Experimental Study of New Laser-Based Alignment System at ... - KEK

KEK Preprint 2010-12
May 2010
A
Experimental Study of New Laser-Based Alignment
System at the KEKB Injector Linac
Tsuyoshi Suwada, Masanori Satoh and Eiichi Kadokura
Accelerator Laboratory, High Energy Accelerator Research Organization (KEK)
1-1 Oho, Tsukuba, Ibaraki 305-0801, Japan
Submitted to Review of Scientific Instruments
High Energy Accelerator Research Organization

High Energy Accelerator Research Organization (KEK), 2010
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Experimental study of new laser-based alignment system
at the KEKB injector linac
T. Suwada, ∗ M. Satoh, and E. Kadokura
Accelerator Laboratory, High Energy Accelerator Research Organization (KEK),
1-1 Oho, Tsukuba, Ibaraki 305-0801, Japan
(Dated: May 21, 2010)
Abstract
A new laser-based alignment system for the precise alignment of accelerator components along
an ideal straight line at the KEKB injector linac is under development. This system is strongly
required in the next generation of B-factories for the stable acceleration of high-brightness electron
and positron beams with high bunch charges and also for maintaining the stability of injection
beams with high quality. A new laser optics for the generation of so-called Airy beam has been
developed for the laser-based alignment system. The laser propagation characteristics both in
vacuum and at atmospheric pressure have been systematically investigated in an 82-m-long straight
section of the injector linac. The laser-based alignment measurements based on the new laser optics
have been carried out with a measurement resolution of ±0.1 mm level by using an existing laser
detection electronics. The horizontal and vertical displacements from a reference laser line measured
using this system are in good agreement with those measured using the standard telescope-based
optical alignment technique. In this report, we describe the experimental study in detail along
with the basic design of and the recent developments in the new laser-based alignment system.
PACS numbers: 29.20.Ej, 42.62.Eh, 06.60.Sx, 42.60.-v, 42.60.Jf
∗ Electronic address: tsuyoshi.suwada@kek.jp.
1

I. INTRODUCTION
A precise alignment of accelerator components along an ideal straight line is essential for
constructing long-distance linear accelerators (linacs) because it enhances the beam quality,
and increases the stability of charged-particle beams during acceleration and transportation,
and, more importantly, maintains a high injection efficiency in storage rings in case of injector
linacs.
The KEK B-Factory (KEKB) project [1] is in progress for testing CP violation in the
decay of B mesons at KEK. The KEKB is an asymmetric electron-positron collider com-
prising 3.5-GeV positron and 8-GeV electron rings. Since KEKB is a factory machine, a
well-controlled operation and a precise alignment of the injector linac is required to maintain
the injection rate, stability of the beam collision, and peak luminosity as high as possible.
An optical alignment system with a high-precision telescope is generally used for relatively
short-distance (lesser than 100 m) linacs; however, alignment measurements with a resolution
of ±0.1 mm cannot be easily performed for long-distance (greater than 100 m) linacs. A
laser-based alignment technique is advantageous as it can not only be applied to alignment
measurements for long-distance linacs but it can also be used for regular monitoring of
straightness of the linac without any interruption during a linac operation.
Although the original laser-based alignment system was constructed for use in the elec-
tron/positron injector linac at KEK more than thirty years ago, this system was only par-
tially developed for the energy upgrade of the KEKB project in 1995 [2]. In this upgrade,
the total length of the injector linac was extended from 400 m up to 600 m. Alignment
measurements of the beam line were actively conducted until 1998; however, since then, no
measurements have been conducted owing to the difficulty in tuning of the optical system
that is required for an adequate control of the quality of a laser beam.
Research and development (R&D) studies for the reconstruction of the alignment system
in the next generation of B-factories commenced in 2009. One of the aims of these studies
is the development of a new alignment system for the Super B-factory project [3]. In these
studies, the laser-based alignment system was reconsidered and we have been proceeding
with experimental studies of the new laser-based alignment system. In particular, we are
developing a new laser source with an optical system for the stable propagation of lasers with
axially symmetric Airy beams that can be generated using two adjacently aligned circular
2

