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Volume 7, 2402112 (2012)

ECW/EBW Heating and Current Drive Experiment Results andProspects for CW Operation in QUEST∗)
Hiroshi IDEI, Hideki ZUSHI, Kazuaki HANADA, Evgeniya KALINNIKOVA1) , Kazuo NAKAMURA,
Akihide FUJISAWA, Yoshihiko NAGASHIMA, Makoto HASEGAWA, Keisuke MATSUOKA,
Tsuyoshi KARIYA2) , Tsuyoshi IMAI2) , Ryutaro MINAMI2), Naoaki YOSHIDA,
Mizuki SAKAMOTO2) , Hideo WATANABE, Kazutoshi TOKUNAGA, Akira EJIRI3) ,Masatsugu SAKAGUCHI1) , Masaki ISHIGURO1) , Saya TASHIMA1) , Atsushi FUKUYAMA4) ,Hiroe IGAMI5) , Shin KUBO5) , Mitsutaka ISOBE5) , Kenichi NAGAOKA5), Hideya NAKANISHI5) ,Nobuhiro NISHINO6) , Shoji KAWASAKI, Hisatoshi NAKASHIMA, Aki HIGASHIJIMA,
Yuichi TAKASE3) , Takashi MAEKAWA7), Osamu MITARAI8) , Mitsuru KIKUCHI9) and Kazuo TOI5)
Research Institute for Fusion Science, Kasuga 816-8580, Japan
Interdisciplinary Graduate School of Engineering Science, Kyushu University, Kasuga 816-8580, Japan
2)
Plasma Research Center, Tsukuba University, Tsukuba 305-8577, Japan3)
Department of Complexity Science and Engineering, University of Tokyo, Kashiwa 277-8561, Japan
4)
Department of Nuclear Engineering, Kyoto University, Kyoto 606-8501, Japan
5)
National Institute for Fusion Science, Toki 509-5292, Japan
6)
Mechanical System Engineering, Hiroshima University, Hiroshima 739-8527, Japan
7)
Graduate School of Energy Science, Kyoto University, Kyoto 606-8501, Japan
8)
Institute of Industrial Science and Technology Research, Tokai University, Kumamoto 862-8652, Japan
9)
Japan Atomic Energy Agency, Naka 311-0193, Japan

1)(Received 12 December 2011 / Accepted 11 May 2012)
A CW phased-array antenna system for electron cyclotron/Bernstein wave heating and current drive(ECWH/CD, EBWH/CD) experiments was developed in the QUEST. The antenna was designed to excite anelliptically polarized pure O-mode wave in oblique injection for the O-X-B mode conversion scenario, and its
good performance was confirmed at a high power level. Long pulse discharges with a plasma current of 10 kA
and 15 kA were non-inductively attained for 37 s and 20 s, respectively, with only radio frequency (RF) power.
Divertor configurations were also obtained in the RF-sustained plasmas. A new operational window for sustained
plasma current was observed in the high-density plasma with a higher RF incident power. Two new heating
and current drive systems with an 8.56 GHz klystron and a 28 GHz gyrotron are being prepared to conduct CW
EBWH/CD experiments in the high-density plasma.
c 2012 The Japan Society of Plasma Science and Nuclear Fusion ResearchKeywords: electron Bernstein wave, spherical tokamak, QUEST, phased-array antenna
DOI: 10.1585/pfr.7.2402112

1. Introduction
The Q-shu University Experiments with Steady-State
Spherical Tokamak (QUEST) was proposed at Kyushu
University, and the QUEST device has been constructed[1]. Spherical tokamaks (STs) can attain a higher βthan conventional tokamaks. The ultimate goal of the
QUEST project is steady-state operation with relatively
high beta (<10%) in the ST configuration under controlledplasma wall interactions. For steady-state tokamak operation, a plasma current drive method should be established. Electron Bernstein wave heating and current drive(EBWH/CD) is an attractive candidate for sustaining aauthor’s e-mail: idei@triam.kyushu-u.ac.jp∗) This article is based on the invited presentation at the 21st International
Toki Conference (ITC21).

