NEW LASER-BASED ALIGNMENT SYSTEM FOR THE 500-M-LONG KEK
ELECTRON/POSITRON INJECTOR LINAC
T. Suwada* and M. Satoh, KEK, Tsukuba, Japan
Abstract
A new laser-based alignment system is underdevelopment. This system is strongly required in the next
generation of B-factories for the stable acceleration ofhigh-brightness electron and positron beams with highbunch charges and also for maintaining the stability ofinjection beams with higher quality. A new laser optics
technique for the generation of so-called Airy beams has
been developed for this laser-based alignment system.
The laser propagation experiment has been performed at
atmospheric pressure in a 120-m-long straight line in theaccelerator tunnel. In this report, the basic design of thenew optical system along with the experimental results is
described in detail.

INTRODUCTION
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
comprising 3.5-GeV positron and 8-GeV electron rings.
Since KEKB is a factory machine, a well-controlled
operation and also a precise alignment for the injector
linac is required to maintain the injection rate, stability ofthe 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(<100 m) linacs; however, alignment measurements witha resolution of ±0.1 mm level cannot be easily performed
for long-distance (>100 m) linacs. A laser-basedalignment technique is advantageous as it cannot only beapplied to alignment measurements for long-distancelinacs but it can also be used for regular monitoring of thestraightness without any interruption during linac
operation. After considering the previous alignment
system, we have been proceeding with experimental
studies to develop a new laser-based alignment system. Inparticular, we aim to develop a new laser source alongwith an optical system for stable propagation of lasers
with axially symmetric Airy beams that are generatedusing two successively aligned circular apertures. An Airybeam is a useful and practical optical source in the laserbased alignment for long distance [2]. Experimental
studies have been systematically performed for testing thelaser propagation with Airy beams in atmosphere on thebasis of the new laser-based alignment system.

LASER-BASED ALIGNMENT OVERVIEW
In this section, we briefly describe the injector linac fora clearer understanding of the laser-based alignmentsystem. A schematic layout of the KEKB injector linac
has been provided elsewhere [3]. The linac comprises

eight sectors (A–C and 1–5) which together constitute
two long straight sections. One straight 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 twostraight sections are connected to a 180° arc section witha circumferential length of 31 m.
A typical sector with a length of 76.8 m comprises
eight accelerator units, each with a length of 9.6 m. The
accelerator unit structure has been described in detailelsewhere [4]. In a typical accelerator unit, an 8.44-mlong accelerator girder is installed on the floor level in theaccelerator tunnel; four 2-m-long S-band accelerating
structures are mounted on the accelerator girder.
Quadrupole magnets for beam focusing are basicallyinstalled on a special magnet girder between two adjacentaccelerator units. The accelerator girder is composed ofan earthquake-resistant, stainless-steel cylindrical tube
(outer diameter: 508 mm) and L-shaped plates connected
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 andare aligned within a standard mechanical precision (±50µm) by reference guide rails fixed on the plates. The
electron and positron beams pass through the center holesof the accelerating structures mounted 1.2 m over thefloor level. A cylindrical laser pipe made of stainless steel(inner diameter: 115 mm) is welded to the upper innersurface of the girder tube. Such a coaxial structure wasoriginally designed in order to reduce convective air flowcaused by any temperature variation and fluctuation in theaccelerator tunnel. A laser beam passes through the centerof the laser pipe installed 780 mm over the floor level.

OPTICAL SYSTEM
A laser source with a laser diode coupled with an
optical fiber has been developed in this experiment. Thelaser beam is focused on the cross-sectional area of asingle-mode optical fiber (diameter: 3.5 µm) through anaspheric lens with a diameter of 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 awavelength 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 toan optical system, which delivers the laser beams with thesuitable beam sizes required for the alignmentmeasurement.
The complete mechanical drawing of the optical system
is shown in Fig. 1 (a). The optical system comprises aspherical reflective mirror and a plane mirror that can becoupled with an optical fiber cable. The sphericalreflective mirror is aluminum-coated and has a diameterof 152.4 mm, a wavefront aberration of !/4, and an
effective focal length of 152.4 mm. The plane mirror iscomposed of quartz and has a thickness of 6 mm anddiameter of 90 mm. Dielectric multilayers with athickness of 2 µm are evaporated in vacuum on thereflection surface of this plane mirror. Its reflectance isgreater than 99.5% at 660 nm, and its wavefront
aberration is !/2. The plane mirror has a circular aperture(diameter: 1 mm) for the laser beam injection and isinclined by 45° with respect to the laser axis.

into the optical system is ~14 mW. The total transmission
efficiency of the laser power has be obtained to be ~1%.

LASER-PROPAGATION EXPERIMENT
A laser beam propagation experiment was performed at
atmospheric pressure along a 120-m-long straight line in
the accelerator tunnel. In order to adjust the laser optics,
the laser beam was focused from the optical system down
to a waist point, and symmetrically expanded again overthe distance of 120 m.

(a)

Reflective mirror

162

Laser beam
ÿ90

Optical fiber2162
6Plane mirror
3.0

152.4

85.66

101.94

Figure 2: Laser profile obtained at a distance of 60 m
away from the laser source.

340

(b)
Reflective surface of plane mirror
1st circular aperture slit

Optical fiber
Laser beam

The beam sizes were measured using a CCD camera
along the line at intervals of 20 m from the laser source.
Figure 2 shows a typical laser profile obtained at 60 m,
which is close to the waist point. Figure 3 shows thevariations in the horizontal and vertical beam sizes as afunction of the distance from the laser source.

