J. Plasma Fusion Res. SERIES, Vol. 9 (2010)

Diﬀerential-Phase Reﬂectometry and Electron Bernstein
Wave Radiometry using Phased-array Antenna Systemin the QUEST
H. Idei1) , K. Nagata2) , M. Sakaguchi2) , K. Dono2) , Y. Wataya2) , S. Ohdachi3) , S. Inagaki1) ,Y. Nagayama3) , K. Kawahata3) , H. Igami3) , T. Shimozuma3) , H. Zushi1) , K. Hanada1) ,K. Nakamura1) , M. Sakamoto1) , M. Hassegawa1) , Y. Higashizono1) , S. Kawasaki1) ,H. Nakashima1) , A. Higashijima1) , Y. Takase4) , T. Maekawa5) , O. Mitarai6) and Y. Kishimoto5)
Research Institute for Applied Mechanics, Kyushu Univ., Kasuga, 816-8580, Japan
Interdisciplinary Graduate School of Eng. Sci., Kyushu Univ., Kasuga, 816-8580, Japan
3)
National Institute for Fusion Science, Toki, 509-5292, Japan
4)
Department of Complexity Sci. and Eng., Univ. of Tokyo, Kashiwa 277-8561, Japan
5)
Graduate School of Energy Science, Kyoto Univ., Kyoto 606-8501, Japan
6)
Inst. of Industrial Sci. and Tech. Research, Tokai Univ., Kumamoto 862-8652, Japan
1)

2)(Received: 20 November 2009 / Accepted: 6 April 2010)

The diﬀerential-phase reﬂectometry has been developed to measure the density proﬁle evolution,
concering electron Bernstein Wave (EBW) heating and current drive in the QUEST. The proper phasedependence was conﬁrmed in developed single-side-band heterodyne diﬀerential-phase reﬂectometryat RIAM microwave/mm-wave test facilities. The phase time evolutions in the QUEST were also
successfully measured, but the weak reﬂected-wave caused the small ratio of signal to noise in themeasurements. The Phased Array Antenna (PAA) system was proposed for the reﬂectometry to obtainthe large reﬂected-wave. The oblique viewing EBW emission can be measured by the precise phasearray measurements between the PAA waveguide elements. The PAA was conﬁrmed to be eﬀective, asa launching antenna for the reﬂectometry, and as a receiving antenna for the EBW radiometry.
Keywords: AM reﬂectometry, Electron Bernstein wave, phased-array antenna, QUEST
Wave Heating and Current Dive (EBWH /CD) is
one of attractive candidates of heating and current
drive method to sustain the steady-state over-dense
plasma in the ST. In the EBWH/CD, some mode
conversions from an Electron Cyclotron electromagnetic Wave (ECW) to an Electron Bernstein electrostatic Wave (EBW) are required. In the Q-shu University Experiment with Steady State Spherical Tokamak(QUEST), the EBWH/CD experiments are planned
at 8.2GHz, to sustain the steady-state ST plasma [1].
The density gradient where the ECW converts to the
EBW is a key parameter to attain high conversion efﬁciency.
In the Compact PWI (Plasma-Wall Interaction)
Device, that is the small ST device in Kyushu University, an AM reﬂectometer system was developed tomeasure the density proﬁle with high time resolution(by the 10 μ s frequency switching) [2]. The developed system successfully measured the phase delay ofthe broadband (6-18GHz) reﬂected-wave at both the
CPD vessel wall and the R-cutoﬀ layers in the plasma.
The performance of the CPD AM reﬂectometry waschecked at RIAM microwave/mm-wave test facilities
in detail. The reﬂected-wave intensity was same levelto the direct coupling component between the launching and receiving antennae in the large propagat-