the beam energy is 1.7 GeV. The 8-GeV electron and 3.5-GeV positron beams are directly
injected into the KEKB rings through each beam transport line.
A typical sector is 76.8 m long and comprises eight accelerator units, each having a length
of 9.6 m. The accelerator unit structure is shown in Fig. 2. In a typical accelerator unit, an
(a)
(b)
(c)
Beam
Laser
Beam height
1200
Laser height
780
Plate springs
Guide rails
Cross-roller bearings
Jack bolts
9600
Guide rails
Accelerating structures Accelerating structures
L-shaped plate
Accelerator girder
Plate springs
FIG. 2: Mechanical drawings of the accelerator unit, (a) top view, (b) front view, and (c) side
view. The length is indicated in millimeters.
8.44-m-long accelerator girder is installed on the floor level in the accelerator tunnel; four 2-
m-long S-band accelerating structures are mounted on this girder. Quadrupole magnets for
beam focusing are installed on special magnet girders between two adjacent accelerator units.
The accelerator girder is composed of a stainless-steel, earthquake-resistant cylindrical tube
(outer diameter: 508 mm) with L-shaped plates attached to both ends of this cylindrical
tube; this girder supports the entire weight of the accelerator unit. The four accelerating
structures are mounted on five separate stainless-steel plates fixed on the accelerator girder
and are aligned within a standard mechanical precision (±50 µm) by reference guide rails
fixed on the plates.
The electron and positron beams pass through the center holes of the accelerating struc-
tures mounted 1.2 m above the floor level. A cylindrical laser pipe made of stainless steel
4

(inner diameter: 115 mm) is welded to the upper inner surface of the girder tube. Such a
coaxial structure was originally designed in order to reduce convective air flow caused by
any temperature variation and fluctuation in the accelerator tunnel. A laser beam passes
through the center of the laser pipe installed 780 mm above the floor level.
B. Alignment system overview
Two independent laser-based alignment systems have been installed in the injector linac.
One is for the alignment of the accelerator components in sectors A and B. A laser source
with a He-Ne laser has been installed below the A1 electron gun. The other alignment
system is for the alignment from sector C up to the end of sector 5. In this experiment, a
new laser source with a laser diode has been developed for the latter long straight section.
The laser source has been installed 16 m upstream from unit C-1 of sector C (see Fig. 1).
The optical system is mounted on a standard optical table in an atmospheric environment,
while the laser pipes are evacuated with a vacuum pump.
A holder is connected to both ends of the accelerator girder through a vacuum flange; a
silicon photodiode (PD) is mounted at the center of the holder. A vacuum level up to the
order of 1 Pa can be attained in the laser pipe . The inner surface of the laser pipe is coated
with a black paint composed of acrylic resin in order to prevent any unnecessary reflections
and scatterings of the laser beams. Fifty eight accelerator units, with both regular and
irregular lengths, are distributed along the section from sector C up to the end of sector 5;
these units are aligned along the ideal straight line of the laser beam. The propagation orbit
of the laser beam should be tuned in order to create as precise a straight line as possible
without any diffractions and instabilities.
The alignment measurements of the accelerator units are carried out at the locations of
the PDs. Each PD can be manually inserted into the center of the laser pipe by means of a
hinge structure in the holder. The horizontal and vertical spatial displacements of both the
ends of the accelerator unit can be determined by analyzing signal readouts from a standard
four-segmented PD that measures the intensity centroids of the laser beam. Such a series of
measurement procedures for the accelerator units provides an accurate view of the alignment
in the case of long-distance linacs.
The mechanical displacements of the accelerator unit in both vertical and horizontal
5

