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

Development of Laser wire beam profile monitor
for measurement of low emittance beam
Yutaka SAKAMURA, Yasuo HEMMI, Hiroaki MATSUO,
Hiroshi SAKAI, Noboru SASAO, Yasuo HIGASHI*,
Timo KORHONEN*, Takashi TANIGUCHI*, Junji URAKAWA *Department of Physics, Kyoto University, Kyoto 606, Japan
High Energy Accelerator Research Organization, lbaraki 305, Japan *Abstract

between two trains is 60 nsec.

We have designed a beam profile monitor to measure the size of a low emittance electron beam down tothe order of ~ lOJ.lm. In the monitor, very thin andhigh intensity laser beam is created inside an opticalcavity. The shape of the electron beam can be measured
by crossing the laser and electron beams and detecting
Compton scattered photons. We constructed a test cavity to create a laser beam with high intensity and size ofthe order of lOJ.lm. We established methods to measure
the beam intensity and the beam size.

1 Introduction
A beam profile monitor has been designed for measuring the beam size in the damping ring of the Accelerator Test Facility (ATF) at KEK. In this ring the beam
size will be reduced to ~ 10J.lm vertically and ~ 130j.lm
horizontally within 80 msec or less from injection. Thus
the monitor must be able to measure the beam size of~ 10 J.lm. Typically wire (car bon or tungsten) scanners
are used for the beam size measurement. However, they
are destructive to the circulating beam in the ring. The
monitor of ref.[l] might be used; however, we would liketo develop a more handy and simple one that matches up
with the quasi-continuous beam of~ 10j.lm in size. Our
monitor is based on a nearly concentric optical cavity inwhich a Gaussian beam with a~ 10j.lm beam waist is realized. Electrons interact with the laser light inside theoptical cavity and emit energetic photons to the original
electron beam direction (Compton scattering). The rateof these energetic photons is measured as a function of
the electron beam position relative to the the laser beam
position. From the rate the beam profile in one direction
can be calculated.
The monitor will not disturb the beam and allows us
to measure its spatial and/or temporal structure. The
optical cavity enhances the effective laser power inside
the cavity. This moderates the requirement for the laser,which is important from the cost viewpoint.
In this paper we describe the design of the monitor
and some experimental results of basic studies on thetest cavity.

2 Design of the Monitor
For the calculations performed in this section, we assume the following parameters (2]. The 1.54 GeV beam
consists of bunch trains. Each bunch contains 1 x 10 10electrons, and its length is about 5 mm. The separation
between adjacent bunches is 2.8 nsec, and the separation

2.1 Compton scattering
We estimated the photon counting rate based on thefollowing assumptions. The laser beam interacts perpendicularly with the electron beam. The light source is a
10 m W He-N e laser and the power enhancement factorof the optical cavity is assumed to be 100. Gamma rays
whose energy is above 10 MeV are detected. With theseparameters the average counting rate is estimated to be
7.8 kHz. This may not be enough to trace the dampingof-the beam since the damping time is typically about
10 msec (ref (2]).

2.2 Optical cavity

It is known that a resonant mode called Gaussian
beam (3] can exist in a resonator cavity. The electricfield of the (TEM 00 ] mode is given bywo

Eo(x, y, z)

A w(z) exp
x exp (ik(x2+y2)- w2(z)x;R~~2 ) exp (i<I>(z))

where..\ represents the wave length, w(z) the beam spot
size at the location z, R(z) the curvature of the wave
front, and <I>(z) the Guoy phase factor. The parameterw 0 is called the beam waist, and represents the smallest
spot size at the middle of the cavity (z = 0). Suppose
two spherical mirrors (optical cavity) with curvatures R
are placed at ±zR. With a stable laser beam in thiscavity whose length is D(D = 2zR), the beam waist isrepresented by2wa..\ JD(2R- D)

=;

2

(1)

From this equation it can be calculated that a beam
waist of, say, 10 J.lm is obtained for ..\ = 640 nm and
R = 20 mm when D = 40mm- 24J.lm. It should be also
noted that the requirement for the positioning accuracy
in D is very strict.
A fraction of the beam incident on the other side of
the cavity is transmitted to the other side. [Fig.1] The
transmission ratio T is given by the Airy function:
4F 2 cos 2
T = 1/ [ 1 + --;:;:2(21rD)]-..\-(2)

The quantity F is called 'finesse'and is given by F =JrVJ{;;/(1- Rm) where Rm is the reflectivity of the mir-

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

rors. From the eq.(2) above, the finesse P can be expressed by F = (AD(peak- to- peak))f(oD(fw hm))
where AD is the difference in D between the two adjacent peaks (equal to >./2), and oD the full width at half
maximl!_m of the peaks. The averag_e power enhancement
factor P inside of the cavity is: P = i~~::T ~ iFT.
When T = 1, for example, we need mirrors of reflectivity
Rm = 98% in order to obtain the power enhancement of100;lllki!IIIIII,2MS/s

1 Acqs3 Experiments

In this section, we. describe some results of studies
on the test cavity: We want to measure the beam waist
w 0 and the average power enhancement factor P. To
our application, the beam waist is the most importantparameter. Thus we tried several independent methods
to measure wo.

Fig. 2 A typical example of the detector output.
This value is consistent with the expected value of 77(19). .

3.3 Three methods to measure the beam waist

Shift-rotation method We employed the following
method [5]. Suppose that the cavity axis is aligned withthat of the laser beam. One of the mirrors is shiftedlaterally. Since the mirrors are both spherical, the cavity
can be realigned by rotating it. A simple calculationshows that the displacement x and rotation angle (} isrelated by

Fig. 1 Schematics of the test setup.