1. Introduction
Microwave reﬂectometry has been widely used tomeasure density proﬁle and ﬂuctuation in the fusionresearch plasma. This technique is based on a phasedelay measurement of a probing-wave propagating
and reﬂected by a cutoﬀ layer in the plasma. In
general, since the wavelength of the probing-wave ismuch smaller to the propagating length, sometimes
the phase jump was occured in the homodyne detection. It induces to mistake the counting-up, whichcauses a phase runaway phenomenon what one call.
The amplitude modulation (AM) reﬂectometry has
been developed to measure correctly the phase delay in the probing-wave propagation. The AM of the
probing-wave can be recognized as a beat between two
frequencies. The AM reﬂectometry was sometimes
called as a diﬀerential-phase reﬂectometry. The phase
diﬀerence of two probing-wave frequencies was measured in the diode detection. Since the wavelength of
the AM (diﬀerential) frequency was comparable to the
propagating length, and the so-called runaway phenomenon never happen in the AM reﬂectometry.
Detailed density proﬁle measurements are essential to study mode conversion phenomena in the spherical tokamak (ST) experiments. Electron Bernsteinauthor’s e-mail: idei@triam.kyushu-u.ac.jp

112©2010 by The Japan Society of Plasma
Science and Nuclear Fusion Research

H. Idei et al., Differential-Phase Reflectometry and Electron Bernstein Wave Radiometry Using Phased-Array Antenna System in the QUEST

ing length. The Single-Side-Band (SSB) heterodyne
diﬀerential-phase reﬂectometry has been developed totreat separately the direct coupling component andthe reﬂected-wave. The developed system was installed to measure the density proﬁle in the QUEST,
concerning the mode conversion study.
An EBW radiometry has been developed to measure time evolutions of electron temperature proﬁlesin over-dense plasmas [3,4]. The Electron Cyclotron
Emission (ECE) radiometry is widely used to measure the electron temperature time evolutions, but
the ECE cannot propagate outside the plasma dueto the cut-oﬀ in the over-dense plasma. The ECW
converted from the EBW as a reversal process of themode conversion for the EBWH/CD might propagate
outside, and detected in the radiometry. The EBW
radiometry is not only a powerful tool to measure theelectron temperature time evolutions, but also to investigate the mode conversion phenomena. The mode
conversion strongly depended on the density proﬁle,the propagating polarization and the refractive index,
N// , in parallel to the magnetic ﬁled. The receiving
angle and polarization in the EBW radiometry areimportant to clarify the mode conversion mechanism,
together with the density proﬁle measured with thereﬂectometry.
The Phased Array Antenna (PAA) was considered as a launching antenna of the probing-wave inthe reﬂectometry, and as a receiving antenna in the
EBW radiometry. The reﬂected-wave in the reﬂectometry was expected to be much stronger than the direct coupling component using the PAA. In the EBW
radiometry, the receiving angle and polarization were
measured with precise phase detection between the antenna elements. The prototype waveguide PAA wasdesigned and fabricated. The antenna performancewas checked in the low power test facilities.
This paper is organized as follows. Section 2 describes the SSB heterodyne diﬀerential-phase reﬂectometry. In Sections 3 and 4, the developed prototype
PAA system for the reﬂectometry and the EBW radiometry are shown, and the conclusion is ﬁnally given
in Section 5.

Fig. 1 : Phase evolution along the propagating length
measured by the AM reﬂectometry developed for
the CPD experiments.

