taking the mutual relation between two straight sections into account. From the measurement we noticed that the bending angle was not 180∗ madoka.tanaka@kek.jp

degrees so that we adopted this value for the new orbit design. On the other hand, the ARC was originally set in thehorizontal plane but this time we defined the plane in thesame as that of the two straight sections to get rid of thevertical kicks at the input and output of the ARC. Though
the optical telescope was used to align the hard wares in
the KEKB construction time, it became possible this timeto align the hard wares more accurately and easily by usinga laser tracker, AT401 of Leica[6]. In order to measure withthe accuracy of several µrad and several µm for the alignment measurement of the ARC with its size of 15 m, thelaser tracker we introduced this time was appropriate since
the typical errors are ±7.5 µm + 3 µm/m in angle, and ±5µm in length.
The measurement extending to 100 m distance is required for evaluation of the two straight sections. Though
the tracker measurable span is ±80 m, we thought that thealignment measurement with connecting the ±10 m-spanmeasurements shown in Fugure2 was better to get the 100
m-size information when considering the big errors coming from the environmental perturbations. To utilize thismethod, the tool to connect many short-span data to integrate into a long-span measurement became important. We
have developed a method to accurately estimate with smallerrors by evaluating the actual measured data. This process
is also described.
Following above strategy, we made the alignment of
all ARC magnets, 6 bending magnets (BM),????? 13
quadrupole magnets (QM), and 5 sextupole magnets (SM).
In order to use the tracker reflectors, the reflector holder
bases were set on the floor, the wall, and at the arm end
extending form laser PD. For magnets, three holder bases
were on BM, while two on QM and one on SM.

Figure 1: The outline drawing of injector linac.

DEFINITION OF ARC REFERENCE
ORBIT
Before aligning the ARC, we measured B sector, ARC,
and C sector with the laser tracker in June, 2013(Figure 2)
and determined the two straight lines.

Figure 2: Measurements using a laser tracker. Blue boxes
are accelerator units, red circles are tracker reflectors onPD, yellow ones reflectors on wall. Green squares are locations where laser tracker is set.

Figure 3: A is plane view, while B is the view seen fromthe side. The green line is A to B sector, while the blueline is C to 5 sector. Dotted lines are for KEKB while solidlines for SuperKEKB.

Definition of Rotation PlaneFirstly, the distance between the two straight sections atthe ARC, i.e. the distance between the inlet point and theoutlet point of the ARC, was measured to be 15 m + d =15013 mm. The design value was 15 m but we defined thenew design distance to be that with this extra ”d”.
Secondly, the angle between the two straight lines wasmeasured so that the rotation angle along the ARC was set
at this value, instead of the previous design value of 180 degrees. The measured angle offset was α=+0.114 mrad. Inaddition, the upstream linac section, sector A-B, was measured and found to be tangential to the ARC at the inlet
point. In order to make the configuration of the two straightlines and ARC to be mirror symmetric with respect to thecenter line between two straight sections, the ARC was rotated by α/2 as shown in Figure3-A.
As for the deflection angles of 6 BMs, those of the 2nd,3rd, 4th, and 5th were set at 30 degrees, while those of the
1st and 6th at 30 degrees +α/2.

Therefore, the error vector in this direction stayed large.
When performing a survey of the ARC section after finishing all of the alignment work, a displacement larger than
0.1 mm was detected. We found that the measurement coordinate system of the laser tracker was rotated by 0.3-0.5
mm / 8 m in the horizontal plane during a day. Because thebeam commissioning had started just after this alignment,
we have not fixed this deviation yet. As described in thenext section, it should be possible to keep the angular parameters more accurately and we are planning perform thealignment again in future.

1[mm]Before

The center of J-arc

After0.5

Design0-0.5-1Definition of Vertical Plane
Since the longer (downstream) one of the two straightsections connects the beginning of the C sector to the endof the 5th sector, the original ARC plane set at horizontal
for KEKB in inclined with respect to the straight section.
As shown in Figure3-B, the angle γ amounted to be 0.0498
mrad. As the third definition, the inclination angle of theARC with respect to the horizontal plane was set at thisvalue. Accordingly, it became necessary to largely movethe magnets upward. Furthermore, there was found a difference of about 1 mm in height between the two straightsections, and at the ARC. Then, we have defined the heightof the start and end points of the ARC to be the same as theconnection point to the A-B sector.

Magnet alignment
After defining the magnet positions, the adjustment wasperformed with frequently tracking the position by using alaser tracker. The refinement result is shown in Figure 4
for the vertical direction. Deviations from the design value
were mostly within 0.1 mm for the directions perpendicular to the beam line. Figure 5 shows the difference in thehorizontal plane. For QM outside the ARC in Figure 5,
we have not adjusted in the direction along the beam line.

-1.5-2The inlet of J-arc
π/2

The outlet of J-arc
3π/2π

[rad]

Figure 4: Measured height of magnets. Red + are beforealignment work, while blue + are after work. Blue line
shows design value and gray boxes are position of BMs.

