STRAIGHTNESS ALIGNMENT OF LINAC BY DETECTING SLOPE ANGLE*
T. Kume#, M. Satoh, T. Suwada, K. Furukawa, KEK, 1-1 Oho, Tsukuba, Ibaraki, 305-0801, Japan.
E. Okuyama, Akita University, 1-1 Tegata gakuen-machi, Akita, 010-8502, Japan.
Abstract
Straightness measurement by detecting slope angle[1]was adopted for evaluating the aligning straightness of
the 600-m-long KEK e-/e+ injector linac[2].
Here, slope angles between the centers of thealignment base plates for the 71-m-long part of the linac
could be detected with the standard deviation () of 9
rad by using Talyvel 4, a precise electronic level system.
As a result, the straightness could be evaluated with thestandard deviation of 26 m fairly easily, which is hardlyachieved by conventional methods.
The estimation based on our error propagation modelshows that the straightness evaluation with thereproducibility of 0.6 mm (2) for 500 m, sufficient foraligning the KEK linac, can be achieved.
It also shows that the straightness evaluation with thereproducibility of better than 1 mm (2) for 10 km
expected for the linacs planed in the ILC project[3] canbe achieved.

INTRODUCTION
The 600-m-long KEK e-/e+ injector linac is expected
to be aligned with an accuracy of sub-mm or better in its
mechanical alignment (primary alignment) for its future
upgrade. The linac is composed of a 125-m-long straightsection and a 483-m-long straight section connected witha 180-degree arc section, forming “J” shape. Therefore, itis necessary to evaluate the 483-m-section, the longer
straight section with sufficient accuracy (sub-mm orbetter) in order to align the whole linac. We adoptedstraightness measurement using a level for evaluating thealigning straightness of the two straight sections,estimating that it is hardly achieved by any otherconventional methods.

Figure 1 shows its schematics. Here, the tangential
angles of the straightness (profile) corresponding to thedifferential of the straightness are measured. The
straightness is derived by integrating the measured
angles without affected by the scanning error e(xi), whichcorresponds to the straightness error, as the detected
angles were not affected by the scanning error.
The straightness fm(xn) at position xn is derived asn 1f m  xn   h1  s   xi  (1),i 0where h1, s, (xi) expresses arbitrarily definedstraightness of the start point, measurement interval, andmeasured slope angle at point xi, respectively.

STRAIGHTNESS MEASUREMENTThe KEK linac is composed of 9.6-m-long accelerator
units. Figure 2 shows a typical accelerator unit. In each
unit accelerator components: 2-m-long S-band (2856MHz) accelerator structures, magnets, and beam
monitors, operating directly on particle beams, aremounted on a 9-m-long pipe-girder and magnet girders.
They are mounted on the girders using the alignment
base plates made of stainless steel. Each top of the plates
is used as a vertical position reference, while one side of
the two alignment rails mounted on the plates is used as ahorizontal position reference. They are aligned with thetolerance of ±0.05 mm for each unit prior to theinstallation.
We evaluated the vertical aligning straightness of the38 base plates for the 71-m beginning part of the 483-m
straight section. It follows that the average measurement
interval was 1.9 m. The slope angles for between theneighboring base plates were measured sequentially witha precise electronic level system, Talyvel 4 (TaylorHobson), having ±600 sec of measurement range and 0.1

Figure 1: Straightness measurement using a level.
___________________________________________*Work supported by KEK#tatsuya.kume@kek.jp

Figure 2: Side view of the typical accelerator unit.

sec of resolution.
Straight bars put on between the centers of the plates
were adopted for ensuring the continuity of thestraightness between the discretely-aligned plates. Pairsof contact feet were also adopted under both ends of thebars for preventing distortions of the plates affecting themeasurements. They are used as shown in figure 3.

4. Here, the real angle to be detected r is obtained
without affected by the systematic error 0 as

r m  n(2),2where m and n expresses the measured angle for before
and after the reversal measurement. They are expressedas m=r+0 and n=r-0, respectively.
Slope angle [mrad]

2

1st
3rd

2nd
4th

50,00060,00070,00050,00060,00070,00010-1-2-30

10,00020,00030,00040,000

Position [mm]Figure 3: Straightness measurement using a level withstraight bars and pairs of contact feet.
Standard deviation [mrad]

0.04
0.03
0.02
0.01
00

10,00020,00030,00040,000

Position [mm](b)
Figure 5 (a): Slope angles anddeviations(b): their standard

4,000
Straightness [m]

We used three kinds of straight bars considering
periods and obstacles between the neighboring plates.
They are made of aluminum alloy. Two of them were 25mm-thick, and 50-mm-wide rectangular-pipes with thepipe-thickness of 3 mm and the lengths of 1998 mm and2306 mm, respectively. They were used with a pair ofgrass plates (optical parallels) with 2-mm-thick, 50-mmwide, 50-mm-long, having flatness of better than =633
nm as their contact feet. The other was a 25-mm-thick,and 50-mm-wide solid-bar with the length of 1640 mm.
It was used with a pair of machined aluminum-cuboidblock with 50-mm-thick, 50-mm-wide, and 160-mmlong as its contact feet.