steady-state ST plasma. In ST experiments, the plasma
frequency may become larger than the electron cyclotron
frequency in the operating density range because of the
low magnetic field, and electron cyclotron waves cannot
propagate into the plasma beyond the cutoﬀ. EBWH/CD
experiments require mode conversion processes from theelectron cyclotron (electromagnetic) waves to the electron
Bernstein (electrostatic) wave.
In O-X-B mode conversion, an obliquely incident
electromagnetic O-mode wave that reaches the cutoﬀ isconverted into an X-mode wave and propagates to the upper hybrid resonance layer. It is then converted to an electrostatic Bernstein- (B-) mode wave. A ray trajectory inan optimum case where the O-mode wave is obliquely injected with an appropriate parallel refractive index N// was2402112-1

c 2012 The Japan Society of Plasma
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analyzed using the TASK/WR ray-tracing code [2], andthe deposition profile was evaluated. The generated current profile was also analyzed using the TASK/FP FokkerPlanck code from the local wave electric fields calculated by the TASK/WR code [3]. Multiple ray propagations were analyzed with the N// spectrum, including
non-optimal cases, taking into account the tunneling eﬀect
through the evanescent layer beyond the cutoﬀ [4]. The
propagation and absorption of each ray in the multipleray analysis was calculated individually, and the total absorption was evaluated as a superposition of all the rays’
absorption. In O-X-B mode conversion experiments, thelaunching angle and elliptical polarization state should becontrolled to achieve high-eﬃciency mode conversion into
the B-mode wave. A phased-array antenna (PAA) systemthat enabled us to control the launching angle and ellipticalpolarization state was proposed [5] for the EBWH/CD experiments in the QUEST. The PAA structure was modified
from the prototype design to reduce the side lobes in the
PAA radiation field [6], and a CW PAA with forced cooling water channels was developed. A low-power test of the
CW antenna confirmed its good performance with small
side lobes [7]. The CW PAA’s performance was recently
evaluated in the QUEST vacuum vessel at a high power
level. RF startup and sustainment experiments using the
CW PAA system have progressed to expand the obtained
plasma current region, but their densities were still lower
than the cutoﬀ density. A new operational window forsustained plasma current was observed in the high-density
plasma at the higher RF incident power.
This paper is organized as follows. Section 2 describes the high-power test of the CW PAA system in the
QUEST device. Recent progress on the heating and current
drive experiments is presented in Section 3. A new heating and current drive system with an 8.56 GHz klystron is
introduced in Section 4. Section 5 describes a new heating system with a 28 GHz gyrotron. Finally, a summary isgiven in Section 6.

tal waveguide transmission lines with a magic tee. Sixteen waveguide transmission lines and a grill antenna wereused to conduct the LHCD experiments in the TRIAM1M tokamak. To make a phased array of the LHCD grill
antenna, 3 dB hybrid phase shifters were installed on thetransmission lines. The phase shifters were also available
for phased array adjustment in the CW PAA system. The
adjusted phase array was measured at the directional couplers of the developed PAA system in vacuum. The phaserelationship among the waveguide ports was calibrated in
the low-power test in which the PAA performance was
evaluated. Because the total transmission system including the developed PAA was complicated, the phase relationship or the fields radiated from the PAA should be confirmed at a high power level in the QUEST device withall the transmission lines, including the CW PAA system.
The 8.2 GHz klystron amplified the exciter input to a highpower output. The amplifier gain was about 43 dB. A
rather high exciter level (∼1 W) was required to generatea nominal 25 kW output from the klystron. Because theexciter system exhibited thermal frequency drift, a Peltier
module was installed to maintain the exciter temperature,
however, a small frequency drift was still observed. Excellent frequency stability is generally required for precise phase measurements. In the low-power test, the frequencies of two synthesizers used to launch a test beamand feed the local oscillator power at the receiving mixers were locked with a stable 10 MHz clock. Figure 1
shows a schematic of the measurement system used in thehigh-power test of the PAA. A single side band (SSB) upconverter was used for heterodyne detection. In this heterodyne system, the intermediate frequency (IF) detected
at the mixers never changed even if the operating frequencyof the klystron changed because of frequency drift in the
exciter. The IF frequency was locked for precise phasemeasurements in the high-power test. To avoid damage
to the receiving mixer, a large attenuation was prepared,
and the pulse duration was limited to 3 ms. A reference