kAM of the AM frequency in the CPD operation range.
In the large length range for the QUEST, the reﬂectometer could not detect the proper phase evolution.
In the large propagating length, the detected phase
was rapidly changed in the speciﬁc range with a period on the wavelength of the probing-wave along the
propagation. In the ﬁgure, the aliasing evolution wasappeared in the large-length operation range. There
was interference in the reﬂected probing-wave and theother components of the probing-wave frequency. The
direct coupling wave between launching and receiving antennae was considered as a counterpart for theinterference. The diﬀerential-phase [2(k1 − k2 )x], or[2kAM x], in two frequencies [ω1 and ω2 ] probing-wave
should be measured at the diode detection in the AM
reﬂectometry. The phases of the direct coupling components were expressed in terms of [k1 x′ and k2 x′ ]with a representative length x′ for the coupling. Spurious phase diﬀerences [ 2(k1 x−k2 x′ ) and 2(k1 x′ −k2 x)] were detected as cross terms at the interference in thediode detection. If the reﬂected signal level was muchhigher than the direct coupling level in the CPD operation range, the spurious components did not aﬀect
the detected phase well.
In the CPD AM reﬂectometry, the two frequency probing-waves were prepared in upper/lowerside bands (USB/LSB) at the up/down frequency converter [1]. In order to avoid the interference with thedirect coupling wave, the USB and LSB components
were separately measured in a heterodyne detection
using an image rejection mixer. The intermediate frequency (IF) signal at the mixer was demodulated in an
IQ operation, and the IF phase was measured at the
IQ demodulation mixer. The diﬀerential- phase dependence [2(k1 − k2 )x] can be evaluated from subtraction of the LSB phase dependence from the USB phasedependence. This operation to detect the diﬀerentialphase was based on the SSB heterodyne detection
technique. Figures 2 show Lissajous curves of the USB
and LSB signals in the large propagation length range
shown in Fig.1. The Lissajous curves were oﬀ-center.
The oﬀset coordinates expressed the direct coupling

2. SSB Heterodyne Diﬀerential-Phase
Reﬂectometry
2.1 Direct coupling eﬀect
Figure 1 shows the phase evolution along the
propagating length measured with the CPD AM reﬂectometry at the low power test facilities. In thetest, the reﬂecting aluminum plate was moved to scan
the propagating length. Here, x was the distance between the reﬂectometry antennae and the plate. The
phase evolution along the propagation was expressedwith a linear dependence [2kAM x] on the wave number

113

H. Idei et al., Differential-Phase Reflectometry and Electron Bernstein Wave Radiometry Using Phased-Array Antenna System in the QUEST

Fig. 2 : Lissajous curves of the (a): LSB and (b): USB
phases in the SSB heterodyne diﬀerential-phase reﬂectometry.

Fig. 4 : Time evolutions of the incident RF power, theHα intensity, the measured phase of the LSB/USB
IF phases, the subtracted phase in the SSB heterodyne diﬀerential- phase reﬂectometer.
Fig. 3 : Phase evolution along the propagation in the developed SSB heterodyne diﬀerential-phase reﬂectometry.

major radius R=0.7m when the plasma was producedby the incident 8.2GHz RF power of 50kW. The electron density at the R-cutoﬀ layer of the 8GHz frequency was evaluated as 4.1 × 1017 m−3 .
Figure 5 shows the Lissajous ﬁgure of the USB
phase in the QUEST. The ratio of the reﬂected wave
(or the Lissajous radius) to the direct coupling component (or the Lissajous oﬀset) became small in the
QUEST, compared to that in the low power test as
shown in Figs.2. In the QUEST, the launching andreceiving quad-ridged waveguide antennae were set infront of a quartz vacuum window. The inner wall of
the QUEST vessel is not a plane. The reﬂected wave
became weak in the QUEST setup. The subtracted
phase in the developed SSB heterodyne diﬀerentialphase reﬂectometor did not show the proper density
decay after turning oﬀ the RF injection due to thesmall reﬂected-wave signal, as shown in Figs.4. Figure 6 shows the counted fringe time evolutions of the
LSB/USB phases and of the subtracted AM phase in
the density decay. The propagating distances of the
8 GHz wave were about 2.6m and 1.6m at the walland the cutoﬀ- reﬂections, respectively. The around27 fringes should be counted in the density decay, but
a number of the fringes ( more than 100 fringes ) werecounted, as shown in Fig,6. The phase jump between
the phases of ±π due to the small reﬂected-wave signal caused the fringe miscount in the density delay.
The reﬂected-wave signal level should be essentially

IQ components. The oﬀset was comparable to the
Lissajous radius which showed the reﬂected signal amplitude. The radius or reﬂected signal amplitude wasdecreased along the propagation length, showing thespiral curve in the ﬁgure. In the larger propagation
length, the center-oﬀset (direct coupling) aﬀected signiﬁcantly the phase measurements in the diode detection at the AM reﬂectometry, and the measured phasewere changed in the speciﬁc region of the Lissajous
ﬁgure. Figure 3 shows the subtracted phase evolution
along the propagation after the removal of the centeroﬀset in the Lissajous ﬁgure. The measured phase evolution along the propagation was properly expressedwith the linear dependence [2kAM x] on the wave number kAM even in the large propagation length.