directions can be corrected using mechanical jigs attached to the accelerator unit (see Fig. 2).
The accelerator unit can be mechanically displaced in the vertical direction using two jack
bolts attached to each end of the accelerator unit. The straightness of the accelerator unit
can be corrected in the horizontal direction by mechanically pushing (or pulling) a plate
spring using a screw bolt. The plate springs are attached to both the sides of the girder
tube and also to the L-shaped plates. The accelerator unit can be smoothly slid in the
horizontal direction using precise cross-roller bearings fixed on the accelerator unit.
C. Laser source and the optical system
Owing to the increase in the beam charges and energies of the injector linac, it is difficult
to avoid radiation damage to a laser source if it is installed on the floor level of the accelerator
tunnel. However this damage can be avoided in a laser transmission scheme in which the
laser source is installed in an upstairs klystron gallery and the laser beam is transmitted
through an optical fiber cable with a low attenuation loss.
A He-Ne laser is one of the well-known stable lasers that are applicable to long-distance
alignment techniques; however, coupling this laser to an optical fiber is not easy owing to the
uncontrollable deformation of the laser tube that occurs due to the temperature variations
during the operation. It is relatively easy to couple a laser diode to an optical fiber; this
engineering technique is used in various industries.
In this experiment, we developed a laser source with a laser diode (Mitsubishi Electric,
ML101J27 [6]) coupled to an optical fiber. The laser beam is focused on the cross-sectional
area of a single-mode optical fiber (diameter: 3.5 µm) through an aspheric lens (diameter:
4.7 mm). The effective focal length of the aspheric lens is 2.95 mm. The maximum output
power (CW) of the laser diode with a wavelength of 660 nm is 120 mW. In such a coupling
scheme, the transmission efficiency of the laser beam has been approximately 20%. The
laser beam is transmitted to an optical system, which delivers it after expanding it to the
suitable beam sizes required for the alignment measurement.
The laser diode delivers a laser beam with a power of ∼108 mW; laser beam is transmitted
to an optical system connected to a 1.5-m-long single-mode optical fiber. The complete
mechanical drawing of the optical system is shown in Fig. 3 (a).
The optical system comprises a spherical reflective mirror and a plane mirror that can be
6

(a)
162
(b)
Optical fiber
2
6
Plane mirror
85.66
ÿ90
3.0
Optical fiber
Reflective mirror
Laser beam
152.4
340
162
Reflective surface of the plane mirror
1st circular aperture slit
3 3
101.94
Laser beam
2nd circular aperture slit
FIG. 3: Optical system with two reflective mirrors. (a) Mechanical drawing of the optical system
and (b) the enlarged schematic drawing (not scaled) of the central portion of the plane mirror.
The length is indicated in millimeters.
coupled with an optical fiber cable. The spherical reflective mirror is aluminum-coated and
has a diameter of 152.4 mm, a wavefront aberration of λ/4, and an effective focal length of
152.4 mm. The plane mirror is composed of quartz and has a thickness of 6 mm and diameter
of 90 mm. Dielectric multilayers with a thickness of 2 µm are evaporated in vacuum on the
reflection surface of this plane mirror. Its reflectance is greater than 99.5% at λ = 660 nm
and its wavefront aberration is λ/2. The plane mirror has a circular aperture (diameter:
1 mm) for the laser beam injection and is inclined by 45 ◦ with respect to the laser axis.
Figure 3 (b) shows the enlarged schematic drawing of the central portion of the plane
mirror. The laser beam is injected into the optical system after being delivered from a 50-cm-
long single-mode optical fiber, which is connected to the 1.5-m-long optical fiber by means of
7

a fiber connector. The laser beam is ejected from the fiber end with a numerical aperture of
0.1 and is transmitted through the first circular aperture slit (diameter: 10 µm) fixed 0.1 mm
behind the end of the optical fiber. Such optical configurations transform the laser beam
into a beam with the well-known Airy patterns. The laser beam is completely diffracted,
and thus, it has the center spot (Airy disc) with causing diffraction fringes. The second
circular aperture slit may generate a so-called Airy beam without any diffraction fringes
because this slit truncates such fringes and retains the central Airy disc. The generation
and propagation characteristics of Airy beams are described in detail elsewhere [4]. This
Airy beam is then transmitted to the spherical reflective mirror, which suitably expands
the beam sizes in accordance with the alignment measurements; these expanded beams are
reflected to the plane mirror. The beam sizes are determined on the basis of the transmission
distance between the centers of the spherical and plane mirrors under the condition of the
fixed focal length of the spherical mirror. The laser beam is reflected by the plane mirror,
and this collimated laser beam is delivered to the central positions of the laser pipe. The
laser power at the plane mirror is ∼1 mW while the laser power injected into the optical
system is ∼14 mW. The total transmission efficiency of the laser power is obtained to be
∼1%.
The injection angles and positions with respect to the laser axis can be adjusted using
a four-axis precision stage on which the optical system is mounted. The injection positions
are adjusted using horizontal (x) and vertical (y) linear stages with one-step resolutions of
1 µm and 0.05 µm, respectively. The injection angles are adjusted along the elevation (θ)-
and azimuthal (φ)-angular directions with one-step resolution of 0.23 µrad and 0.35 µrad,
respectively, using rotational linear stages.
D. Detection electronics
The horizontal and vertical spatial displacements of the accelerator unit perpendicular to
the laser line are measured using a standard four-segmented PD. The PD with a diameter of
10 mm and a sensitivity of 0.43 mA/mW at λ = 660 nm (OSI Optoelectronics, Model SPOT-
9D [7]) outputs a photocurrent signal from each photocell. The signal intensity depends on
the spatial displacements of the accelerator unit. The photocurrent signals are sent to a
detector for measuring the two-dimensional intensity centroids of the laser beam. A block
8

