The lith Symposium on Accelerator Science arul Technology, Harima Science Garden City, 1997

A MEASUREMENT OF BEAM SIZE OF AURORA BY THE USE OF
SR-INTERFEROMETER AT SR CENTER OF RITSUMEIKANUNIVERSITY
Toshiyuki MITSUHASHI, Hiroshi IWASAKI* ,Yasukazu YAMAMOTO*Tosinori NAKAYAMA*, and Daizo AMANO**High Energy Accelerator Research Organization, Oho, Tsukuba, lbaraki, 305 Japan*SR Center, Ritsumeikan University, 1916 Noji-cyo, Kusatsu, Shiga, 525-77 Japan**Lab. for quantum Equipment, Sumitomo Heavy Ind. Ktd.,2-1-1 Yato-cho, Tanasi,Tokyo 188 JapanAbstract
A vertical beam size of the AURORA at SR center ofRitsumeikan University was measured by the use ofSR-interferometer. A spatial coherence of the visible
SR beam was measured at the region of spatial
frequency from 15 to 41 mm-1. Tbe result of the beam
size is 16.5Jlffi and it is good agreement to the estimatedbeam size of lOJlm by means of tousheck life timemeasurement. The beam size is also measured for large
beam mode which is used for normal operation of thefacility.

1. INTRODUCTION
The principle of object-profile measurement by meansof the spatial coherency of the light is known as the vanCitterut-Zemike's theorem{l). It is well known that A.
A. Michelson was measured the angular diameter ofstars by his famous stellerinterferometer. Recently, thisprinciple was applied for the measurement of verticalelectron beam profile in the storage ring by one of theauthors by the use of SR-interferometer(interferometerfor synchrotron radiation)(2). Since this method is basedon spatial coherence of the SR beam, it is suitable tomeasure a small electron beam size having a good
spatial coherence. The beam size of AURORA at SR
center of Ritsumeikan University was estimated about
10J.Lm by means of tousheck life time measurement(3).
In this time, we measured this small beam size by theuse of SR-interferometer.

Then the interferogram which observed with the SRinterferometer as shown in Fig.1 is given by the use ofy;/(8) = (sinc(8))2 {[1 + lr<D~cos[kD(8 + q>)]}~2)

where e denotes the observation angle of theinterferogram, sine function denotes a diffraction of one
silt in the interferometer and cp denote a phase of theinterference fringe. Using the equation 2), we canmeasure degree of spatial coherence from theinterferogram, and using the equation 1), beam profile
will be obtained from the degree of spatial coherence.
Furthermore, to assume a Gaussian proflle of the beam,
we can measure the rms beam size from one
interferogram.

3. SR-INTERFEROMETERThe SR-interferometer designed by one of the authors(2)was used for the measurement. The SR-interferometeris basically a wavefront division type two beaminterferometer by the use of polarized quasimonochromatic rays. A schematic drawing of the SRinterferometer is shown in Fig. I.

80mm (max)5m

2. SPATIAL COHERENCE ANDBEAM PROFILE AND SIZE
According to van Cittert-Zernike's theorem, theprofile of the object is written by Fourier Transform ofthe complex degree of spatial coherence. Let f denotes
beam profile as a function of angular diameter ,and 'Y
denotes the complex degree of spatial coherence as afunction of distance of double slit of the interferometerD, y is given by the Fourier transform off as follows;er(D)=I /(9)exp(-ikD9)d9-1)

IlOft• 0=63 mm, 1'=600 mm

io------'--------'11 band1'as• :fdter .u~IO runFig.l Outline of the SR-interferometer.
An aperture of lxlmm2 was used in the double slits
assembly. A diffraction limited doublet-lens having adiameter of 63mm and focusing length of f=600mm wasused as an objective lens of the interferometer. A band
pass filter of 1Onm band width was used to obtain aquasi-monochromatic ray. A magnifier lens, CCD(plinix,TM765) and image processor (spilicon,LBAIOOA) were used for the observation of interferogram.

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The 11th Symposium on Accelerator Science and Technology, Harima Science Garden City, 1997

The SR-interferometer was set at Sm apart from thesource point.

(!)

b.Oclo..

'+-4 . MEASUREMENT OF SPATIALCOHERENCE OF THE SR BEAM(!)

7650c(!) 4The absolute value (visibility) of complex degree ofspatial coherence was measured at SR monitor beamlineof AURORA. The opening angle of SR monitor
beamline was limited by the dimension of the extraction
mirror for SR beam and it was 2.7mrad. This opening
angle limits the measurement .of interferograms in thelarger region of spatial frequency. Under this condition,
the interferogram was measured by changing thedistance D of the double slits from Smm to 13.5mm by
O.Smm step. Corresponding spatial frequency region(D/fA) is from 15 to 4lmm-lfor the wqavelength of550nm. The interferograms are measured for threeoperation modes of the AURORA. One is small beam
operation mode(beam size is estimated to 1Of..Lm bymeans of the tousheck lifetime measurement). Secondis lager beam operation mode No.1. Third is Largebeam operation mode No.2. Large beam mode No.1 isthe operation mode having a fat beam obtained bymeans of beam-ion scattering which realized bywillingly ion trapping. Large beam mode No.2 is theoperation mode having a fat beam obtained by the useof RF kicker. The results of interferograms for thesethree operation mode are shown in Fig.2.

32lo..
(!)+' 1clo..