2.2

Phase time evolution measured in
the QUESTThe developed SSB heterodyne diﬀerential phasereﬂectometer was installed to the QUEST. Figures
4 show time evolutions of the incident 8.2GHz RF
power, the Hα intensity, the phases of the LSB/USB
IF phases, and the subtracted phase in the developed
reﬂectometer. The operating frequency was 8GHz,
and the magnetic ﬁeld was 0.137T. First the probingwave was reﬂected at the inner wall of the QUEST
vessel, and was reﬂected at the R-cutoﬀ layer of the114

H. Idei et al., Differential-Phase Reflectometry and Electron Bernstein Wave Radiometry Using Phased-Array Antenna System in the QUEST

Fig. 5 : Lissajous ﬁgure of the USB phase in the QUEST.

Fig. 8 : Measured ﬁeld intensity and phase proﬁle, andthe calculated intensity and phase proﬁles with
1 waveguide element and 8 elements of the PAA
at a radiation position of z=600mm. (a):Ex (x),(b):Ex (y), (c)Ey (x) and Ey (y)Fig. 6 : Counted fringe time evolutions of the LSB/USB
phases and the subtracted AM phase in the density
decay after turning of RF injection.

It was expected the PAA system might focus the radiated ﬁeld with good directionality even at the larger
propagating length.
Figure 7 shows the developed prototype PAA with
8 [ 4 × 2 ] square waveguide elements. There were
8 square waveguide elements to excite two orthogonal electric ﬁeld components. The phases between
waveguide elements were adjusted to obtain a welldeﬁned straight beam for the reﬂectometry. Figure 8 shows the ﬁeld intensity and phase proﬁles,measured at the low power test facilities, at a radiated position of z=600 mm. Here, the phased-array
was set as [ ∆φ2−1 , ∆φ3−1 , ∆φ4−1 , ∆φ5−1 , ∆φ6−1 ,∆φ7−1 ,∆φ8−1 ) = ( −0.054π, −0.054π, 0, 0, −0.054π,−0.054π, 0 ) ] as a reference of the phase at the
waveguide element 1 (see Fig.7). In the ﬁgure, thecalculated ﬁeld intensity and phase proﬁles, radiatedfrom the PAA with 1 waveguide element and 8 elements, were also plotted. The calculated ﬁeld proﬁlesEx,y (x, y, z = 600) from the PAA were evaluated witha Kirchhoﬀ integral as follows,∫ a/2 ∫ a/2
ik
Ex,y (x, y, z) =dx′ dy ′(1)2πz −a/2 −a/2

increased to measure the proper phase evolution. The
PAA system was considered as a launching antenna in
the reﬂectometry to receive the signiﬁcant reﬂectedwave.

3. Prototype Phased-Array
System
3.1 Reﬂectometry Use

Antenna

The far ﬁeld radiation is important for the reﬂectometry use in the larger propagating length. In the
low operating frequency around 8GHz, the directionality of the quad-ridged antenna was not so good, andthe diﬀraction eﬀect was rather large. The direct coupling eﬀect signiﬁcantly aﬀected the performance of
the AM reﬂectmetory in the low operating frequency.

rFig. 7 : Developed prototype phased-array antenna. The
coordinates in the low power test and the numbersof waveguide elements are also shown.