constant as T = 1 sec (slow) or T = 0.1 sec (fast) with a selectable switch. The integrating
amplifier has a selectable switch (G = 1 in low gain and G = 5 in high gain). The voltages
Vx and Vy are output to monitor ports terminated with a 100 Ω resistor.
Figure 5 (a) shows a typical result of the input-output characteristics of a PD depending
on the laser intensity in the case of a He-Ne laser with a spot size of 2 mm. In this test,
(a)
25
20
15
10
Output [V]
5
PD Cell #1
Linear fit
0
0 1 2 3 4 5 6 7 8
Laser Power [mW]
(b)
x [V]
V
10
5
0
-5
Experimental data
Calculation
-10
0 2 4 6 8 10
V2 [V]
FIG. 5: Typical characteristics of the detection electronics. (a) Input-output characteristics as a
function of the laser power, and (b) output voltage (Vx) as a function of the input test voltage V2.
the laser beam is illuminated at the center of the PD, and the voltage signals are measured
at the monitor ports of the detector. According to the results, the dependence of input-
output characteristics on the laser-intensity shows good linearity up to ∼4.5 mW, where the
nonlinearity has been measured to be ∼3%. Considering the maximum nonlinearity (0.5%)
of the detection electronics and the laser intensity measurement error (2%), the nonlinearity
of the PD has been estimated to be less than 0.5%. The maximum nonlinearity of the
detector system including the PD response is estimated to be less than 1%.
Figure 5 (b) shows the dependence of the output voltage Vx on the input test voltage V2
when the test voltages for other channels are kept constant. This result shows a calibration
curve that maps out the voltage signals to the spatial displacements with respect to the laser
axis. The maximum difference from a curve is calculated by Eq. (4) to be 0.5%. Considering
the nonlinearity of the integrator circuit and the accuracy of the analog signal processing,
the accuracy of the detection electronics is observed to have a contribution of ∼1% to the
10

alignment measurement.
III. EXPERIMENTAL SETUP
Laser-based alignment experiments are carried out in sector C of the injector linac. The
total length of the laser propagation is 82 m, while the total length of seven accelerator
units in this beam lines is appoximately 66 m. Figure 6 shows a schematic drawing of the
experimental setup along with the new vacuum system that is under development.
LD
1.5-m-long
optical-fiber cable
Optical system
Laser pipe
C-1 C-2 C-3 C-4 C-5 C-6 C-7
Vacuum port
Vacuum pump
Photodetector
Vacuum gauge
Vacuum window
FIG. 6: Setup of the laser-based alignment experiment.
The temperature in the accelerator tunnel is kept at 23±0.1 ◦ C by air conditioners during
this experiment. Furthermore, the laser source along with the optical system is completely
surrounded by heat reserving material to maintain a stable local temperature and to suppress
unnecessary air flow around the optical system. The laser source is installed along with the
optical system on the same optical table, and a Pertier device is attached to the laser source
unit to stabilize the temperature of the laser diode.
The laser pipes penetrating till the end of unit C-7 are evacuated for stable laser propaga-
tion. The total volume of the laser pipes is 847.2 l. A vacuum port is installed at the center
of the laser pipe between units C-3 and C-4. This vacuum port is connected to an oil-free
scroll pump that has a pumping speed of 1000 l/min. Nine Pirani gauges are distributed
at almost regular intervals up to the end of unit C-7. It is possible to conduct the vacuum
measurements of these gauges in the range of atmospheric pressure to ∼6 × 10 −2 Pa.
An inlet (outlet) vacuum window with a relatively high radiation hardness is used for laser
injection (ejection) from atmosphere (vacuum) to vacuum (atmosphere) with a transmittance
of ∼95% at λ = 660 nm. These windows are composed of synthetic quartz (Shin-Etsu
11
PC
CCD