2. High-Power Test of PAA System in
the QUEST Device

A [4 × 2] CW antenna system with eight waveguideports was designed to reduce the side lobes observed in
the prototype antenna. The waveguide size and wall thickness of the PAA waveguide port were smaller in the CW
PAAs than in the prototype. A strong forced cooling structure was designed to remove the heat load at the interface
regions of the PAA waveguide ports. The CW antenna
performance was evaluated at Kyushu University’s lowpower facilities. An 8.2 GHz system with eight klystrons
has been used for ECW/EBW experiments in the QUEST.
The system was prepared for the lower hybrid current drive(LHCD) experiments in our earlier TRIAM-1M tokamak[8]. Each klystron generated a nominal 25 kW oscillating power, and its output was divided into two fundamen-

Fig. 1 Schematic of field measurement system of developed[4 × 2] CW phased-array antenna with a high power levelin the QUEST device.

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Fig. 2 Experimental setup of high-power test of the [4 × 2] CW
phased-array antenna in the QUEST device.

Fig. 4 Intensity contour plots in the x − y plane perpendicular tothe propagating z direction for perpendicular and oblique
injection.

Fig. 3 (a) Intensity and (b) phase profiles along the propagatingz direction when one of the [4 × 2] waveguide ports is
excited in the high-power test.

IF signal was also measured with a vector network analyzer to determine the amplitude ratio and phase diﬀerence
for the receiving side after propagation from the PAA. The
dynamic range of the amplitude measurement was 90 dB.
Figure 2 shows the experimental setup of the PAA highpower test in the QUEST device. The PC-controlled threedimensional scanner was set to measure the field distributions radiating from the PAA in the QUEST vacuum vessel.
The setting error of the scanner position was less than 0.1
mm. The antenna position was controlled within 1/300thof the wavelength. The QUEST vacuum vessel may work
as a large oversized cavity in the case of RF injection to thedevice. The major and minor (plasma) radii of the QUEST
device are 0.64 m and 0.16 m, respectively. The vacuum
vessel was quite oversized for the wavelength (∼ 0.037 m)of 8.2 GHz. The standing wave components were sometimes dominant in the cavity condition, preventing us fromcreating the phase array. First, the field radiated by the
PAA was measured along the propagating z direction todetermine whether the propagating wave-field component
was properly measured. Figure 3 shows the intensity andphase profiles along the propagating z direction when oneof the [4 × 2] waveguide ports was excited. The proper kz
phase evolution was measured along the propagation direction, where k was the 8.2 GHz wavenumber. The intensity profile exhibited complicated fine structures caused

Fig. 5 Phase contour plots in the x − y plane perpendicular tothe propagating z direction for perpendicular and oblique
injection.

by phase interference along the kz evolution, including a
global interference eﬀect in the oversized cavity condition.
Figure 4 shows intensity contour plots in the x−y plane perpendicular to the propagating z direction for perpendicularand oblique injection. Although the profiles were complicated because of the interference eﬀect, the beam was focused at the center of the antenna in perpendicular injection
and was steered in the x direction at a focusing point ( [x,z] = [0.17 m, 0.42 m] ) in oblique injection. In oblique injection, the intensity in front of the antenna center was lessthan the intensity of the steered beam center by 20 dB or
more. Figure 5 shows phase contour plots in the x−y plane
perpendicular to the propagating z direction for perpendicular and oblique injection. In perpendicular injection, theparabolic phase profile showed a focused beam expanding
along the propagation direction. In oblique injection, a gradient in the phase profiles was observed in the x direction
at the focusing point, indicating that the beam was steeredin the x direction. The x derivative of the phase profile expressed the x component of the wavenumber, k x . Figure 6

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Fig. 6 Phase profiles in the x direction at y = 0 measured in thehigh-power test and calculated by a developed Kirchhoﬀ
integral code without considering the standing wave effect.