3.1 Setup of the experiment
Figure 1 shows a schematic diagram of our test
setup. It consists of a He-Ne laser, an optical isolator,
input lens system, the cavity and a detector.
These optical elements are installed on adjustable
positioners. In particular, the downstream cavity mirror
is equipped with a piezo translator so that the mirror
can be scanned along the beam direction z. The piezotranslator can be controlled remotely and its position
is monitored with a strain gauge sensor with a 10 nm
position resolution. We can position the piezo translator
manually or scan it by applying a voltage signal to thecontroller.
The transmitted light intensity is monitored with a
PIN photodiode at the exit of the cavity. Output signalof the diode is amplified with a simple current-to-voltage
amplifier and monitored with an oscilloscope.

3.2 Measurement of the power enhancement factor
We measured the finesse to get the power enhancement factor. A function generator was used to produce
a .-v100 Hz sawtooth signal. The signal was fed into thepiezo controller. The amplitude of the signal was set sothat the cavity length D was scanned over several AD.
A typical example of the detector output is shown in
Fig.2.
The finesse F was found to be 70 (22) for the mirrors
with Rm = 96%(85%) (enhancement factor is 47 (15)).

2R-D=

X
'""~
tan {arcsin (sin(} fn)} - (}(The approximate formula is valid for small 9) By measuring x and(}, we can determine 2R- D by the eq.(1),which in turn determines the beam waist w 0 • Fig.3
shows the results of the measurements.
Measuremen t of a beam divergence angle In thefar field (z ~ zo), the beam width w(z) is proportionaltoz,i.e. w(z) ~ (w 0 fz 0 )xz. Thusonecande terminew0
by measuring the beam divergence. For convenience, we
define a half-cone angle a 1;..;e at which the beam power isreduced to 1/Ve of its maximum value. This quantity isrelated to the beam waist by a 1 ;..;e ~ n>.f(27rwo) where
the effect due to the concave mirror (with a refractive
index n) is taken into account.
We inserted a 200Jlm slit in front of the diode. The
diode was scanned horizontally to measure the beamprofile, from which 1/ve-widths were be reduced. The
profile measurements were repeated at several differentz positions. Fig.4 shows 1/ve-widths at several differentz positions. The straight line is a linear fit to the data;a half-cone angle a 1;..;e is given as a slope of the fit.
Higher order transverse modes A phase of thehigher transverse mode TEMmn shifts (rn + n)()(z) at-57-

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

z(mm)w0=.30,u:mz(mm)2R- D (mm)w0=20,u.mFig. 4 Measurement of a beam divergence.

Fig. 3 Measurements of 2R- D by the shift-rotation
method.
z on the beam axis from TEM 00 . A straightforward cal-culation shows that the condition above is equivalent toA{(D; · arccos
7r
Dp = 2 p + m+n+l1)}

where p is integer. The quantity Dp in the right handside may be replaced by some representative value since
its dependence is weak. Therefore, the spacing between
the adjacent peaks due to the higher mode excitation(whose m + n differs by 1) is [ ~ arccos ( ~ - 1)] times
the spacing of the corresponding(.A/2) [4]. Thus we cancalculate D by measuring the spacing of these peaks.
The results of the three methods are summarized inTablel.

In this paper we described a conceptual design of abeam profile monitor for an electron beam with a sizeof,...., 10j.lm. Assuming a laser beam with a beam waistof 10J.lm and an effective power of 1 W, the expected
counting rate is ,...., 10 kHz when scattered photons withenergies>10 MeV are detected. We measured the finesse
F to obtain the power enhancement factor of the test
cavity. Using mirrors with reflectivity of Rm = 96%, we
obtained an enhancement of 50, which is consistent withthe expected value. We confirmed three methods of measuring beam waist in the test cavity. As seen in Table 1,
the beam waist was measured with 10% accuracy.
Next, we plan to use mirrors with reflectivity of
98 ,...., 99% for an optical cavity of a prototype monitor.
We also plan to replace the He-Ne laser with a higher
intensity output laser like a diode laser for example. A
further design work is now underway.

Acknowledgments
nominalwa

20 J.l m
25 J.l m
30 J.l m
35 J.l m

shift-rotation
method
20.0
± 1.0
25.0
± 1.3
30.0
± 1.5
35.0
± 1.8

alive

measure
ment
20.4
± 1.7
24.8
± 1.2
3LO
± 1.6
37.5
± 1.4

transverse
mode
20.1

gestion of Laser wire beam profile monitor using Optical
Cavity.
References

24.9
30.0
36.4

Table 1Comparison of beam waist measurements

4 Conclusions

It is our pleasure to thank Dr. M.C.Ross for his sug-

[1] Tsumoru Shintake; Nucl. Instr. and Meth. , A311
(1992) 453.
[2] F .Hinode,S.Kawabata,H.Matsumoto,K.Oide,
K.Takata,Seishi Takeda and J .Urakawa;'ATF Design and Study Report'(1995)[3] A. Yariv; Optical Electronics (Holts, Rinehart andWinston, New York, 1991), 4th ed. ; M. V. Klein
and T. E. Furtak; Optics ( New York, 1991), 2nded.
[4] D. M. Kane; Am. J. Phy. ,59(3) (1991) 235.
[5] Y. Sakamura; Master thesis (Kyoto University,1997), unpublished.

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