Quartz, SUPRASIL-P20 [8]). The inlet and outlet windows are 20 mm and 15 mm thick,
respectively.
A commercially available silicon CCD camera (OPHIR, USB L11058 [9]) has been in-
stalled just behind the outlet vacuum window in order to measure laser profiles and to mon-
itor the propagation stabilities. This camera scans a two-dimensional area of 36 × 24 mm 2
and records the beam profiles at a speed of approximately 2 Hz. The profile parameters,
namely, the peak intensity, intensity centroids, beam sizes, etc., are calculated by fitting a
two-dimensional Gaussian function to the intensity distribution, which is implemented in
real time using a Windows-based PC.
IV. EXPERIMENTAL RESULTS
A. Vacuum performance
The vacuum performance in the laser pipe has been measured before investigating the
laser propagation characteristics. Figures 7 (a) and (b) show the results of this measurement.
Figure 7 (a) shows a 2-h time trace of the vacuum pressure at the point between units C-3
(a)
10 4
1000
100
Atmospheric pressure level
Vacuum 10 Pressure [Pa]
C3-C4
1
0:00:00 0:30:00 1:00:00 1:30:00 2:00:00
Time [h]
10 5
10 4
1000
100
Vacuum Pressure [Pa]
10
1
atmosphere
5 min
10 min
20 min
C-1 C-2 C-3 C-4 C-5 C-6 C-7
0 20 40 60 80 100
Distance [m]
FIG. 7: Time traces of the improvement in the vacuum pressure in the laser pipe evacuated from
atmospheric pressure. (a) 2-h time trace of the vacuum pressure improvement, and (b) the time
development of the vacuum pressure measured along sector C. The green squares indicate the
locations of the vacuum gauges with respect to the laser source.
12
(b)
40 min
1 h
2 h
20 h

and C-4. This figure indicates that the vacuum pressure is rapidly reduced from atmospheric
pressure to the vacuum level of 25 Pa in ∼10 min, and is further reduced to 5 Pa in 2 h even
though the pumping speed becomes slow. Similar vacuum characteristics were obtained for
other gauges in this measurement. Figure 7 (b) shows the time development of the vacuum
pressure as a function of the distance from the laser source. The ultimate attainable vacuum
after 20 h is ∼3 Pa; this vacuum level is restricted owing to the critical pumping speed.
B. Characteristics of the laser propagation
After the optical system is properly tuned in terms of the injection angles and positions
with respect to the laser pipe, the laser profiles at the location just behind the end of
unit C-7 are measured both at atmospheric pressure and in vacuum using a CCD camera.
The laser profiles obtained at atmosphere and in vacuum are shown in Figs. 8 (a) and (b),
respectively. The results indicate that the beam sizes are clearly different from each other
(a) (b)
FIG. 8: Laser profiles measured at the end of unit C-7 (a) at atmospheric pressure and (b) in
vacuum.
while the projected distributions of the profiles seem to be Gaussian distributions in both
the horizontal and vertical directions. The beam sizes obtained at atmospheric pressure
are larger than those in vacuum because the laser beam may be refracted according to the
refractive index of air when it passes through the laser pipe at atmospheric pressure.
Figures 9 (a) and (b) show the time traces in the horizontal and vertical intensity cen-
troids, respectively, along with the vacuum pressure measured at the end of unit C-7.
The results show that both the intensity centroids become sufficiently stable at a vacuum
level of less than 1000 Pa. The vertical intensity centroid indicates very unstable behavior
13