Fig. 7 Recent progress in obtained plasma currents for various
incident RF powers. Red symbols represent QUEST results.

shows phase profiles in the x direction at y = 0 measured in
the high-power test and calculated by a developed Kirchhoﬀ integral code without considering the standing wave
eﬀect. The measured phase gradient, or k x , coincided wellwith that calculated using the Kirchhoﬀ integral code at
the focusing point, whereas the measured profile deviatedfrom the calculated one owing to the standing wave component in regions where the intensity was small, such as thecenter of the antenna. The high-power test confirmed thatthe developed PAA has good focusing and steering properties.

3. Recent Progress in Heating andCurrent Drive Experiments in
QUEST
3.1 Long pulse discharges in limiter and divertor configurations
The plasma currents obtained in the QUEST are plotted as a function of the incident RF power in Fig. 7.
Figure 8 shows the obtained pulse duration for each plasma
current.
Long pulse discharges at plasma currents of
10 kA and 15 kA were attained for 37 s and 20 s, respec-

Fig. 8 Recent progress in obtained pulse durations for various
plasma currents. Red symbols represent QUEST results.

Fig. 9 Reconstructed magnetic fluxes in the divertor configuration with a plasma current of 15 kA.

tively, in the limiter configuration. A hot spot appearedin the outer limiter, and metal contamination was observed as well as recycling enhancement with the increased
Hα intensity of the long pulse discharges. Non-inductive
divertor experiments were conducted with poloidal fieldcoil control. Figure 9 shows the reconstructed magnetic
fluxes in the divertor configuration with a plasma current of
15 kA. The elongation, triangularity, and aspect ratio were1.53, 0.41, and 1.98, respectively. To obtain a single-nullconfiguration, the vertical plasma position was controlled
to be 0.04 m lower for the midplane of the QUEST device.
The single-null divertor configuration with a high plasma
current (<∼25 kA) was also attained in the 17 s plasma sustainment.
The obtained density was typically low(∼ 2 × 1017 m−3 ) compared to the O-mode cutoﬀ density (∼ 8 × 1017 m−3 ) in these experiments. Eﬀective
EBWH/CD experiments in the O-X-B mode conversion
scenario were not anticipated in the low-density plasma
with the developed PAA. The RF powers plotted in Fig. 7
were entirely injected using two 8.2 GHz systems with andwithout PAA operation. The hard X-ray intensity from2402112-4

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Fig. 10 Time evolutions of plasma current and density obtainedin high-density discharge.

current-carrying electrons accelerated by the incident RF
power was ramped up in the energy range of 10∼30 keV,following the plasma current evolution. An asymmetricconfinement structure of high-energy electrons on the parallel velocity in velocity space may explain the generated
current. The vertical magnetic field BV along the toroidal
field BT is required to start up the plasma current by RF
injection alone. Specific electrons can be confined well if
the vertical motion due to the toroidal drift vdT is cancelledby the vertical component of the parallel velocity due
to the magnetic field pitch angle v// (BV /BT ) [9]. These
confined electrons can contribute to the plasma currentof the RF-sustained plasma. The direction of plasma
current depends on the direction of BV because only the
co-moving electrons for which v// (BV /BT ) is opposite
to vdT can be confined well. In addition, banana orbits
are possible even on open field lines. Thus, the confined
trapped electrons also contribute to current generation
owing to the precession in the toroidal direction.

