Plasma and Fusion Research: Regular Articles

Volume 14, 3402122 (2019)

Prototype of a Quasi-Optical Launcher System of a 4 mm
Round-Trip Interferometer for the QUEST Spherical Tokamak
Experiments∗)
Miu YUNOKI, Hiroshi IDEI1) , Kazuo NAKAMURA1) , Masaharu FUKUYAMA, Ryuichi ASHIDA,
Daichi OGATA, Takumi ONCHI1) , Ryuya IKEZOE1) and Masayuki YOSHIKAWA2)Interdisciplinary Graduate School of Engineering Sciences, Kyushu University, Fukuoka 816-8580, Japan
1)
Research Institute for Applied Mechanics, Kyushu University, Fukuoka 816-8580, Japan
2)
Plasma Research Center, University of Tsukuba, Ibaraki 305-8577, Japan(Received 9 January 2019 / Accepted 16 April 2019)
A launcher system for a round-trip interferometer, with a corrugated horn antenna and two quasi-opticalmirrors, has been developed for the QUEST spherical tokamak experiment. The corrugated horn antenna has
been designed using a three-dimensional (3D) electromagnetic simulator. At low power bench test, intensityand phase profiles at 0.1 m from antenna aperture show coaxial patterns as predicted by the 3D simulator, inagreement with the calculation results using an in-house developed Kirchhoﬀ integral code. The designed waist
sizes of the focused beam at a target position are 22 mm in the horizontal x direction and 43 mm in the vertical y
direction. The beam reaches the target plate at QUEST’s center-post and is reflected back along the line-of-sightround-trip. A well-focused beam of 32 and 36 mm in size (x, y) has been obtained at the target position. The HE11
mode excitation, beam transmission, and focusing properties are discussed for the prototype launcher system.
c 2019 The Japan Society of Plasma Science and Nuclear Fusion ResearchKeywords: QUEST, spherical tokamak, interferometer, electron density measurement, corrugated horn antenna,quasi-optical mirror, Gaussian beam
DOI: 10.1585/pfr.14.3402122

1. Introduction
The millimeter wave interferometer is a major diagnostic tool for measuring plasma electron density in nuclear fusion research. A new 4 mm heterodyne interferometer has been developed for the QUEST spherical tokamak
experiments. The QUEST device is equipped with a hot
first wall to control hydrogen recycling [1]. A complex
water cooling system has been installed behind the hot walland the flat-end plates. Vertical chords were not available
for the interferometer setting in the vacuum vessel due tointerferences with the flat top and bottom divertor-plates
and the water cooling system.
Since the tangential chords with a magnetic axis in
the plasma are substantially long, a line-of-sight roundtrip was considered for the interferometer at the mid-plane.
The proposed launcher system consists of three components, i.e., a corrugated horn antenna and two quasi-optical(QO) mirrors. The Gaussian beam, converted from an output HE11 mode of the corrugated horn antenna, is focusedat the center-post target with two QO mirrors. The incident and reflected waves are sampled by three-port directional couplers at a stage prior to the launcher system. The
reflected-wave phase is measured by contrasting it with theauthor’s e-mail: 2ES17232W@kyudai.jp, idei@triam.kyushu-u.ac.jp∗) This article is based on the presentation at the 27th International Toki
Conference (ITC27) & the 13th Asia Pacific Plasma Theory Conference(APPTC2018).

incident wave phase, after being transmitted twice throughthe plasma.
The corrugated horn antenna was designed with athree-dimensional (3D) electromagnetic simulator, using
the software COMSOL Multiphysics. The performanceof the horn antennas was verified in low-power test at
Kyushu University facilities [2]. Because of limited space,
we adopted the configuration using a two-mirror system
so that the QO beam can be 99% transmitted for the interferometer. The two QO mirror surfaces were designed
using a developed Kirchhoﬀ integral code and Gaussian
optics with a phase-matching concept [3]. A similar twomirror launcher system has also been developed for the
28 GHz ECHCD and EC plasma ramp-up experiments at
QUEST [4]. The total QO-transmission and focusing performances of the launcher system in the interferometer
were also benchmarked with low-power tests.
In this paper, Sections 2 and 3 describe the development of the corrugated horn antenna and the two-mirror
system, respectively. A summary is given in Section 4.

