The 12th Symposium on Accelerator Science and Technology, Wako, Japan 1999

Measurement of the Beam Size at SR Center of Ritsumeikan University
by the SR Interferometer

Yasukazu YAMAMOTO, Ichiro SAKAI*, Toshiyuki MITSUHASHI**,Daizo AMANO*** and Hiroshi IWASAKISR center, Ritsumeikan University, Kusatsu, Shiga 525-8577, Japan*Faculty of Science and Engineering, Ritsumeikan University, Kusatsu, Shiga 525-8577, Japan**High Energy Accelerator Research Organization, Oho, Tsukuba, Ibaraki 305-0801, Japan***Research & Development Center, Sumitomo Heavy Industries, Tanashi, Tokyo 188-8585, JapanAbstract

2. Spatial Coherence and Beam Profile

The beam size in the compact superconducting
storage ring at SR center of Ritsumeikan University
was measured using the SR interferometer( interferometer for synchrotron radiation ) developedby one of the present authors. The spatial coherence ofthe radiation beam in visible range was measured at theregion of spatial frequency from 25.0 to 140.4 mm- 1.
Analysis of the data has yielded the beam size to be
10.5Jlm in the vertical direction. The beam size wasalso measured for the large beam controlled by RF
kicker, and the lifetime was measured at the same time.
The lifetimes observed for small beam size agreed withthe theoretical lifetime ( Touschek lifetime).

According to van Cittert-Zernike's theorem, thecomplex degree of spatial coherence J{ v) is given as a
Fourier transform of the object profile./{y0) as follows;

1. Introduction
The beam size in the electron storage ring is an
important parameter for the use of the radiation
emitted. In many synchrotron radiation facilities, thefocusing-lens imaging method were employed toobserved the beam size. The resolution of this method
is limited by diffraction phenomena, the size smaller
than 50Jlm can not accurately be measured. Recently
one of the present author (T.M) developed a new
method, in which the van Cittert-Zemike' s theorem[ 1]was applied to lead to the determination of the beamsize[2]. It is applicable to the measurement of the beam
size of the order of 1Jllll.
The beam size of AURORA at SR center ofRitsumeikan University was estimated of the order of
10 Jlm in the vertical direction by means of the lifetimeof the stored electron beam[3]. We have applied theSR-interferometer to the measurement of the verticalbeam size.

where v is the spatial frequency, y 0 is the position on
the source plane. J{ u) can be obtained from theintensity profile I(y 1) of an interferogram formed using
the interferometer through the relation

the y 1 being position on the observation plane, D thedouble slit separation, 'A the wave length of light, R1
the distance between the secondary principal point of
the lens and the interferogram, a the half of the slitheight, R 0 the distance between the object beam andthe double slit.

3. SR Interferometer
The SR interferometer is basically of thewavefront-division two beam type using polarized
quasimonochromatic rays. The SR interferometer wasset up at BL-9 of AURORA at a distance of 3750mm
from the source point. The opening angle in verticalplane was fixed to llmrad by the slit of the radiation
damper. A thick beryllium mirror is set to reflect theprimary beam to extract the visible component. An
aperture of lxlmm was used in the double slits
assembly. A diffraction limited doublet-lens with thefocal length f=600 mm was used as an objective lens ofthe interferometer. The slit separation D is variablefrom 6.7mm to 37.7mm, corresponding range of the-504-

The 12th Symposium on Accelerator Science and Technology, Wako, Japan 1999

spatial frequency u being from 25.0mm' 1 to 140.4mm· 1.
The band-pass filter centered at 450nm and thepolarization filter are inserted in the beam path. Aschematic drawing of the SR interferometer is shownin Fig. 1.

E DC

1.0,......

2?-

0.8Q)

uc::....Q)Q) 0.6..c::0u 0.4---N~40E~~)source• experimental data- - exp(-a/u2/2)~~0.

"' 0.2

I0.0

T ~ T'20

4. Result of Degree of Spatial Coherence andVertical Beam Profile
Figure 2 shows an measured interferogram I(y 1) at
u=28.7mm· 1 (D=7.7mm). The spatial coherence y(v) isevaluated from the visibility of the interferogram.
Figure 3 shows the spatial coherence y(v) plotted as afunction of spatial frequency. Assuming the Gaussian
profile, the beam size( cry) can be calculated from thespatial coherence y(v) by using the formula given by(3)
Least squares fitting has yielded cry to be 10.5J.!m.
Almost the same value was obtained from themeasurements usmg the radiation of anotherwavelength, 520nm.

1>-o.seo.aCD.J::........