(a)
22
21
20
19
18
17
16
15
Vacuum pump ON
Centroid X [mm]
Atmospheric pressure
Valve open
C3-C4 vacuum
Horizontal
14
1
0:00:00 0:02:00 0:04:00 0:06:00 0:08:00 0:10:00
Time [min]
10 4
1000
100
10
16
15
14
13
12
11
10
9
Vacuum pump ON
Centroid Y [mm]
Atmospheric pressure
C3-C4 vacuum
Vertical
8
1
0:00:00 0:02:00 0:04:00 0:06:00 0:08:00 0:10:00
Time [min]
Valve open
FIG. 9: Time traces in (a) the horizontal and (b) vertical centroids of the laser intensity along
with the vacuum level measured at the end of unit C-7.
at the beginning of the evacuation, and the vertical intensity centroid moves by more than
3 mm. These phenomena may occur due to air flow in the vertical direction around the
vacuum port during the evacuation, which, in turn, is due to the fact that the vacuum port
is attached to the laser pipe in the vertical direction.
Figures 10 (a) and (b) show the time traces in the horizontal and vertical beam sizes,
respectively. Here, the beam sizes are defined as a beam width of a four-times standard
(a)
12
11
10
9
8
Horizontal
Vacuum pump ON
Beam Size [mm]
Atomospheric pressure
Valve open
7
0:00:00 0:02:00 0:04:00 0:06:00 0:08:00 0:10:00
Time [min]
Vacuum pressure level
~10 3 [Pa]
(b)
11
10
9
8
7
Vertical
Vacuum pump ON
Beam Size [mm]
10 4
1000
Atomospheric pressure
6
0:00:00 0:02:00 0:04:00 0:06:00 0:08:00 0:10:00
Time [min]
Valve open
Vacuum pressure level
~10 3 [Pa]
FIG. 10: Time traces in (a) the horizontal and (b) vertical beam sizes measured at the end of C-7.
14
(b)
100
10

deviation (4σ) which is derived on the basis of a two-dimensional Gaussian fitting procedure.
The results show that both the beam sizes become sufficiently stable at a vacuum level of
less than 1000 Pa, and that the beam size in vacuum varies in the horizontal and vertical
directions by ∼0.5 mm and ∼0.2 mm, respectively, in comparison with that at atmospheric
pressure.
Figures 11 (a) and (b) show the time traces of the stabilities in the horizontal beam
position and beam size, respectively, in the vacuum pressure of 3 Pa, for 4 h.
(a)
18
17
16
Centroid X [mm]
15
Horizontal
ΔCX ~ 0.4 mm
14
0:00:00 1:00:00 2:00:00 3:00:00 4:00:00
Time [h]
in vacuum
(b)
9
8
Beam Size 7 [mm]
Horizontal
ΔW ~ 0.3 mm
x
6
0:00:00 1:00:00 2:00:00 3:00:00 4:00:00
Time [h]
in vacuum
FIG. 11: 4-h time traces of the stabilities in (a) the horizontal beam position and (b) beam size
measured at the end of unit C-7.
The results show that for 4 h, the peak-to-peak stabilities in the horizontal position
and beam size are ∼0.4 mm and ∼0.3 mm, respectively, while for one standard deviation,
these stabilities are 0.1 mm and 0.06 mm, respectively. Similar stabilities are obtained in
the vertical direction, and there are no differences in the stability measurements both at
atmospheric pressure and in vacuum. On the other hand, in front of the laser source, the
peak-to-peak position stability is measured to be less than 10 µm without any variations in
the beam sizes. If the peak-to-peak position stability is transformed to the angular stability
of the laser source, this peak-to-peak angular stability is observed to be ∼5 µrad. This
angular stability is not very small and may be due to the local convective air flow, which in
turn, might be caused by temperature variation and fluctuation at the location of the optical
system. Although this slight air flow is acceptable in the current experiment, it should be
reduced in order to carry out further experiments.
15

C. Beam-size measurements
The laser beam sizes should be measured at each PD location with respect to the laser
source because the position sensitivity of the PD strongly depends on the beam sizes. The
beam sizes have been measured along the beam line at intervals of 20 m from the laser source
at atmospheric pressure. They have been also measured at the end of unit C-7 in vacuum.
Figure 12 shows the variations in the horizontal and vertical beam sizes as a function of
the distance from the laser source. In Fig. 12, the analyzed beam sizes are simultaneously
30
25
20
15
Beam 10 Size [mm]
5
0
Horizontal
Vertical
Horizontal analyzed
Vertical analyzed
C-1 C-2 C-3 C-4 C-5 C-6 C-7
0 20 40 60 80 100
Distance [m]
FIG. 12: Variations in the horizontal and vertical beam sizes as a function of the distance from
the laser source. The plotting of the analyzed beam sizes obtained in the calibration procedure is
shown with the up and down triangles.
plotted; these beam sizes have been obtained in the calibration procedure (described later)
in vacuum with a movable PD installed at the location in front of unit C-1. The beam
sizes at atmospheric pressure have been calibrated to those in vacuum by normalizing them
using the beam sizes measured at the end of unit C-7 and those obtained at the calibration
procedure in vacuum.
The laser optics is tuned in such a way that the laser beam is focused from the optical
system down to a waist point and then symmetrically expanded over a distance of 120 m.
The obtained results are analyzed on the basis of a least-squares fitting procedure with
16