3 mm 3 mm
2nd circular aperture slit

Figure 1: Optical system with two reflective mirrors. (a)Mechanical drawing of the optical system and (b) theenlarged drawing (not scaled) of the central portion of theplane mirror.
Figure 1 (b) shows the enlarged schematic drawing of
the central portion of the plane mirror. The laser beam isejected from the fiber end with a numerical aperture of
0.1 and is transmitted through the first circular apertureslit (diameter: 10 µm) fixed 0.1 mm behind the end of thefiber. Such optical configurations transform the Gaussianlaser 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.
This Airy beam is then transmitted to the sphericalreflective mirror, which suitably expands the beam sizes
as per requirements in the alignment measurements; these
expanded beams are reflected to the plane mirror. The
beam sizes are determined on the basis of thetransmission length between the centers of the reflective
and plane mirrors under the condition of a fixed focal
length. 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 delivered by
the plane mirror is ~1 mW, while the laser power injected

Figure 3: Variations in the horizontal and vertical beam
sizes as a function of the distance from the laser source.
It can be observed that the horizontal and verticalvariations in the beam sizes along the line are slightly
asymmetric. This may be due to the insufficient angularadjustment of the spherical reflective mirror.

LASER-PROPAGATION ANALYSISThe obtained results are analyzed on the basis of aleast-squares fitting procedure with well-known Gaussianlaser optics [5] as2# z " z0 &! = !0 1+ %,$ zR ('(1)

where ! is the beam size at each location depending on
the distance (z) from the laser source; !0, the beam size atthe waist point (z = z0); and zR, the Rayleigh length. The
results show that at the waist points that are 53.7 m and62 m away from the laser source, the horizontal andvertical beam sizes are 2.9 mm and 3.1 mm, respectively.
In addition, the Rayleigh lengths in the horizontal andvertical directions are 9.8 m and 11.5 m, respectively. The
observed values are in good agreement with thoseobtained by numerical analyses.
This optical system generates an Airy beam, which is a
Gaussian beam that is truncated after it passes through thetwo successively aligned aperture slits. The opticalconfiguration is shown in Fig. 4. In this section, we
briefly discuss the dependence of the Fresnel number (F)on the propagation distance along the laser axis; thisdependence is owing to the fact that after the Airy beam
passes through the second slit, it becomes a truncatedGaussian beam and is then focused by a thin lens with a
focal length of f at an observation point (m). It should be
noted that the physical meaning of the Fresnel number
gives the number of Fresnel zones contributing to thediffraction fringe pattern at the observation point.

The first (second) term in eq. (3) indicates thecontribution of the first (second) aperture slit to theFresnel number.
Figure 5 shows the variations in the Fresnel number
calculated in the horizontal and vertical directions as afunction of the propagation distance from the laser source.
The parameters, ! = 660 nm, a1 = 5 µm, a2 = 0.5 mm, d0 =0.1 mm, d1 = 6 mm, and L0 = 146.76 mm (L0 = 146.71mm) have been applied to the calculations in thehorizontal (vertical) direction. The parameters, L0, havebeen estimated in the numerical simulations on the basisof the results shown in Fig. 3.

Optical lens

2nd aperture slit

Figure 5: Variations in the Fresnel number calculated in
the horizontal and vertical directions as a function of thepropagation distance.

1st aperture slit R

2R1

R3

R0Sa2

a1

Laser axis

V1 V2

S'd1

d0

L0m

L1d2Figure 4: Schematic of the laser propagation withdiffractions in an optical configuration with two apertureslits and a thin lens.
The laser beam generated at the source (S) is diffracted
at the first aperture slit that has a radius of a1. The solidline indicates the diffracted wave, while the dashed line
indicates the wave passing through the first slit without
diffractions; the virtual source point for the latter is at V1.
It is again diffracted at the second aperture slit that has aradius of a2. The solid line indicates the diffracted wave
for which the virtual source point is at V2, while thedashed line indicates the wave without diffractions. Thus,
the wave originates at V1 and is focused at S’ by the lens,
while the diffracted wave originates at S and is focused at
m. The Fresnel number subtended at m is derived by
calculating the difference (") of the pass lengths with andwithout diffractions as follows:! = F(" / 2),(2)By extending the theoretical analysis described in ref. [6],the Fresnel number in this optical system is given by
F=a12 # 1
a & a2 # 1 1 &" 2 ( + 2 % " (.
%! $ d0 a1d1 ' ! $ d1 d2 '(3)

1 ! L0 (1 / L1 + 1 / f ).
(1 / L1 + 1 / f )(4)Here,d2 =The results show that the Fresnel numbers obtained are
not very small; that is, |F| ! 1 over the propagation
distance. However, the diffraction pattern fringes of theobtained profiles are not very large. The experimental
results may indeed indicate stable propagation
characteristics of Airy beams.

SUMMARY
We have successfully applied a new optical system tothe laser-based alignment system at the KEKB injector
linac. The experimental results show that an Airy beam
has been stably generated from the new optical system.
The propagation characteristics at atmospheric pressure
have been investigated, and a good applicability of theAiry beam has been confirmed in this experiment. The
present result encourages us to consider the application of
the laser-based alignment system to the next generation of
B-factories.

REFERENCES[1] K. Akai et al., Nucl. Instrum. Methods Phys. Res. A499
(2003) 191.
[2] S. Wang, Q. Lin, D. Zhao, and Q. Chen, Optics and Laser
Technology, 31 (1999) 437.
[3] I. Abe et al., Nucl. Instrum. Methods Phys. Res. A499
(2003) 167.
[4] T. Suwada et al., to be submitted to Rev. Sci. Instr.
[5] A.E. Siegman, Lasers (University Science Books, California,1986), p.777.
[6] R.G. Wenzel et al., J. Opt. Soc. Am. A 3(6) (1986), 838.