.....en

8 0.4·c:::I

as-~ 0.2Q.
en-e
1:.E

100

The beam sizes are also measured for the larger
beam controlled by RF kicker at the region of thepower (Pk) from 4mW to 500mW, and the lifetimes
were measured at the same time. Figure 4 shows thespatial coherence y(v) of the large beam controlled invertical direction for the various power of RF kicker.
Absolute value of spatial coherence at Pk=240mW and
90mW become zero at the frequency u=30mm· 1 and59mm· 1, respectively. These distributions suggest thatthe beam profiles are trapezoid. Assuming the central
symmetry for the beam profile, the profile is given as a
Fourier transfonn of the spatial coherence. The beamprofile obtained by using the formula(l) at Pk=240mW
is shown in fig. 5. For comparison, Fig. 5 also shows
the beam profile measured by the focusing-lensimaging method at P..=240mW.

..

CD.....CD80

5. Beam Size controlled by RF kickergCl)

60

Fig. 3 Spatial coherence y(v) plotted as a function of
the spatial frequency v. The curve is a Gaussian curve.

Fig. 1 Structure of the SR interferometer. A: doubleslit; B: diffraction limited doublet-lens; C: polarization
filter; D: band-pass filter (A.=450nm, ~A.=lOnm); E:interferogram.

.e-40

spatial frequency u(mm- 1)

3750

111
'-'

...................___.
120 140.__~._~._~._~.__~....__.~

0n*•'J:go mW\~a.. ..

•J7mW

DD.g'!

+++ +••+33m~ ••x

Bgtt

240mVf~\• +4 mW+ + +X0JJl~':c0?

+*1

IC

•:,~X ~X; It I:!

2550~~a••••I::: IIi~ •••• II 8 D75I

100125ao150

spatial frequency v (mm-l)

vertical position (arb. units)
Fig. 2 The measured interferogram at u=28.7mm· 1(D=7.7mm), A.=450nm.

Fig. 4 Spatial coherence y(v) plotted as a function of
the spatial frequency v for the various beam size.
Plusses, full triangles, open squares, full circles andcrosses denote for 4mW, 17mW, 33mW, 90mW and240mW of the power ofRF kicker, respectively.

-505-The 12th Symposium on Accelerator Science and Technology, Wako, Japan 1999

The solid curve (SR interferometer) and the dashedcurve (focusing-lens imaging method) in fig. 5 show
trapezoidal distributions. We can consider thetrapezoidal beam profile is due to a sinusoidal potentialof RF kicker.

BOO
Energy 575MeV
Current 200mA

700..-..600
c:·esoo• Experimental-Tousheck'-'~400~300- - SR interferometer·········· imaging method:.J2oo1000020406080100120140 160

Beam Size (J.Lm)

Fig. 6 The lifetime as a function of the vertical beam
SIZe.

-400 -300 -200 -100

0100200300

400

Acknowledgments

position (J..tm)
Fig. 5 Beam profiles at Pk=240mW. Solid and dashedcurves correspond to the curve obtained by using theSR interferometer and the focusing-lens imaging
method, respectively.

Authors with to thank to Mr. T. Nakayama andMr. M. Yamamoto for their aid in the recording of theinterferogram.

Reference
6. Beam Size and Lifetime
Figure 6 shows the measured lifetimes and theTouschek lifetime[ 4,5] as a function of the beam size.
The Touschek lifetime is given by

Yz'72 vr

1=-E_ _h14.nr

20 C Nhl(IJ,&J)(4)

where, vh is the bunch volume, Nh the number ofelectrons per bunch, &j nns transverse momentum inunit of m 0c, '7 the maximum relative energy deviation
accepted by the RF system, YE the stored electronenergy in unit of m 0 c2 , r 0 the classical electron radius.
The function J is given byJ"

(l~t'l'' + 2~H~l- 2: + H~:~::~::-::]+ ~ ln(tP +(1 + qiY 2 )}[1] M. Born and E. Wolf, "Principles of Optics",
Pergamon press. ( 1980)[2] T. Mitsuhashi, N. Hiranmtsu, N. Takeuchi, M. ltoh
and T. Yatagai, Proc. 11 1h Symp. on Accelerator
Science and Technology, Harima, pp273 ( 1997)[3] D. Amano, T. Hori, H. Iwasaki andY. Yamamoto,
Abstract of Inter. Workshop Study the Future
Functions of Small Storage Rings and Free Electron
Lasers, Okazaki, p 11 ( 1997)[4] C. Bernardini, G. F. Corazza, G. Di Giugno,
G. Ghigo, J. Haissinski, P. Marin, R. Querzoli andB. Touschek, Phys. Rev. Lett., 10 (1963) 407[5] R. P. Walker, Proc. of IEEE Particle Accelerator
Conference, p.491(1987)(5)

In the case of the small beam size, the measured
lifetime agree with the Touschek lifetime, otherwise
the lifetime obtained for the large beam size deviate
the Touschek lifetime. This result suggest that theT ouschek effect is dominant factor and gas scattering
affect the lifetime for the large beam size.

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