× Ex,y (x′ , y ′ )[exp(−ikr)/r],√(x − x′ )2 + (y − y ′ )2 + z 2 ,=where the coordinates of (x′ , y ′ ) and (x, y) were at
the antenna aperture position(z=0) and at the radiated z position, and a was a side of the square-115

H. Idei et al., Differential-Phase Reflectometry and Electron Bernstein Wave Radiometry Using Phased-Array Antenna System in the QUEST

waveguide, respectively. The beam was diverged in
the large propagating length of z=600 mm with 1
waveguide element, but was focused with good directionality with the phased-array of the 8 waveguide elements. The measured intensity and phase proﬁleswere well explained with the Kirchhoﬀ integral calculation in general, but the measured intensity proﬁleEy (y) was narrower than the calculated proﬁle. The
ﬁeld Ey (x′ , y ′ ) at the waveguide aperture was excited
nearby at the waveguide boundary walls between 4 upper waveguides and lower ones. There were the direct
couplings between the upper and lower waveguide series. The Ey (y) radiated from each waveguide element
was anti-symmetric in the y direction due to the direct
coupling eﬀect. Since there were only the 2 waveguideseries in the developed PAA, the phased-array eﬀect
was weak to focus the beam in the y direction. The
broader Ex (y) and Ey (y) proﬁles were obtained, compared with Ex (x) and Ey (x), due to the weak phasedarray eﬀect in the y direction.
The beam radiated from the PAA was focused
well, in particular in the x direction. The PAA shouldbe eﬀective to take the large reﬂected wave signal in
the reﬂectometry. Figure 9 illustrates the setup of thelaunching phased-array antenna and a receiving antenna for the reﬂectometry. Since the broader beam
was obtained in the y direction, the signiﬁcant reﬂected wave can be detected by the receiving antenna.
In order to reduce the direct coupling eﬀect between
the launching and receiving antennae, the receiving
antenna was set up at a distance from the launching
PAA. Figure 10 shows the phase evolutions along the
propagation in the SSB heterodyne detection, withand without removals of the Lissajou oﬀsets (direct
coupling eﬀect), and with 1 or 8 waveguide elements at
the PAA. Although the Lissajous oﬀsets were numerically removed in the Fig.3, the oﬀsets depended on
the scanning operation-frequencies to obtain the density proﬁle. In the Fig.9, the RF circuit components
were added to remove the oﬀsets. The oﬀsets can beremoved by the voltage control of the phase shifterand the attenuator with enough time resolution. The
good phase evolution was obtained along the propagation even with 1 waveguide element by the additional
RF circuits. The proper phase evolution was also obtained along the propagation using the PAA without
the oﬀset removal. Although the reﬂected wave signal was reduced in the QUEST experiments, the PAA
will work well to obtain the signiﬁcant reﬂected wave
in the larger propagating length. The launching PAA
and the additional RF circuits for the oﬀset removal
at the receiving antenna will be adopted in the reﬂectometry.

Fig. 9 : Illustration of launching phased-array and receiving antennae for the reﬂectometry in the low power
test facilities.

Fig. 10: Phase evolutions along the propagation: (a) without the oﬀset removal by 1 waveguide element of the
PAA, (b) with the oﬀset removal by 1 waveguide element of the PAA, (c) without the oﬀset removal
by 8 waveguide elements of the PAA, and (d) withthe oﬀset removal by 8 waveguide elements of the
PAA.

3.2

EBW Radiometry Use

The ray tracing and Fokker-Planck analyses werereported in the O-X-B scenario for the EBWH/CD
experiments in the QUEST [1]. The incident oblique
ECW met the O-mode cut oﬀ layer and was converted
to the X-mode ﬁrst. This X-mode was converted into
the EBW at the upper hybrid resonance layer. The
power deposition and driven current proﬁles were obtained in the analyses. The electron density and temperature, and plasma current proﬁles were assumed
in the analyses. The electron temperature proﬁle wasalso important, in particular to the driven current
evaluation with the Fokker-Planck analysis, together
with the density proﬁle.
The EBW radiometry has been developed to measure time evolutions of electron temperature proﬁles in116

H. Idei et al., Differential-Phase Reflectometry and Electron Bernstein Wave Radiometry Using Phased-Array Antenna System in the QUEST

Fig. 11: Calculated and measured ﬁeld intensity and phaseproﬁles at z=200mm, obliquely radiated from the
PAA. (a):Ex (x), (b):Ey (x).