2. Development of the CorrugatedHorn Antenna
The corrugated horn antenna has been widely used toexcite a linearly polarized coaxial beam in various QO applications. In the corrugated horn antenna, a fundamental

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c 2019 The Japan Society of Plasma
Science and Nuclear Fusion Research

Plasma and Fusion Research: Regular Articles

Volume 14, 3402122 (2019)

circular TE◦11 mode at the antenna input is transformed into
the HE11 mode, polarized linearly at the antenna output.
The amplitude profile of the HE11 mode is expressed as a0-th order Bessel function J0 similar to a Gaussian profile,and the curvature of the phase front depends on the open
(half cone) angle of the antenna.

2.1

Design of the antenna

The corrugation parameters and profile of the antenna
determine its performance. Figure 1 illustrates the coaxial
series profile of the j-th corrugation slots, with top-radiia j and depths d j ( j = 1..., ..., N), together with the ai andao of the input and output aperture radii of the antenna,
where N is the total number of the slots. The corrugation
pitch and slot widths, p and w, are also shown in the figure.
The antenna length L, is expressed as L = (N − 1)p + w.
A broadband antenna with operating minimum and maximum frequencies of fmax = 75 GHz and fmin = 108.6 GHz
are considered here. Some of the antenna’s corrugation
parameters were selected along some design of the corrugated horn antenna [5], as shown in Table 1.
The first five corrugation slots from the input, ofj ≤ Nmod (= 5), were used for the incident TE◦11 mode
to be mode converted to the output HE11 mode. A modeconverter method with variable-depth slots was adopted.
The corrugation depths d j of [Nmod < j ≤ N] should normally be equal to the quarter wavelength, except for themode conversion section, but the depth d j was considered
as a function of the aperture radius a j along with the designs. The input aperture radius of the antenna ai was
1.59 mm, which is a fundamental circular waveguide size.

2.2 Simulated results and discussion on thedesigns
The radiation field was evaluated using a 3D electromagnetic model, using COMSOL, in the operating frequency of 75.09 GHz. The corrugation profile and parameters of the antenna listed in Table 1 were modeled using
COMSOL, and the incident TE◦11 mode was excited at the
input to be transformed into the HE11 mode in the first fiveslots. Figures 2 (a) and (b) show the input and output field
amplitudes indicated by arrows. The arrow size and direction express the magnitude and the polarized direction of
the amplitude, respectively. The magnitudes are also indicated in the color mapping by means of arrows. The incident circular TE◦11 mode is mainly polarized in the horizontal direction, but it is bent toward the normal direction to
the waveguide wall because of zero tangential fields on thewall. The incident wave was correctly transformed into theHE11 mode, polarized horizontally at the output. A linear
polarization was properly obtained at the output aperture.
The HE11 mode contents of the simulated complex field pattern were evaluated. The mode contents,
C f g , of a target complex amplitude f (x, y) against theHE11 eigenmode g(x, y) is written as [6],2 f (x, y)g∗ (x, y)dxdyCfg = ,| f (x, y)|2 dxdy · |g(x, y)|2 dxdy

(1)where complex amplitudes are definedby the intensityI(x, y) and phase Φ(x, y) profiles as I(x, y) exp[ j Φ(x, y)].
The target complex field f (x, y) at the output aperture wasinterpolated from the grid field data in the COMSOL using

Fig. 1 Geometric parameters of the corrugated horn antenna.
Table 1 Design parameters of corrugated horn antenna.

Subject
Aperture radii ai , ao [mm]Pitch and slot width p, w [mm]N, mode-converter slot number Nmod
Depth d j ( j = 6, ... , 60 ) [mm]Opened ( half cone ) angle [degree]

Parameters
1.59, 8.60
0.67, 0.47
60, 50.89 - 0.74
9.07

Fig. 2 (a) Input and (b) output field amplitude indicated by arrows. The arrow size and direction express the magnitude
and polarized direction of the amplitude. The magnitudes
are also indicated in the color mapping by means of arrows. (c) Directivity of the forward (FWD) and backward(BWD) components. (d) Radiation field pattern. Figures(c) and (d) are plotted in logarithmic scales.