3.2 High-density operation
To study the EBWH/CD eﬀect, a high-density plasma
should first be produced and sustained in the ECWH/CD
experiments. High-density operation was conducted in the
inboard null configuration [10]. The divertor configurations formed single- and double-null points upper and/or
lower for the midplane in the QUEST device. In the inboard null configuration, a null point appeared on the highfield side of the QUEST device. The high-energy electrons could be confined by the strong positive n-index field.
Figure 10 shows the time evolution of the plasma current
and density obtained in this configuration. A series of gas
puﬀs was applied to obtain the high-density plasma. The
plasma current decreased initially, but, remarkably, it wasobserved again in the higher-density plasma. In addition toa hydrogen discharge, helium and neon discharge experiments were conducted to obtain a high-density plasma inthe inboard null configuration. Figure 11 shows the obtained plasma currents and the stray radiation componentsof the incident RF power for the line-integrated density inthe hydrogen and helium discharges. A new operational
window for sustained plasma current was more clearly ob-

Fig. 11 Obtained (a) plasma current and (b) stray radiation component of the incident RF power for line-integrated density in hydrogen and helium discharges.

Fig. 12 Obtained plasma current with respect to the lineintegrated density at 70 and 100 kW incident power injection in helium discharges.

served in the helium discharge experiments. The stray radiation decreased as the density increased in both the helium and hydrogen discharges, indicating that most of theincident power was absorbed by the high-density plasma.
Figure 12 shows the obtained plasma current with respect
to the line-integrated density at 70 and 100 kW power injection in the helium discharges. The high-density window
was not achieved at the lower RF incident power.

4. New High- Power and Frequency
Systems
4.1

8.56 GHz High-power klystron system

A higher incident power was required to obtain the
new operational window with a significant plasma current
in the high-density plasma. A new high-power 8.56 GHz
klystron (VKX-7864B1) manufactured by Communications & Power Industries was prepared for the EBWH/CD
experiments in the QUEST. Figure 13 shows photographsof the new klystron. Its nominal oscillating power is
250 kW in CW operation, and its operational beam voltage and current are -52 kV and 13 A, respectively. This
klystron will be operated using a gyrotron power supply
prepared for the ECWH/CD experiments in the TRIAM1M tokamak. The maximum beam voltage and current of
the gyrotron power supply are -75 kV and 25 A. Regulator tube and crowbar systems were prepared to protect the2402112-5

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Fig. 13 Photographs of new 8.56 GHz klystron (Communications& Power Industries: VKX-7864B1).

gyrotron. The protection system can cut the high voltage
applied to the gyrotron within 10 µs of the detection of an
overcurrent due to an arcing event inside the gyrotron. Theenergy entering the gyrotron owing to arcing should be lessthan 10 J. A lower incoming energy of 5 J is required for
klystron operation. A protective resister system was also
prepared to limit the incoming energy to 5 J. Some waveguide components such as an isolator, an arc sensor, and a
directional coupler were prepared. An exciter system composed of a synthesizer and a high-power amplifier is being
prepared. The high-power klystron system will be operated with the modified gyrotron power supply in summer
2012.

4.2 28 GHz gyrotron system
The O-mode cutoﬀ density increases as the square of
the operating RF frequency. If a high-frequency powersource is available for the ECWH/CD experiments, the accessible density in the experiments increases. Figure 14
shows the fundamental and second electron cyclotron resonance frequencies, fce and 2 fce , at BT = 0.25 T, and the
O-mode cutoﬀ frequencies fpe for various density profiles.
The 2 fce at 28 GHz was located at the high field side, as
was fce at 8.2/8.56 GHz near the plasma center, as shownin Fig. 14. The O-mode cutoﬀ density is 1 × 1019 m−3 at
28 GHz. The incident 28 GHz ECW can propagate into
the plasma beyond the cutoﬀ density for 8.2/8.56 GHz(> 8 × 1017 m−3 ). EBWH/CD experiments are planned
that will use two frequency range sources of 28 GHz and8.2/8.56 GHz. The plasma will initially be produced by the
8.2/8.56 GHz system, and then the density will be ramped
up with the 28 GHz system. The 8.2/8.56 GHz EBWH/CD
experiments can be conducted in the overdense plasma sustained by the high-frequency 28 GHz system. Kyushu University, Tsukuba University and the National Institute for
Fusion Science (NIFS) have begun bi-directional collaborative research. A 77 GHz CW gyrotron has been successfully developed for the Large Helical Device experimentsby collaborative research between Tsukuba University and
the NIFS. The research program at Tsukuba University has
developed a 28 GHz CW gyrotron. It will be used for the

Fig. 14 Fundamental and second electron cyclotron resonancefrequencies fce and 2 fce at 0.25 T in CW operation,
and O-mode cutoﬀ frequencies fpe for various density profiles. The density profiles are assumed tobe parabolic with diﬀerent central densities ne0 of
0.1/0.2/1.0 × 1019 m−3 .