Fig. 12: Frequency dependence of VSWR at the developed
orthomode transducer.

over-dense plasmas. The ECE radiometry was widelyused to measure the electron temperature time evolutions, but the ECE cannot propagate outside theplasma due to the cut-oﬀ in the over-dense plasma.
The ECW converted from the EBW as a reversal process of the mode conversion at the EBWH/CD propagated outside, and detected in the radiometry. The
PAA was also considered as a receiving antenna in theradiometry to measure the oblique viewing EBW.
Figure 11 shows the ﬁeld intensity and phase proﬁles Ex (x) and Ey (x) at z=200 mm, obliquely radiated from the PAA. Here, the phased-array wasset as [ ∆φ2−1 , ∆φ3−1 , ∆φ4−1 , ∆φ5−1 , ∆φ6−1 ,∆φ7−1 ,∆φ8−1 ) = ( 0.55π, 1.21π, 1.97π, 0, 0.55π,
1.21π, 1.97π ) ] as a reference of the phase at the
waveguide element 1. The measured ﬁelds were in excellent agreement with the calculated ﬁelds from theKirchhoﬀ integral. The oblique beam was obtained
at two orthogonal electric ﬁeld components by thephase adjustments between the PAA waveguide elements. The oblique viewing EBW emission will beobserved by the precise phase-array measurements between the waveguide elements. The broadband OrthoMode Transducer (OMT) has been developed for
the EBW radiometry to measure the two ﬁled components. Figure 12 shows the frequency dependence of
VSWR at the developed OMT. The low VSWR (< 2)was obtained in the broadband frequency range of 814.5 GHz, and it was expected to work well for the
EBW radiometry. The ellipse polarization states for
the X and O-modes can be measured by the intensityratio and phase-diﬀerence measurements between the
two OMT ports at each PAA waveguide element.

nent between the launching and receiving antennae
aﬀected the measured phase evolution along the propagation. The SSB heterodyne diﬀerential-phase reﬂectometry was proposed to remove the direct coupling component. The proper phase evolution in thelarger propagation length was conﬁrmed in the developed reﬂectometry at the low power test facilities.
The phase time evolutions in the QUEST were also
successfully measured, but the weak reﬂected-wave affected the measurements. In order to receive the larger
reﬂected-wave, a phased-array antenna was proposed
for the reﬂectometry. The oblique viewing EBW emission can be measured by the precise phase-array measurements between the PAA waveguide elements. The
prototype phased-array antenna was designed using
Kirchhoﬀ integral calculation. The PAA was eﬀective
to excite straight and oblique beams for reﬂectometry
and EBW radiometry. The broadband OMT has beendeveloped to measure the O/X-mode polarizations in
the radiometry. The developing phased-array antenna
will be co-operated to measure the EBW emission toinvestigate the mode conversion phenomena, together
with the reﬂectometry measurements.

5. Acknowledgment
This research was supported by the Ministry of
Education, Science, Sports and Culture, Grant-in-Aid
for Scientiﬁc Research (B) , the NIFS LHD collaboration(NIFS09KOAH024), and the NIFS bi-directional
collaboration (NIFS09KUTR046).
[1] H. Idei et al., Journal of Plasma and Fusion Research
Serie vol.8, 1104-1107 (2009).
[2] H. Idei et al.,Proc. of 32nd Int. Conf. on Infrared andmm-Waves, 518 (2007).
[3] H. Laqua et al., Phy. Rev. Lett.,81 2060 (1998).
[4] S.J. Diem et al., Phy. Rev. Lett.,103 015002 (2009).

4. Conclusion
The diﬀerential-phase reﬂectometry has been developed to measure the density proﬁle evolution thatis a key issue for the EBWH/CD experiments in the
QUEST. The reﬂectometry based on the diode detection did not work correctly in the larger propagating
length for the QUEST. The direct coupling compo-

117