[mm]

[mm]

8000

8000

6000

6000

4000

4000

2000

2000

01 mm0-2000-2000-4000

-4000

-6000

1 mm-6000-8000-8000 -6000 -4000 -20000-8000
2000 4000 6000 8000 [mm]-8000 -6000 -4000 -2000[A] Before.

02000 4000 6000 8000 [mm][B] After.

Figure 5: Magnet positions in ARC plane. A is before
realignment, while B is after. Vectors are differences between magnet positions and design values. Gray boxes
show BMs.

CONNECTION METHOD OF TRACKER
MEASUREMENTS
To combine the short-span laser tracker data into a common coordinate system, we have used the following threemethods for evaluating coordinate transformation matricesof two measurements of adjacent tracker locations.

Method 0
For a preliminary determination of the angle parameters
α and γ for the ARC magnet realignment, we used the software, ”Polyworks v12”[7] by InnovMetric Software Inc.,
recommended by LEICA for the data connection. Nevertheless, accuracy of the calculate positions of the datapoints were not clear. Hence, we have developed the following two methods and compared the results.

Method IFirst, a set of four points are selected out of the common points from measurements at locations 1 and those at
2 to calculate the coordinate transformation. The matrix M
is defined as a homogeneous coordinate transformation of
12 parameters, including linear transformation for the XYZ
coordinate system and parallel translation. We can obtainthe matrix M by solving the linear equation as shown below by requiring that the four points overlap.
B = MA(1))T( ′)T
A= x y z 1, B = x y′ z′ 1
Here A is the homogeneous coordinate value of the common point at the location 1, while B is those at the location
2. All the possible combinations are calculated and we cite
the matrix which gives the smallest sum of squares of theresidual for all the points other than the four point.
(Method IIThe transformation matrix M is the same as the method
I. However, we calculate the χ2 value of the data from allof the common points as shown below.
χ2 =n∑(B − MA) ,(2)i=1where n is the number of common points. We obtain theM by minimizing this.

Connection Result
We applied these three methods to the laser tracker data,
determined the orientations of the two straight sections andevaluated the angle parameters α and γ. The method 0,I, II gave slightly different values ranging as α=0.11-0.16
and γ=0.050-0.086. Here, we could not have any confident
criteria which result to cite. Then, in order to check theaccuracy of the coordinate transformation in the method
above, we measured again wider region from A-B sector
to C-1-2 sector through ARC. Note that in this measurement region, there was included a straight line connecting

a point at sector 1 to another point at sector A (30◦ line inFigure1). Then a closed loop is formed, so that the deviation of the end point from the start point, actually the samepoint, indicates the degree of error in doing connection ofmany data. A deviation of 6 mm was obtained in the horizontal direction by the method I, while that of the method
II within 1.5 mm, smaller than the former but still remains
big. Thus, we could not get any confidence at this stage
and we concluded that the measurement method and theconnection method to calculate the transformation matrix
should further be improved.

SUMMARY AND PERSPECTIVE
For the upgrade to SuperKEKB, the misalignment of thebeam line components in the straight lines of the injector
linac are required to be locally within 0.1 mm in sigma. Inturn, the magnets of ARC are required to set within 0.1mm
and the laser-tracker based present method can meet the requirement. For doing this alignment, the ARC design orbit
was determined by measuring two straight sections of thelinac and trying to define the ARC plane and bending angle to be close to the present situation. Because we could
not solve a problem when using the laser tracker for a longtime, we will realign the ARC in the future especially thelocation of the large errors. Furthermore, it is necessary toobtain the better tool to connect the accurately measured
data to estimate the alignment along long straight lines.
Aiming to this accuracy improvement, we started the development of the data processing system. A transformation
system by taking the minimum χ2 value gave us a better
result but we think that the tracker measurement method
and the calculation of the transformation matrix should beimproved.

REFERENCES[1] I. Sato et al., “KEK Report 95-18”, National laboratory forhigh energy physics, March, 1996.
[2] T. Suwada et al., “Propagation and stability characteristics
of a 500-m-long laser-based fiducial line for high-precisionalignment of long-distance linear accelerators,” Rev. Sci. Instrum. 84, 093302 (2013).
[3] T. Higo, “Linac alignment”, ICFA Mini-WorkshoponCommisioningofSuperKEKB
ande+/eColliders,
KEK,
Tsukuba,November,2013,
http://kds.kek.jp/confRegistrationFormDisplay.
py?onfId=12760[4] K. Furukawa et al., “High-Intensity and Low-Emittance
Upgrade of 7-GeV Injector Linac Towards SuperKEKB”,TUPME010, IPAC2013, Shanghai, China, May, 2013.
[5] M. Satoh, “Injector commissioning”, The 19th KEKB Accelerator Review Committee, KEK, Tsukuba, March, 2014,
http://www-kekb.kek.jp/MAC/2014/[6] Leica 401AT website: http://www.prismarit.fi/user
Data/prismarit-oy-voima-f1311c/Leica-AbsoluteTracker-AT401 en.pdf[7] Polyworks v12 website: http://www.dirdim.com/pdfs/
DDI PolyWorks New Features.pdf