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

A New Estimate Method of Micro-pulse Width Using Standing Wave Measurement
Hiroyasu ITOH, Shusuke NISIYAMA*, Naoki ISHII*, Satoshi TOMIOKA* and Takeaki ENOTO*
Faculty of Fine Arts, Dohto University, Kitahiroshima, Hokkaido, 061-11 JAPAN*Division of Quantum Energy Engineering, Faculty of Engineering, Hokkaido University,Sapporo, Hokkaido, 060 JAPANAbstract
A new method for estimating the micro-pulse widthof electron beam using the measurement of the standing
wave distribution is discussed. When a conducting plateis set transversely in the vicinity to an electron beam's
path, the standing wave distribution is formed by interference between two waves. One is an incident wave radiated directly from electron beam. Another is a reflectedwave returned from the conducting plate. Further thewave radiated from the edge of plate exists. This radiated wave propagates spherically and affects the above
standing wave distribution. We measured the standing
wave distributions by using Hokkaido University 45MeV
Linac. The micro-pulse width was estimated by using
this new method, i.e. using the ratio and width of eachdip of the standing wave distribution. The estimatedvalues showed well agreement with the expected pulse
width of this linac.

1 Introduction
As a measurement method of the micro-pulse widthwithout distorting the electron beam, we have proposeda measurement method using the standing wave distribution created by electric fields radiated from electronbeam. It is easy to measure a standing wave distribution, because it only measure the rectified voltages ofthe spatial distribution. On the other hand, real time
direct measuring[!, 2] of an electric field radiated fromultra short micro-pulse electron beam requires a wide
frequency range measurement equipments.
Thus far, we placed two conducting plates in a cylindrical waveguide, and we measured the standing wave
distributions. Further, on an analytical model analogous
to this experimental system we calculated the standing
wave distributions using the finite difference time domain (FD-TD) method[3]. We investigated in frequency
domain the experimental and analytical results[4]. Correlation for frequency spectra between the standing wave
distributions and electron beam micro-pulses have beenstudied, however, it was not easy to estimate the micropulse width from frequency spectra, because the spectraof standing wave distributions are affected by the modesof electromagnetic fields in a cylindrical waveguide, sizeof the waveguide, the positon of antenna and so on.
In this paper we placed only one conducting platetransversely in the vicinity to the electron beam surrounded by microwave absorbers, and we measured thestanding wave distributions. In this experimental system, the reflection on the plate is done only once, andthe standing wave distribution is formed by discrete interferences. When electron beam passed near a conducting plate at a speed close to light velocity, two waves

are radiated in an opposite direction of beam. One isa reflected wave from the conducting plate, which has
the inverse phase to an incident wave. The standing
wave distribution is formed by interference between incident waves and the reflected waves. Another is a radiated wave from the edge of a conducting plate, whichis created by interaction between electron beams andpositive image charges induced on the edge of a plate.
Radiated waves affect the above standing wave distribution. In this paper we describe a new estimate methodof the micro-pulse width using this standing wave measurement and the result of measurement.

2 Standing Wave Measurement
Standing wave distributions were measured using
45MeV Linac at Hokkaido University. The FWHM ofa macro-pulse was IOns, and the average current was45nA.
Fig. 1 shows the experimental system. we set aconducting plate transversely near to the electron beam
and we measured the spatial distribution by moving thestage in 0.5mm steps along the z axis using the steppingmotor. The edge of a plate was at a distance 25mm
apart from beam center. In this experiment a quarterwavelength monopole antenna was used. It was madeof coaxial cable of Semi-Rigid type, and center wireof 2.9mm long. The tip of antenna was at a distance
103mm apart from beam center. Rectified voltages ofantenna were observed on oscilloscope through a crystal
detector (HP423B: lOMHz-12.4GHz). And the maximum output voltage (ground to peak) was plotted ateach point.

3 Experimental ResultFig. 2 shows the measured standing wave distribution. The axis of abscissa denotes the relative positionof antenna with respect to the position of a conducting
plate, considering z = Omm, and the axis of ordinate denotes rectified voltages (ground to peak) on oscilloscopethrough a crystal detector HP423B.
Large dips were observed at intervals of 53mm because the spatial interval of micro-pulses was about
105mm. Therefore dips are the result of interference
between pulsed incident waves and the reflected waves.
Minimum values of the dip changed as antenna became
further from the plate because the amplitude of micropulses change according to the macro-pulse shape.
On the other side, the maximum values of distributions resulted from the interference between incident
waves and radiated waves from the edge of a plate.
While reflected waves have inverse phase to incident
waves, but radiated waves have same phase, and so out--415-

The II th Symposium on Accelerator Science and Technology, Harima Science Garden City, I997

wave ratio. A regression line approximated by the leastsquares method for this result is also shown in Fig. 3.
The micro-pulse width can be estimated from the dipwidth at the ratio is unity. The result width estimatedfrom the dip width was 5.996mm and so the FWHM ofmicro-pulse was estimated as 26.03ps. At 45MeV Linacof Hokkaido University, it is assumed that the micropulse width is about 20ps in FWHM, but changes dependent on the condition of adjustment on the accelerator.
Therefore it is considered that the pulse width estimatedfrom this measured distribution gives the valid result,and radiated waves are not so affected for estimating
the pulse width.

MICROWAVE ABSORBER

Data Ao
Y=4.260X+1.736 - -14E'.§.

~

Fig. 1 Schematic of the experimental system.