well-known Gaussian laser optics [10] as
√ (
z −
)
z0
2
ω = ω0 1 + , (6)
where ω is the beam size at each location depending on the distance (z) from the laser
source; ω0 the beam size at the waist point (z = z0); and zR, the Rayleigh length. The
results show that at the waist points that are are 53.7 m and 62.0 m away from the laser
source, the horizontal and vertical beam sizes are 2.9 mm and 3.1 mm, respectively. The
Rayleigh lengths in the horizontal and vertical directions are 9.8 m and 11.5 m, respectively.
It can be observed that the variations in the beam sizes along the beam line are slightly
asymmetric in the horizontal and vertical directions. This may be owing to the insufficient
angular tuning of the spherical mirror. However, the observed values are in good agreement
with those obtained by numerical analyses. More detailed analyses in the laser optics will
be reported elsewhere [11].
D. Calibration procedure of the PD
The PD should be calibrated in order to investigate the relationship between the laser
positions and the readouts of the detector. The calibration procedure is performed with a
mechanically movable PD installed in front of unit C-1. The calibration can be performed by
moving the PD in both horizontal and vertical directions with a step length of 0.5 mm over
the ranges of ±3 mm while keeping the laser beam fixed. The horizontal (Vx) and vertical
(Vy) voltages are measured by averaging the data 100 times with an oscilloscope at each PD
position. Figures 13 (a) and (b) show the typical calibration results as a function of the
horizontal position with respect to the laser axis in two-dimensional and three-dimensional
spaces, respectively.
As shown in Fig. 13 (b), both the horizontal and vertical outputs in the detector readouts
show a good linear relationship with the corresponding horizontal and vertical position of
the movable PD within the measurement range. In addition, the vertical depends on the
horizontal position slightly. This phenomena may be due to the inclination of the laser
beam with respect to the laser axis, which may be owing to the slightly different optics in
the horizontal and vertical laser propagations. The sensitivities of the PD with a low-gain
mode in the horizontal and vertical directions are obtained to be 2.1 V/mm and 2.0 V/mm,
17
zR

(a)
Horizontal Output, Vx [V]
5
0
-5
2
0
X [mm]
-2
2
0
-2
Y [mm]
10
5
0
-5
Vertical
Horizontal Output, V [V]
Horizontal
Vertical Position = 0 mm (Low gain)
-10
-10
-3 -2 -1 0 1 2 3
Horizontal Position [mm]
FIG. 13: Typical calibration results obtained with a movable PD installed in front of unit C-1. (a)
Variations in the horizontal output as functions of the horizontal and vertical positions, and (b)
variations in the horizontal and vertical outputs as a function of the horizontal position.
respectively. The beam sizes can be analyzed by assuming that the laser propagation obeys
the laws of Gaussian optics. These beam sizes have been calculated on the basis of a least-
squares fitting procedure with a two-dimensional Gaussian distribution for the intensity
profiles. This procedure is used to map the curve of the relationship between the laser
positions and the detector readouts; thus, the beam sizes can be obtained by assuming
Gaussian optics. The results of the 4σ beam width in the horizontal and vertical directions
are obtained to be 10.4 mm and 12.0 mm, respectively; these results are plotted in Fig. 12.
The mapping curves for other PDs have been obtained on the basis of a similar analysis
with the calibrated beam-size data at each PD location.
E. Alignment measurements
(b)
The alignment measurements have been finally carried out at each location of the PD
under a vacuum condition. Before the alignment measurements, the laser line was corrected
by tuning the positions and angles of the lasers ejected from the optical system with the
precision four-axis stage in order to create a straight line connecting two points, namely, the
PD location in front of unit C-1 and one at the end of unit C-7. The determined laser axis
has been fixed during the alignment measurements.
The horizontal (Vx) and vertical (Vy) voltages were measured by averaging the data 100
18
x
10
5
0
-5
y

