The 13th Symposium on Accelerator Science and Technology, Suita, Osaka, Japan, October 2001

FD-TD ANALYS IS OF SLOT ANTENN AS FOR LINAC BEAM
POSITIO N MONITO R
Shusuke NISIYAMA, Satoshi TOMIOKA and Takeaki ENOTO

Division of Quantum Energy Engineering, Graduate School of Engineering, Hokkaido University
Kita 13, Nishi 8, Kita-ku, Sapporo, Hokkaido 060-8628, Japan

Abstract
In this report, simplified slot antennas for beam
position monitor were analyzed numerically to determine the antenna structure. Generally, a slot antennais the antenna where a narrow slot was installed ona large conductor surface. However, to use a slot
antenna for a beam position monitor, the conductor
should be small to avoid the beam trajectory. Therefore, the conductor dimension and the slot configuration should be considered to get the suitable characteristics. By this study, it was found that the sensitivity
and the frequency characteristics of the slot antenna
are mainly influenced by the slot length and the slot
position on the conductor surface.

1 INTRODU CTION
We have studied on the slot antenna characteristics for a non-destructive beam position monitor[!]. In
general, a slot antenna is composed of a narrow slot
on a conductor surface. An incident electromagneti cfield induces currents on the conductor surface and thesurface current across the slot makes electric potential
difference between the slot edges. Therefore, incident
electric field across the slot can be detected by theslot antenna. To use slot antennas for a beam position
monitor, the conductor surface should be placed perpendicularly adjacent to the beam trajectory. This isbecause the electric field of a relativistic charged beam
is concentrated to perpendicular direction of the trajectory. Therefore, the conductor should be small to
avoid the beam trajectory.
In our recent experimental studies[2][3], slot antennas were made on H-wall of small and thin rectangular waveguide resonators. The detected signal power
was almost inversely proportional to the square of thedistance between the beam and the slot. The beam
position between two slot antennas was calculated by
the ratio of the sum and the difference of the detectedsignals. However, the sensitivity and the frequency
characteristics of these slot antennas were influenced
by the resonator dimension, the slot length, and thefeed point structure. It was difficult to characterize theslot antennas by the experiments using S-hand multibunch LINAC because of the discrete electromagneti cfield spectrum.
In this report, to determine the suitable conductor dimension, slot position, and slot size for a beam

monitor, the current density on the conductor surface
of a simple model is calculated by the finite-differencetime-domain (FD-TD) method[4].

2 INDUCED CURRENT ANALYSIS
2.1 Analysis System
First, the induced current on the conductor surface was calculated numerically. The numerical analysis system is shown in Fig. 1. A thin perfect conductor
plate was placed perpendicularly adjacent to the beam
trajectory. The plate dimension was 30 mm x 30 mm
and the thickness was infinitely small. The beam was asingle bunch 45 MeV electron beam. The distance between the beam trajectory and the nearest plate edge
was 15 mm.
This analysis was carried out by the scattered field
FD-TD method using point charge responses[5]. Theanalysis space consisted of 1 mm cubical unit cells andthe discrete time step was 1.9 ps. With these space andtime resolution, the electromagneti c field could be calculated with enough accuracy up to 30 GHz frequency.
To simulate free space, all outer 12 cells of the analysis space were the Berenger's perfectly matched layer(PML) absorbing boundary[6].

r<:beam trajectory

yobservation point

Figure 1: Schematic of the numerical system for induced current analysis.

2.2 Numerical result-364-The 13th Symposium on Accelerator Science and Technology, Suita, Osaka, Japan, October 2001

Fig. 2 shows the surface current waveforms at observation points, A-E. Because of the system symmetry, the surface currents at these observation points
had x direction components only. The beam bunch
FWHM was 10 ps.
At t = 105 ps, the beam bunch passed the sideof the conductor plate and the incident electric field
induced surface current directed to the beam all overthe upstream side surface simultaneously. The surface
current density was inversely proportional to the distance to the beam trajectory.
Positive charges were concentrated at the nearest
point to the beam on the conductor plate by the induced current. Then the positive charges moved to theopposite edge. At the observation point A, the moving charges made current peak at 23.5 ps after passing
the beam. The 23.5 ps delay is equivalent to 7.0 mm
distance with the velocity of light. However, the distance of the point A and the edge was 5.5 mm. The
peak time difference at point A and B was 17 ps. It
is equivalent to 5 mm, that is the distance between
these points. The excess 1.5 mm (5 ps), therefore,
seems the capacitance effect of the edge. The positive
charges passed at the observation point from A to E
sequentially with 17 ps interval and the peak current
density decreased exponentially with the distance fromthe edge.
Since the second current peak was opposite polarity with the first peak, current spectrum was enhanced
at the frequency that the cycle time was twice of thetime difference between these peaks. Fig. 3 shows
the contour map of the surface current spectrum on
the center of the conductor surface. The abscissa isdistance from the beam side edge of the plate andthe ordinate is frequency. At 10 GHz or higher frequency, the large current density area was found at 3-8mm away from the edge. The distance, however, wassmaller than a half of the wavelength. It was nearly aquarter of the wavelength. Because of the capacitanceeffect of the edge, and because at closer position to thebeam the surface current was greater, the large current
density area shifted to the beam side. At 4 GHz, thehalf wavelength resonant occurred and at lower frequency the current density was small. In other analyses with different conductor plate dimension, similar
results were obtained.