.s::::.

64235

A : Beam to Plate = 25mm
Maximum of Dip

300o0g>

0.2

0.4

0.6

0.8

25Fig. :3 Relation between the dip width and measured
voltage standing wave ratio.

20Q)

08a.

i:5

Ol

10-u~>
.§.

1215
105

4 Estimate Method of Micro-pulse Width

0-250-200-150-100-50

0Position [mm]Fig. 2 Measured standing wave distribution.

put voltages at this points of interference were larger
than only incident waves. This results shows that incident waves interfered with reflected waves and radiatedwaves at different positions. Furthermore it was foundthat radiated waves propagated in retard from reflected
waves because the positions of maximum values weremore or less away from the dip to the side of the conducting plate.
The micro-pulse width is estimated using the voltage
standing wave ratio and the width of each dip. This estimate method of the micro-pulse width is explained at
next section. In obtaining the voltage standing wave ratio, as the maximum value of each dip, the points (wherethe squares were marked in Fig. 2) were picked out so
as to minimize the effect of radiated wave from the edgeof a plate.
Relation between the standing wave ratio and thedip width at each dip is shown in Fig. 3. It is consideredthat the dip width is linearly dependent on the standing

Incident waves interfere with reflected waves and radiated waves at different positions. Therefore we canalso separate the standing wave distribution in two interferences. One is the interference between incident waves
and reflected waves. Another is the interference between
in'cident waves and radiated waves. So in this paper weanalyzed the standing wave distribution formed by incident waves and reflected waves using a one-dimensionalmodel.
When incident waves are electric fields radiated frommicro--pulses of electron linac whose amplitudes are constant, the maximum value of this distribution is equal to
the rectified output dependent on incident waves only,
and its minimum value is zero. Therefore the standing
wave ratio of this distribution is unity. It was foundthat the dip width at the level of 55.88% of maximum
is equivalent to the spatial bunch length of micro-pulse.
Further it was found that the dip width of the rectified
voltages extends 1.809 times by taking into account thesquare law characteristics of the crystal detector and therise time of oscilloscope.
On the other side, when micro-pulses amplitudes
change according to the Gaussian macro-pulse, thestanding wave distribution formed by the electric fields
is shown in Fig. 4. The FWHM of micro-pulse was 20ps,
and the FWHM of macro-pulse was lOns.

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E~"0(j)u:0·;::u(I)

iii

500
450400350300250200150100500FWHM20ps - -FWHM 20ps

14E

.§.

~.r;

12108i5~6Q.

415o

Y=-1.152X+3.702 - -20-250-20Q--150-100
Position [mm]

-50

000.2

0.4

0.6

0.8(E,rax-E,,;,.)/ (E,,=+E,,;,;)

Fig. 4 Calculated electric fields of standing waves excited by the Gaussian macro-pulse.

Fig. 6 Relation between the dip width tl.dk and thestanding wave ratio of the electric fields.

In this case, minimum values of the dip change dependent on the positions, so the dip height H k is calculated by the following equation,detector and oscilloscope, the dip width extends 1.809
times in the same manner.

Hk = 0.5588 (Emax- Emin,k) + Emin,kwhere Emax denotes the maximum value of electric fieldof the standing wave distribution, and Emin,k denotes
the minimum value of the k~th dip Dk from the plate.
This is illustrated schematically in Fig. 5. Furthermore

lEI0.5588( Emax- Emin3)~.

I'(~d3t-I- ~d2-\ Emax

'D3'TEmin2

D2

We proposed a new method for estimating the micropulse width of electron beam using the standing wave
distribution. The standing wave distribution was measured in the experimental system where a conducting
plate set surrounded by microwave absorbers. In thismethod the estimated micro-pulse width of electron
beam agreed well with the expected value, though theradiated waves from the edge of a conducting plate affected this standing wave distribution. It is advisable
to use simultaneously other instruments as well to show
the validity of this method.

~d1

Acknowledgments
The Authors wish to express '>Ur appreciation toH. Tanida and K. Sato of 45MeV Electron Linac,
Hokkaido University.

H3Emin35 Conclusion

(1)

D1

References

0Fig. 5 The way to determine the dip height Hk toobtain the dip width tl.dk.
relation between the dip width tl.dk and the standing
wave ratio of the discrete standing wave distribution,
defined by (Emax- Emin,k)/(Emax + Emin,k), is shownin Fig. 6. It is considered that the dip width is linearlydependent on the standing wave ratio. A regression line
estimated by the least squares method is also shown inFig. 6.
Since the dip width, at the ratio is unity, corresponds
to one of constant .amplitude, the estimated value isequivalent to the spatial bunch length of micro-pulse.
The result obtained by the regression line was 2.550mm,
and so the FWHM of micro-pulse was estimated as
20.03ps. Further, considering characteristics of a crystal[1] Y. Hosono et al., "Development of picosecond pulsed
electron beam monitor (3)", Proc. 21st Linear Ace.
Meeting in Japan, Tokyo, Japan, (1996) 293.
[2] A. Homma et al., Nucl. Instr. and Meth. A371
(1996) 355.
[3] K S. Yee, IEEE. Trans. Antennas Propagat. AP-14,(1966) 302.
.
[4] H. Itoh et al., "Spectrum Analysis of an Electromagnetic Field Generated by LIN AC Eiectron Beams",
Proc. 1994 Int. Linac Conf., Tsukuba, Japan, (19.94)
860.

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