(!)

'+-1
0.5
position (mm)c) in~erferogram for large beam operation mode No.2.
A.=700nm, D=Smm
Fig. 2 The results of interferograms for these threeoperntion mode
These interferograms are measured at the distance of
double slits of Smm

5. EXPERIMENTAL RESULTS OFDEGREE OF SPATIAL COHERENCE
The absolute value of complex degree of coherence isevaluated from the visibility of the measured
interferogram. The results for three operation modes areshown in Fig. 3.
1.2.-------------------~

5....---------------.
11)

on 4·- 3~

0.8 -t.t::i;>--11)

0.6 -0~11)

2

0.4 -

.......s 1

0.2 1-l-;

~l-;
Q)

0.1

0.2

0
0

0.3

24IIII

68

101214D (mm)position (mm)a) interferogram for small beam operation mode.
A=550nm, D=SmmIa) small beam operation mode. The solid line denotes aleast square fitting curve by Gaussian beam profile.

1~------------------~

11)

gfs;.a4
3g0.811)~;>--~220.6

0.4.s 10.2o-..-L--L------~--~

0

1
0.5
position (mm)15105
distance of double slit (mm)b) interferogram for large beam operation mode No.I.
A=700nm, D=Smmb) large beam operation mode No.1-442-

The lith Symposium on Accelerator Science and Technology, Harima Science Garden City, 1997

2.5 r----___,..---: --------,---,

120.8

1.5

0.6

10.5?-0.4

0~----~

0.2-0.5 L-----1----'--.J..- ----''-----1--...J
1 1.5-1.5 -1 -0.5 0 0.5

005

10

beam size (mm)15

Fig.4. beam profile of large operation mode No.1

distance of double slit (mm)2.5 r-----...,..---:---~----.----.
2c) large beam operation mode No.2
Fig.3. Absolute value of the complex degree of spatial
coherence

1.5

1AS shown in figures 3-a) and 3-b), the absolute valueof complex degree of coherence for small beam
operation mode is still 0.9 at the spatial frequency
D=l3.5mm and the absolute value of complex degree ofcoherence for large beam operation mode No.1 is almost
zero at D=7.5mm. As shown in Fig.3-c), the absolutevalue of complex degree of coherence for large beammode No.2 becomes one time zero at D=9mm. Thissine function like distribution of the degree of coherence
suggest us a trapezoidal distribution of the beam profile.

6 RESULT OF VERTICAL BEAMSIZE AND PROFILES
To assume the gaussian beam profile, we can evaluate
the beam size of small beam operation mode fromdegree of spatial coherence data as shown in Fig.3-a).
Least squire fitting of degree of the spatial coherence bygaussian beam profile is shown in Fig.3-a). The resultof the beam size from this fitting is 16.5Jlm.
According to the van-Cittert-Zemike's theorem (1),(2),the profile of the object is obtained by Fouriertransform of the complex degree of spatial coherence.
To assume the central symmetry for the beam profile,
Fourier transform of the complex degree of spatial
coherence reduces Fourier cosine transform of absolutevalue of the complex degree of spatial coherence(2). For
two of the large beam operation modes, we make a
Fourier cosine transform of absolute value of thecomplex degrees of spatial coherence as shown infigures 3-b) and 3-c). The result of beam profiles forlarge beam operation modes 1 and 2 are shown infigures 4 and 5. The beam profile of the large operation
mode No.1 is Gaussian like and this profile of the beam
is obtained by means of beam-ion scattering which
realized by willingly ion trapping. In the case of Largebeam mode No.2 ,the beam profile is little bit
trapezoidal and it is obtained by the use of RF kicker.
We can consider the trapezoidal distribution in the beamprofile is due to a sinusoidal potential of the RF kicker.
The rms beam sizes are 202Jlm for mode No.1 and 176
Jlm for mode No.2.

.
''----,-------,--0.5
0~----~-0.5 ....____.__ _.__.....____......____.__. . . .
-1.5-1-0.500.5

11.5

beam size (mm)Fig.5. beam profile of large operation mode No.2

7 CONCLUSIONSThe beam size of the small beam operation mode andthe beam profile of the large beam operation mode of
the AURORA was measured by SR-interferometer. We
conclude the beam size in the small beam operation
mode is measured to 16.5JJ.m and it is agree with thebeam size estimated from Toushecks life timemeasurement(3). The beam profile for large beam
operation modes are Gaussian like distribution for thebeam of mode No.1 which obtained by means of beamion scattering which realized by willingly ion trapping
and trapezoidal distribution for the beam of the mode
No.2 which obtained by the use of RF kicker. The ofrms beam sizes are 202JJ.m for mode No.1 and
176JJ.m for mode No.2.

8 ACKNOWLEDG MENTS
Authors wish to thank to Professor H. Kobayakawa ofNagoya University to his encourage of this work.
Authors also thank to Mr. N. Takeuchi of Tsukuba
University for him help of deta analysis.

REFERENCES(1) M.Bom and E. Wolf,"Principles of Optics, P459
Pergamon press. (1980).
(2) T. Mitsuhashi, to be published in proceedings ofParticle Accelerator Conference (1997) ,Vancouver.
(3) D.Amano,T.Hori,H. Iwasaki and Y. Yamamoto
abstract of international workshop to study the futurefunctions of small storage ring and free electron lasers,
Okazaki(l977).

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