22P148-P
Optimization of Millimeter-Wave Components using FDTD Simulation
FDTDシミュレーションによるミリ波コンポーネントの最適化
Hiroaki NAKAMURA1,2, Koji UKITA3, Yuichi TAMURA3, Takeshi OKAMURA2, Keiji
SAWADA4, Shin KUBO1,2
1,2
中村浩章 , 浮田康司3, 田村祐一4, 岡村豪士2, 澤田圭司5, 久保伸1,2
1

National Institute for Fusion Science, Oroshi 322-6, Toki 509-5292, Japan1
核融合科学研究所 〒509-5292 岐阜県土岐市下石町322-6
2
Department of Energy Engineering and Science, Graduate School of Engineering, Nagoya University,Furo-cho, Chikusa-ku, Nagoya, Aichi 464-8603, Japan2
名古屋大学大学院工学系研究科エネルギー理工専攻 〒486-0946 愛知県名古屋市不老町
3
Department of Information Science and Systems Engineering, Graduate School of Natural Science, Konan University,
Okamoto 8-9-1, Higashinada-ku, Kobe, Hyogo 658-8501, Japan3
甲南大学大学院自然科学研究科情報システム工学専攻 〒658-8501 兵庫県神戸市東灘区8-9-1
4Department of Intelligence and Informatics, Konan University,
Okamoto 8-9-1, Higashinada-ku, Kobe, Hyogo 658-8501, Japan4
甲南大学知能情報学部 〒658-8501 兵庫県神戸市東灘区8-9-1
5Department of Engineering, Shinshu University,
Wakasato 4-17-1, Nagano, 380-8553, Japan5
信州大学工学部 〒380-8553 長野県長野市若里4-17-1
In order to improve the shape of waveguide to transport with lower-loss energy than the present
waveguide, we built up finite-difference time-domain (FDTD) simulation system for the waveguide.
In our code, the time evolution of electromagnetic field in corrugated waveguide is simulated in
two-dimensional (r,z)-coordinates calculation with perfect matched layer (PML) boundary condition.
According to this simulation, it is confirmed that the total energy of the electromagnetic fields in thewaveguide is conserved.

1. Introduction
It is necessary to provide low-loss transmissionof electromagnetic wave for electron cyclotron
heating (ECH) system to realize the nuclear
fusion generation. To achieve this purpose, a lotof researches have been being done (see Refs.
[1,2]). As one of the brilliant successes, it was
found that corrugating the walls reduces the loss
further not only in straight runs but also at bends(Fig.1) and that the corrugation makes thewaveguide robust against small deformations [1].
Moreover theoretical calculations, which arebased on a space-harmonic analysis ofelectromagnetic waves, contribute for theseproperties to be maintained over very wide
bandwidths [1]. According to their work [1], thetheoretical calculations were validated by themeasurements on waveguides.
In order to improve the waveguide to transportwith lower-loss energy than the previous design
in Ref. [1], we challenge to optimize thewaveguide structure by simulating the time
evolution of electromagnetic fields in the
waveguide by finite-difference time-domain
method (FDTD) method (see Refs. [4-6]).

corrugatedwaveguide

miter bend

Fig.1. Milli-meter transporting components, which aredesigned for Large Helical Device (LHD) in NIFS.

2. FDTD Simulation
In FDTD method, the three-dimensional
Maxwell equation is solved numerically, in theperfect matched layer boundary condition [7], forthe same situation as the experimental
configuration (Fig. 2).
Because the corrugated waveguide has thecylindrical symmetry, (i.e., continuous rotationalsymmetry) for the azimuthal angle φ, the three
dimensional simulation can be reduced to thetwo-dimensional (r,z)-coordinates calculation,
where the electromagnetic fields are proportional
to a function exp(imφ), where m is an integer(related to the angular momentum of the field).
The simulation parameters are as follows: thewave length is 3.57 mm (the frequency 84 GHz),
the spatial mesh is 0.025 mm, and the time stepΔ t = 0.33×10-11 sec. As the initial configuration,
the electromagnetic fields are set to zero in thewhole space.

Acknowledgments
The present works were supported by
Grant-in-Aid for Research (No. 19055005 and No.
23710135) from MEXT, NIFS Collaboration
Researchprogram(NIFS09KNSS002,
NIFS11KNTS008,
NIFS11KNSS020,
andNIFS11KNTS010), and NINS Program forCross-Disciplinary Study. A part of numericalsimulation was carried out by the use of the Plasma
Simulator at the National Institute for Fusion
Science.
(a)(b)

Fig. 3. The r component of magnetic field in (r, z)
plane at time 700×Δ t. (a) The normal waveguide: (b)The corrugated wave guide.
Fig. 2. Cross section diagram of the geometry in our
3D computer simulations for the corrugated waveguide(p denotes the period, w is the width and d the depth ofthe corrugation geometry).

3. Results
In Fig. 3, we draw the isosurfaces of the rcomponent of the magnetic field for the two typesof the cylindrical waveguides, that is, (a) “normal”
waveguide and (b) corrugated waveguide. In the z
direction, the shape of the electromagnetic field
seems to the plane wave, i.e., exp(ikzz), where kz is
the wave number in the z direction. We plot thetotal electromagnetic energy v.s. time t whose unit
isΔ t) in Fig. 4. When the time t is less than 100
step, the total energy is increasing. Around t~100,
there is a peak. After it, the total electromagnetic
field is stabilized. This property denotes the energy
is conserved in the simulation.
4. Conclusion
We performed FDTD simulation with PML
boundary condition for cylindrical corrugatedwaveguide in two-dimensional coordinates. The
conservation of the total electromagnetic field in the
waveguide is confirmed. In the next step, it isexpected to optimize the shape of the waveguideusing this simulation.

Fig. 4. Time dependence of the total energy forelectromagnetic field in the corrugated waveguide. Theenergy is normalized by the saturated total energy.
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Saiki: Journal of Microscopy, 202(2001) 50.
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