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the two dimensional (2D) cubic spline method. The mode
contents of the expected HE11 mode in the simulated field
was calculated as 0.94 by Eq. 1, indicating proper excitation of the HE11 mode at the antenna. The antenna wassurrounded by perfect matching layers in the COMSOL
modeling, and the forward (FWD) and backward (BWD)
radiation fields were evaluated. Figures 2 (c) and (d) show
the directivity of the FWD and BWD components, and theradiated amplitude pattern. Excellent directivity and radiation pattern, without noticeable side lobes, were also
obtained in the COMSOL simulation.

2.3

Low-power antenna tests

Fig. 3 Schematic diagram of 75 GHz low-power test facilities.

2.3.1 Measurement system for low-power tests
The operating frequency was 75.09 GHz for the 4 mm
interferometer. A schematic diagram of the measurement
system is shown in Fig. 3. The fine frequency was selected to have low reflectance at a quartz vacuum windowof 12 mm of thickness, as shown in Fig. 6 (a). The millimeter wave of the frequency was generated with a synthesizer
output (3.128750000 GHz) and two active-frequency doublers and an six times active-frequency multiplier. The
75 GHz wave generated was fed to the corrugated hornantenna via a transducer and a WR10 directional coupler. Here, a conventional transducer from fundamental
WR10 rectangular to circular waveguides was also used.
The propagating wave from the corrugated horn antenna
was measured for heterodyne detection, using a sixth harmonic mixer. A local oscillator wave (12.526666667 GHz)
generated by the synthesizer (3.131666667 GHz) and two
active doublers were used for the heterodyne detection,and the intermediate-frequency wave of 70 MHz was measured using a network analyzer. The two synthesizers werephased-locked with a 10 MHz reference wave. Band-passand high-pass filters were used to reject unwanted harmonic components from the doubler. The intensity ratio
and phase diﬀerence between the propagating and reference waves were detected at the analyzer. The reference
wave was sampled at the directional coupler installed before the corrugated horn antenna. A 3D stage controlled
by a PC was set in front of the corrugated horn antenna,or the launcher system, when measuring the propagating
beam profile.
2.3.2

Radiated-field measurement results and discussion
The intensity and phase profiles of the beam radiatedfrom the antenna were measured at a propagating distancez of 0.1 m. In the antenna test, the vertical electric field
was excited and measured. Figure 4 shows the measured
intensity and phase contour plots, indicating the coaxial
Gaussian-like intensity and parabolic phase patterns. Here,the x and y coordinates (horizontal and vertical directions)are perpendicular to the propagating direction, z.
The measured radiation profiles on the x and y axes

Fig. 4 Measured (a) intensity and (b) phase patterns of the corrugated horn antenna at a propagating distance z = 0.1 m.

are compared with those computed in the COMSOL simulation and calculated using a developed Kirchhoﬀ integral
code. The Kirchhoﬀ integral of the radiation field E rad isexpressed as [6]: 
1exp(− jk0 r)
rad
E (x, y, z) =E(x2 , y2 )
4π
r

1z
× jk0 +
dx2 dy2 ,(2)r r
r = (x − x2 )2 + (y − y2 )2 + z2 ,(3)
where (x, y, z) and (x2 , y2 ) are the coordinates of the radiation point and of the antenna output aperture, with a coordinate origin at the center of the aperture. The integral
range is within the aperture radius ao . The aperture field
E (x2 , y2 ) was interpolated from the COMSOL grid datausing the cubic spline method, and was integrated inside
the aperture.
Figure 5 shows the intensity and phase profiles on thex and y axes, measured at low-power level, simulated using COMSOL, and evaluated using the Kirchhoﬀ integral,at the propagation distance z = 0.1 m. The measured intensity and phase profiles are in good agreement with the simulation results. The Kirchhoﬀ integral results agreed wellwith the measured and COMSOL simulated data, althougha remark should be made: in the irradiant beam-profiles
shown in Fig. 5, measured and COMSOL results containdiﬀraction but results for the Kirchhoﬀ integral not.