(a)
0.05

1st
3rd

2nd
4th

50,00060,00070,00050,00060,00070,000

3,000
2,000
1,000
0-1,000-2,0000

10,00020,00030,000

40,000

Position [mm](a)Figure 4: Reversal measurement of the level with astraight bar and a pair of contact feet.
It is important to eliminate systematic errors in themeasurements as they introduce large systematic error in
the derived straightness through integration (cf. Eq. (1)).
We eliminate the systematic error in the measurements
caused by offset of the level, distortions of the straightbars and height differences between the each pair ofcontact feet by reversal measurement as shown in figureStandard deviation [m]6050403020100010,00020,000

30,00040,000

Position [mm](b)Figure 6 (a): Straightness and (b): their standarddeviations.

DISCUSSION
Figure 7 shows accuracies for the straightness as afunction of measurement distance. It shows those of theachieved by filled circles with those of the conventional
methods, in which TOF expresses for the systems basedon the time of flight of the measurement light, such as
the total station and GPS expresses for the global
positioning system. It expresses that the straightness with
better accuracy than those for the TOF and GPS could be
evaluated at longer measurement distance than those forthe straight edge or interferometer, which can hardly
achieved by these conventional methods.
Assuming that error in each measurement which is theerror in each (xi) for equation (1) is random and that it
propagates to the error in derived straightness fm(xn) as
error propagating rule, the error p in the derived
straightness can be estimated as p  s  l   ma(3),where s, l, ma expresses measurement interval,
measurement distance, and error in each measurement,
respectively.
Figure 7 also shows those for the estimated usingequation (3) with ma=9 rad, that is the average
standard deviation obtained. They are for the two
measurement intervals, s=1.9 m (open circles) and 20 cm(triangles), respectively. The achieved is approximately
one third of the estimated for s=1.9 m. The reason has
not yet resolved; however, the tendency that the achieved
is better than the estimated is not a problem in practicalusage, considering it as a safety margin.

As shown in figure 7, the straightness evaluation withthe reproducibility of 0.6 mm (2) for 500 m, which is
sufficient for aligning the KEK linac, can be achieved,
using a measurement interval of 1.9 m. It also shows thatthe straightness evaluation with the reproducibility ofbetter than 1 mm (2) for 10 km, which is expected foraligning the 10-km-long linacs planned in the ILC
project, can be achieved, using a measurement interval of
20 cm.
100,000

Straight edge
Interferometer

Accuracy [m] (Definitions /2)As a result, slope angles between the neighboring baseplates could be obtained with the standard deviations of 9rad (average) and 42 rad (maximum), respectively.
Figure 5 (a) expresses angles derived from the reversal
measurements using the equation (2) and figure 5 (b)expresses their standard deviations. They are for the fourtimes of the repeat measurements during successive threedays. It took 2 to 4 hours for each measurement. The
temperature of each accelerator component is controlled
to be 30±0.1 deg by water cooling system. The room
temperature is also controlled to be around 23 deg. They
prevent the linac distorted by temperature fluctuations ordistributions.
The aligning straightnesses of the base plates areshown in figure 6 (a). They are derived from themeasurements shown in figure 5 using equation (1).
They are normalized by their least square approximationlines. They agree well with those measured by standard
telescope-based alignment technique. Figure 6 (b) shows
the standard deviations of the derived straightness. Theyare 26 m (average) and 50 m (maximum), respectively.

TOF

10,000GPS
Achieved(s=1.9m)
Estimated(s=1.9 m)
Estimated(s=20 cm)

1,000

100

101
1

10100

1,000

10,000Measurement distance [m]Figure 7: Accuracy in straightness as a function of themeasurement distance.

CONCLUSIONStraightness measurement by detecting slope angle
was adopted for evaluating the aligning straightness of
the 600-m-long KEK e-/e+ injector linac.
As a result, slope angles with the average standard
deviation of 9 rad could be detected and consequently
straightnesses with the average standard deviation of 26
m could be obtained for the 71-m-long part of the linac.
Error estimation shows that straightness evaluations
sufficient for aligning the KEK linac, and expected foraligning the linacs planned in the ILC project can beachieved with this technique.

ACKNOWLEDGEMENT
Authors thank Yukinori Kobayashi and members of
the Accelerator Division 7 in Accelerator Laboratory in
KEK and Masahiro Katoh of Institute of Molecular
Science for providing us Talyvel 4.

REFERENCES[1] T. Kume, et al., “Long Distance Straightness
Alignment Based on Software Datum,” Proceedingsof Particle Accelerator Society Meeting 2009, 118120 (in Japanese)[2] I. Abe et al., “The KEKB injector linac”, Nucl. Instr.
and Meth. A 499, (2003) 167.
[3] http://www.linear-collider.org.