The 9th Symposium on Accelerator Science and Technology, Tsukuba, Japan 1993

Experimental and Theoretical Analysis of the Spectrum ofTransient Electromagnet ic Field Created by Linac Electron Beam
Hiroyasu Itoh, Satoshi Tomioka, Takeaki Enoto
Department of Nuclear Engineering, Hokkaido University
Kital3 Nishi8 Kita-ku Sapporo 060 Japan
Abstract

Wave information about micro-pulses of electron beams
is required in order to control an electron beam precisely,
and it may be possible to obtain such information by analyzing the spectrum of the electromagnetic field createdby a linac electron beam. In order to derive the spectrum, we measured the spatial distribution generated by astanding wave. Furthermore we caluculated the transient
electromagnetic field excited by a bunched electron beam,using the finite-difference time-domain (FD-TD) method,and compared two spectra in the frequency domain, into
which the calculated value in time variation and the measured values in spatial variation are transformed by using
the fast Fourier transform (FFT) respectively.

I. INTRODUCTION
Wave information about micro-pulses of electron beams,
half width, peak value, energy distribution of bunches, etc.,
are required in order to control an electron beam precisely.
It may be possible to obtain this information by analyzing
the spectrum of the electromagnetic field created by a linac
electron beam. However, it is difficult to measure the time
variation of a. bunch, whose half width is only several tensof psec.
In this case, it is effective to measure not time variation of a bunch, but rather spatial variation generated bya standing wave, which is created by interference between
a progressive wave and a reflective wave both generated
with an electron beam and two reflective plates. Furthermore the wavenumber spectrum is estimated by using theFFT for measured values. This method enables measurement of the half width of a bunch easily even by using anosciloscope with a lower frequency bandwidth limit of, forexample, 1001\tiHz.

reflective plate

Figure 1. Measurement of a standing wave.
voltage (ground to peak) is plotted. After the measured
values (256 points) were windowed by the hanning window, we transformed them into the wavenumber spectrum
by applying the FFT. The expected distribution of thespectrum is equal to the convolution of the true power
spectrum with the transform of the window function.
1. 2'r-.---r--r--r---.,-.-- ,---,---,---,--,---.--,ANTENNA LENGTH:5.0mm

ANTENNA LENGTH:3.0mm
100
D !STANCE [mm]0200

Figure 2. Spatia.! variation in the waveguide.
FFT( 256 POINTS )II. MEASUREMENTANTENNA LENGTH: 3. Omm

1o. 72

We placed two reflective plates, spaced 355mm apart,
perpendicular to the axis in the cylindrical waveguide, andmeasured the spatial distribution, by moving the stepping
motor controlled stage in lmm steps along the axis. Measurement system is shown in Fig.l. In the experimentreported here, dipole antennas used are made of coaxial
cable of Semi-Rigid type, and antenna lengths are 3mmand 5mm, such that resonance frequencies correspond to25GHz and 15GHz respectively.
Fig.2 shows the spatial variation of electrical fields along
the axis in a cylindrical waveguide. The maximumoutput-362->-I-

1~. 55'2~. 92(J)z

29. -i4w

r !", VJvA"/\J/ij)·/~~-y

1. 7

20. 0\..

40. 0
FREQUENCY

60. 0[GHz]80. 0

Figure 3. Frequency spectrum (antenna length is 3mm).

Fig.3 and Fig.4 show the frequency spectrum into which B. Numerical Result
the wavenumber spectrum is converted, taking into acFig.5 shows time variation of electric field in the cylindricount the dispersion ofTM 01 mode in the cylindrical wavegwaveguide. After the calculated values were windowed
caluide. u· is confirmed in Fig.3 and Fig.4 that the resonanceby the banning window, we transformed them into the frefrequency and their higher harmonics exist.
quency spectrum by using the FFT as shown in Fig.6.
FFT( 256 POINTS )FFT( 1024 POINTS )ANTENNA LENGTH:S.Omm
2. 93

7.. 26jj 10.72>-1-·~-· 38<I)zw>-31-71i

1-36. .49

21.23!zs,... &t

51. 76

1. f

633! /

1. 7

20. 0

60. 0
40. 0
FREQUENCY [GHz)

80. 0
0. 0

Figure 4. Frequency spectrum (antenna length is 5mm).

60. 0
40. 0
FREQUENCY [GHz)80. 0

Figure 6. Frequency spectrum by FD-TD method.

III. NUMERICAL ANALYSIS

IV. CONCLUSION

A. Analytical Model

The finite-difference time-domain(FD-TD) method wasproposed for the solution of Maxwell's equations by Yee[1). It is a popular technique to calculate the transient
electromagnetic fields [2]. In applying FD-TD techniqes,
Maxwell's curl equations are solved by replacing them withdifference equations in the solution domain, which is divided by a finite'-difference grid. Electric and magnetic
fields are calculated at alternative half-time steps.
We considered an electron beam passing along the axis ofa cylindrical waveguide at almost the speed of light, andsolved the difference equations in cylindrical coodinates
for this analytical model [3]. The Solution domain is theaxial cross-section of the cylindrical waveguide used in themeasurement of the standing wave.
We assumed that the electron beam has the uniform diameter of 6mmcf>, and is a Gaussian pulse with the half
width of 20psec in the direction of propagation, also injects
periodically (every 350psec) according to the acceleration
period of the clystron.
<•E.r4<--.----.--,-....--...-.----r--.----,-__,..,

eTo obtain the wave information about 'pulses, we measured a standing wave and calculated the transient electromagnetic field. As a result of comparing the frequency
spectrum of them, we found that several frequencies corresponded, specifically for 25.92GHz, 31.79GHz etc .. Thesefrequencies also depended on the resonance frequency andtheir higher harmonics of the antenna. Therefore it is necessary to measure standing waves for a lot of antennas
which have diferent resonance frequencies, in order to ob~tain the true power spectrum. This technique potentiallyis effective to analyze the spectrum of the electromagnetic
field created by linac electron beam.

80?: 40c....1wu..

0frl....1-8
0. 00

0. 33

1. 00
0. 67
TIME [nsec)

1. 33[1) K. S.Yee, "Numerical solution ofinital boundary value
problems involving Maxwell's equations in isotropicmedia," IEEE 1hlns. on Antennas and Propagation,
vol.AP-14,pp.302~307,May 1966.
[2] A. Taflove and M: E. Brodwin, "Numerical solution ofsteady-state electromagnetic scattering problems using the time-dependent Maxwell's equations," IEEE1hlns. Microwave Theory Tech.,vol.23,pp.623-630,·Aug. 1975.
[3) T.Weiland, "On the numerical solution of Maxwell'sequations and applications in the field of accelerator physics," Particle Accelerators,vol.15,pp.245-292,
1984.

:= -40w

V. REFERENCES

1. 67

Figure 5. Time variation of the electric field Er at point(r,z)=(47,400),and Llt = 1.668psec,. Llr = Llz = l.Omm.

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