times with an oscilloscope at all the PD locations in series; these measurements were repeated
four times. The horizontal and vertical readouts measured at each PD location are trans-
formed to the corresponding position displacements with each mapping curve. Figures 14 (a)
and (b) show the obtained results in the horizontal and vertical directions, respectively. In
(a)
3
2
1
0
-1
Displacement [mm]
-2
Horizontal
Laser-based alignment
Telescope-based alignment
-3
0 20 40 60 80 100
Distance [m]
(b)
3
2
1
0
-1
-2
Vertical
Displacement [mm]
Laser-based alignment
Telescope-based alignment
-3
0 20 40 60 80 100
Distance [m]
FIG. 14: Alignment measurement results (a) in horizontal and (b) vertical directions along sector
C.
Fig. 14, the average data with measurement errors are plotted. For the sake of comparison,
the displacement values measured with a high-precision optical telescope (Taylor-Hobson,
Micro-Alignment Telescope [12]) are also shown. The maximum displacements are obtained
to be larger than 2 mm at the end of accelerator unit 3 in the horizontal direction, and also
in front of accelerator unit 4 in the vertical direction.
The maximum deviations from the average displacement data in the four successive mea-
surements are within ±0.1 mm in both the directions. This result shows that the measure-
ments have been stably performed with good repeatability; however, these results do not
correspond well with the telescope-based alignment results at the PD locations with dis-
placements greater than ±1 mm, while they correspond relatively well at the PD locations
with displacements less than ±1 mm. This phenomenon may be due to the fact that the
calibration procedures may have had some systematic errors, for instance, the maximum
estimated errors of 10% in the beam-size measurements performed at atmospheric pressure.
These systematic errors may reduce the reliability of the mapping curves obtained in the
calibration procedures. The improvement of the measurement precision in the calibration
19

procedures is one of the important issues for the further development of a full-length align-
ment of the injector linac.
V. CONCLUSIONS AND DISCUSSIONS
We have applied a new optical system to the laser-based alignment system at the KEKB
injector linac and have successfully carried out the alignment experiments along a 82-m-
long beam line of the injector linac. The displacements of the accelerator units have been
measured with a measurement resolution of ±0.1 mm level in both horizontal and vertical
directions with respect to the laser axis. An Airy beam has been stably generated from
the new optical system, and the propagation characteristics in vacuum and at atmospheric
pressure have been investigated. A good applicability of the Airy beam was confirmed in
this experiment. This experiment is the first step towards the development of the full-
length alignment of the injector linac. With this experiment, we obtained useful technical
information concerning the laser propagation and proper optical-lens configurations. The
present result encourages us to consider the application of the laser-based alignment system
to the next generation of B-factories.
Acknowledgments
The authors would like to thank Professors K. Furukawa and A. Enomoto of the Acceler-
ator Laboratory at KEK for their continuous support over the duration of this tudy. They
would like to thank Mr. K. Kakihara of KEK for his assistance in the development of the
vacuum system and Mr. Y. Iino of Toyama Co., Ltd. for providing his mechanical engineer-
ing expertise. The authors would like to express their gratitude to Mr. Y. Mizukawa, Mr.
N. Toyotomi, and Mr. S. Ushimoto of Mitsubishi Electric System & Service Co. for their
assistance with the experimental setup. Thanks are also due to Mr. K. Hirano of Oshima
Prototype Engineering Co., for his contributions to the design and tuning of the optical
system in this experiment.
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20

[2] Y. Ogawa, A. Enomoto and I. Sato, Proceedings the 16th. IEEE Particle Accelerator Confer-
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Texas, U.S.A., 1995, p. 2087.
[3] Mi. Yoshida et al., Proceedings the Fourth Asian Particle Accelerator Conference (APAC’07),
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[4] S. Wang, Q. Lin, D. Zhao, and Q. Chen, Optics and Laser Technology, 31 (1999) 437.
[5] I. Abe et al., Nucl. Instrum. Methods Phys. Res. A499 (2003) 167.
[6] Mitsubishi Electric, http://www.mitsubishichips.com/.
[7] OSI Optoelectronics, http://www.osioptoelectronics.com/.
[8] ShinEtsu Quartz, http://www.sqp.co.jp/e/index.htm.
[9] Ophir Optronics, http://www.ophiropt.com/.
[10] A.E. Siegman, Lasers (University Science Books, California, 1986), p. 777.
[11] M. Satoh and T. Suwada, to be prepared for submission.
[12] Taylor Hobson, http://www.taylor-hobson.com/.
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