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Fig. 5 Measured intensity and phase profiles in horizontal x
and vertical y axes, along with the COMSOL and Kirchhoﬀ integral code calculations at a propagating distancez = 0.1 m.

3. Development of a Two-Mirror
Launcher System
A two-mirror launcher system was required to focus
the beam on the center-post for the round-trip interferometer, as mentioned in Section 1. The center-post wasboarded up with small stainless-steel flat plates of 70 mm
in width and 170 mm in height. If the waist position of thebeam, z0 , can be placed on a flat plate at the center-post,
the beam can be correctly received by the same optics forthe injection. The two-mirror launcher (and receiver, in asense) system is a key component in the round-trip interferometer, together with the corrugated horn antenna.

3.1

Design of the launcher

First, geometrical mirror sizes should be considered
for the launcher system to be installed in limited spaces.
The mirror size should be larger than 3w. Here w is thebeam size in Gaussian optics [7] at the mirror. When thesize is larger than 3w, beam intensity of more than 99%
can be covered [8]. The waist sizes w0x of 22 mm and w0yof 43 mm were chosen on the target plate to provide the 3w
sizes at the center-post plate in the x (width) and y (height)
directions, respectively. The second mirror size of 3w wasevaluated by propagation analysis from the center-post to
the mirror, in Gaussian optics. The beam radiated fromthe corrugated horn antenna must be correctly transmitted
to the second mirror. The first mirror position aﬀects thebeam transmission function. The incident angle to the mirror should be considered to be as small as possible in orderto reduce asymmetry at the beam center in the beam steering direction. If the first mirror position is too far from thecorrugated horn antenna, the first mirror would be larger insize to attain 99% transmission, whereas the incident angle
to the mirror would be smaller. The mirror edges sometimes have interferences on the transmission, depending on
the mirror configuration. The position and size of the firstmirror were determined in order to attain 99% transmission

with a smaller incident angle to the mirror. Figure 6 shows
the two-mirror configuration of the final launcher systemin the design work, along with the target.
The irradiant beam from the antenna would be expanded to obtain a larger beam for focusing onto the target center-post plate by the second mirror. The irradiantHE11 mode phase front at the first mirror was converted
into a Gaussian beam phase front to achieve the designed
expanding beam to the second mirror. The propagatingphases before and after the first mirror reflection were evaluated using the Kirchhoﬀ integral and Gaussian optics, respectively, and the first mirror surface was designed using
a developed, phase-matching code with the Kirchhoﬀ integral. The phase front of the expanded Gaussian beamat the second mirror would be converted into a designed
Gaussian-focusing beam with w0x and w0y at the target
plate. The second mirror surface was designed using a similar phase-matching code using only Gaussian optics.
The designed mirror height contour plots of the firstand second mirrors (M1 and M2) are also shown in
Figs. 6 (b) and (c). The mirror height profiles are asymmetric in the beam steering xm direction, as expected, particularly at M2. The mirror coordinates (xm , ym ) are illustrated in the figure. Since strong focusing is requiredin the x direction (width) of the target center-post plate,the beam should be further expanded in this direction withthe convex mirror curvature toward the second mirror. The
first mirror surface was saddle shaped, or a hyperbolic
paraboloid structure; i.e., it was concave and convex in
the xm and ym directions in order to obtain the diﬀerent
expanding properties in two directions, respectively, withasymmetry in the xm direction. The second mirror surface
was an elliptical paraboloid structure with relatively strong
asymmetry in the xm direction. A photograph of the twoaluminum-mirror system fabricated is shown in Fig. 6 (d).

3.2 Low-power tests on the launcher anddiscussion
The launcher performance was verified at the lowpower test facilities described in Section 3.1. The receiver of a sixth harmonic mixer with a fundamental WR10
waveguide was set at the target plate position where itis 1.354 m away from the M2, as illustrated in Fig. 6 (e).
Figure 7 shows the intensity and phase contour plots ofthe focused beam measured at z = 1.354 m. The vertically elongated rectangular frames are shown as the target center-post plate area in the figure. Here, the beam
fields were measured without the quartz window shown in
Fig. 6 (a). The detailed eﬀect of the quartz window on the
beam focusing will be a topic of discussion for a future
work, although a less eﬀect has already been verified byour measurements.
In the launcher test, the horizontal field Ex was excited
to demonstrate the O-mode operation of the interferometer
in QUEST. The beam was accurately focused on the target plate with a relatively flat-phase front. Figure 8 shows

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Fig. 6 (a): Launcher configuration with a focusing target. (b) and (c): Designed height h contour plots on the first and second (M1 andM2) mirror surfaces. The mirror coordinates (xm , ym ) are illustrated in the figure. Photographs of (d): fabricated, aluminum M1
and M2 QO mirrors and (e): receiver for the low-power test. A quartz vacuum window of 12 mm in thickness is also shown in (a).