3 SLOT VOLTAGE ANALYSIS
Next, a slot was placed on the perfect conductor
plate and electric potential difference between the slot
edges was calculated. The numerical analysis system
is shown in Fig. 4. A 20 mm, a 10 mm, and a 6 mm
length slots were analyzed, respectively. These slots
were 2 mm width and were placed on the plate 5 mm
away from the beam side edge. At the slot position,
the surface current spectrum intensity variation wasi'2 o 1------oo;;:,······+········r···b·F-~:_.····.~..... _----- _,,0.5 !-······································'··················/···>"'\·\········/"·······,··_+j:·····.········································+·····································~--"-'-"~,•0.5 •• ••~om••••••••••••••••••+••••••••••••••••••••••••••••••••••••••••••••••••;•••••••••••••••••••••••••••••••••••••••••••

1-zw·1a:a:::::>(.)-1.5w~a:~~!--·······································

pointA - B ••••••••.

c .......... .

HJ·································+··········································

D-•·•·•·•·•·-2.5 L.-_ _ __.__ _ _ _.....__ _ ____.....__E___.

10050200150
TIME [ps[250Figure 2: Surface current density at each observation
point.

CURRENT SPECTRUM INTENSITY [arb. unit]

3.530

325'N

2.5iSz 15

2::::>

1.5~ 20w~a: 10lL

50.500051015202530DISTANCE FROM BEAM SIDE EDGE [mm]Figure 3: Contour map of surface current densityspectrum.
small in 10 GHz or higher frequency range. The slot
voltage spectra are shown in Fig. 5. Each spectrum
made a peak at half wavelength resonant frequency.
The peak intensity of the spectrum was almost proportional to the slot length. Since these slots wererelatively wide, each slot length was about 0.45 wavelength at the resonant frequency.
Fig. 6 shows spectra of same 6 mm length slot at
different slot positions. Each distance between the slot
and the beam side edge of the plate was (a) 5 mm,(b) 10 mm, and (c) 15 mm, respectively. In Fig. 3,
the surface current spectrum contour map, it is foundthat at 22 GHz or higher frequency current spectrum
decreased at position (b). The slot voltage spectrumat position (b) also decreased at 22 GHz or higher frequency. At position (c), the surface current spectrum
was decreased at 12-22 GHz, and the slot voltage spectrum was also decreased in the same frequency range.
Consequently, the slot position should be determinedwith considering the surface current distribution at thesignal frequency.

-365-

The 13th Symposium on Accelerator Science and Technology, Suita, Osaka, Japan, October 2001

~beam trajectory:$i

Position ~a~: d= 5mm - b: d=10mm ---··
c:d~15mm ··········'i0.8--··········-····-···5...·-···········-···-···;·····-...················r-···--·:·-·····-··t·······-······-··-··i...-·-·-····-·········

0.6.
.........,1 --·-·····--·--------~----------·····:··- ..............,.J._____________

::;;

:::1
II:

y~
30mm x 30mm~

(!)

~

i

__J

0.4~

~

0.2

2.5 r---,---.,....--"T""--"""'::sl:-:ot-::2x2:-.::0:-m.-m-----_---,

·;::
""
::>

i::;;

2x10mm ······-·
2x6mm ··-·······

2 1--··--··········-·····i-····lt·--+·-·····-·······1·······-----j:::1~

ii!-····--····--··-·+··- ···················-····+-···--··············...

1.5 1-····--······--·········+-··f

D..

enw

~
~~

0.5

0~~~~~~--~--~--~~==~
05

101520FREQUENCY [GHz]2530

Figure 5: Slot voltage spectrum. Each slot length was
20mm, lOmm, 6mm, respectively.

4 CONCLUSION---~-----·----····-······- ........1!

5Figure 4: Schematic of the numerical system for slotvoltage analysis.

iiFigure 6:101520FREQUENCY [GHz]Slot voltage spectrum at various position.

76[2] S. Nisiyama et al., "Spectra Measurement of theLINAC Beam Nearfield Using Slot Antennas", The
22nd Linear Accel. Meeting in Japan, Sendai, Japan{1998) 81[3] S. Nisiyama et al., "A Harmonics Selective Slot Antenna for Beam Position Monitor" , The 23rd LinearAccel. Meeting in Japan, Tsukuba, Japan {1999) 181(4] K. S. Yee, "Numerical Solution of Initial Boundary Value Problems Involving Maxwell's Equations inIsottopic Media", IEEE Trans. Antennas Poropagat.,14 {1966) 302(5] S. Nisiyama et al., "FD-TD Analysis of Scattered Fields
Excited by a High Energy Pulsed Beam of Charged
Particles Using Point Charge Responses", IEEE Trans.
Magnetics, 36 {2000) 888[6] J. P. Berenger, "A Perfectly Matched Layer for theAbsorption of Electromagnetics Waves", J. of Comp.
Phys., 114 {1994) 185

In this report, simple slot antenna models wereanalyzed numerically with the scattered field FD-TD
method. It was found that the slot antenna has goodsensitivity at the half wavelength resonant frequency
even if the electromagnetic field is not a plane wave but
is generated by an adjacently passing beam. The sensitivity is almost proportional to the slot length. Theslot position on the conductor surface affects the sensitivity. The sensitivity is enhanced at the frequency
that the distance between the slot and the beam sideedge of the plate corresponds to a quarter of the wavelength.
For more exact analysis, the feed point structure
and the impedance of the antenna should be considered.

5 REFERENCES[1] T. Enoto et al., "Beam Position Monitor by Slot Antennas", The lOth Linear Accel. Meeting in Japan, (1985)-366-