Fig. 7 Measured intensity and phase contour plots at the target
of propagation position z = 1.354 m from the second mirror. Vertically elongated, rectangular frames show the target center-post plate area of 70 mm × 170 mm.

the intensity and phase profiles on the x and y axes. The
beam sizes w x and wy in the x and y directions were 32 and
36 mm, whereas the designed sizes were 22 and 43 mm,
the same as the waist sizes, respectively. The beam was
focused almost within the target plate, as shown in Fig. 7.
The covered contents of the focused beam within the plate
were evaluated as being 0.97 from the 2D integral of theintensity pattern within a plate of 70 mm × 170 mm.
Since the phase x profile is rather flat, the target position was close to the waist in the x direction. The beam
expanded slightly in the y direction, which was suggested
from the phase y profile. The beam is rather large andsmall in the x and y, directions, respectively. The narrow phase profile evaluated using the Kirchhoﬀ integral in

Fig. 8 Measured intensity and phase profiles on the horizontal x
and vertical y axes.

Fig. 5 might aﬀect the focusing property, slightly diﬀeringfrom the design. The first mirror position of z = 0.103
was very close to the propagation position of z = 0.1 m in
Fig. 5. Again, the Kirchhoﬀ integral used for the mirror
surface design did not include the diﬀraction eﬀect. The
Kirchhoﬀ integral using the complex amplitude following
some propagation will be used to include the diﬀractioneﬀect for better focusing. The modified design and verification of its performance remain to be studied in future
works.

4. Summary
The launcher system of the round-trip interferometercomposed of a corrugated horn antenna, and two QO mirrors have been developed for the QUEST spherical toka-

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mak experiments. The corrugated horn antenna was considered along the designs and COMSOL simulation. The
proper HE11 mode beam excitation was confirmed in thesimulations. The coaxial intensity and phase patterns wereobtained at a propagating distance of z = 0.1 m in the lowpower tests. These profiles matched considerably well with
the COMSOL simulations. The Kirchhoﬀ integral results
agreed well with the measurement and simulations.
The two-mirror configuration was considered in order
to attain 99% of transmission with a smaller incident angle
to the mirrors. The mirror surfaces were designed usinga Kirchhoﬀ integral code and Gaussian optics along withthe phase-matching concept. The well-focused beam, withbeam sizes of w0x = 32 mm and w0y = 36 mm, was obtained at the target position in the low-power tests. The
designed sizes were 22 and 43 mm, the same as the waist
sizes. The covered contents of 97% within the target plate
were attained for the focused beam. For better focusing,the Kirchhoﬀ integral using complex amplitude following

some propagation, including the diﬀraction eﬀect, will be
used to determine the mirror surfaces in future works.

Acknowledgment
This work was
NIFS13KUDR085.

partially

supportedbythe[1] K. Hanada et al., Nucl. Fusion 57, 126061 (2017).
[2] H. Idei et al., Nucl. Fusion 46, 489 (2006).
[3] S. Kubo et al., Fusion Eng. Des. 26, 319 (1995).
[4] H. Idei et al., Fusion Eng. Des., accepted for publication(2019).
https://doi.org/10.1016/j.fusengdes.2019.02.027[5] C.D. Granet and G.L. James, IEEE Antennas Propag. Mag.
47, 76 (2005).
[6] H. Idei et al., J. Infrared Millim. Terahertz Waves 36, 662(2015).
[7] Amnon Yariv, Quantum Electronics (John Wiley Sons Inc.,
1975).
[8] M. Sakaguchi et al., Plasma Fusion Res. 8, 1405163 (2013).

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