Fig. 15 Oscillating output power and eﬃciency at beam voltageof -70 kV as a function of the beam current for the 28 GHz
gyrotron. Power supply current limits of 12 A and 25 A
appeared for operation scenarios with and without the8.56 GHz klystron in parallel, respectively.

EBWH/CD experiments with the gyrotron power supply
at Kyushu University. The 28 GHz gyrotron was operated
at a beam voltage of -80 kV to obtain a maximum oscillating power level of 1 MW at Tsukuba University. The
maximum beam voltage was -75 kV in the Kyushu University power supply for the gyrotron. The operating parameter region of the 28 GHz gyrotron was surveyed inorder to operate it with a lower beam voltage at Kyushu
University. Figure 15 shows the oscillating output powerand eﬃciency at a beam voltage of -70 kV as a functionof the beam current. The maximum beam current for the
Kyushu University power supply was limited to 25 A. A
power level of 500∼600 kW was available within the operating limits of the power supply. The oscillating eﬃciencies will be improved in the operating region at Kyushu
University. The Tsukuba 28 GHz gyrotron was operated
with a triode magnetron injection gun (MIG), whereas a
170 GHz gyrotron for the TRIAM-1M tokamak was operated with a diode MIG. The maximum anode voltage was
42.5 kV for operation with the -70 kV beam voltage. A
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Fig. 16 Oscillating output power for long pulse operation of the
28 GHz gyrotron.

pared to control the anode voltage. A high-speed, highvoltage CW switch system that integrates multiple stagesof MOSFETs connected in series is being prepared to turnthe anode voltage on and oﬀ and to cut the voltage uponovercurrent detection. An overcurrent detection system forthe anode current and a gyrotron tank with insulators forthe anode and body electrodes were prepared in addition
to the gyrotron system at Kyushu University.
If the 28 GHz gyrotron will be operated in parallelwith the 8.56 GHz klystron using the same high-voltage
power supply, collector potential depressed (CPD) operation should be considered. In CPD operation, the total
voltage accelerating an electron beam in the gyrotron isthe voltage diﬀerence between the cathode and the body.
The withstand voltage between the body and collector electrodes was evaluated at Tsukuba University, and its maximum value was 17∼18 kV. The electric potential at the collector electrode, which connects to the ground through abeam-current-monitoring resistance, was essentially zero.
The gyrotron can be operated with a cathode voltage of-52 kV and a body voltage of +17 to +18 kV in CPD
operation together with the 8.56 GHz klystron. The total voltage accelerating the electron beam becomes 69∼70[52+ (17∼18)] kV. An additional body power supply at the
20 kV level will be required for CPD operation. The total
beam current should be less than 25 A on the Kyushu University power supply. Because the operating current of the
8.56 GHz klystron is 13 A, the gyrotron may be operated
in parallel at a beam current of 12 A. The oscillating power
level of the gyrotron will be limited to 250∼300 kW. Long
pulse operation of the 28 GHz gyrotron was demonstrated
at a rather low power level at Tsukuba University. Figure
16 shows the gyrotron oscillating power for long pulse operation. The power level of 400 kW was available for 1.8 s.
In principle, the 28 GHz gyrotron can be operated continuously in parallel with the 8.56 GHz klystron.

5. Summary
The performance of the developed [4 × 2] CW antenna
was tested at a high power level in the QUEST device.

A heterodyne detection system with frequency-locking IF
signals was used in the high-power test. The beam wasproperly steered to the focusing point in oblique injection,
taking the gradient of the phase profile there. Long pulse
discharges with plasma currents of 10 kA and 15 kA wereattained for 37 s and 20 s in the limiter configurations, respectively. The single-null divertor configuration was obtained with the 15 kA plasma current. The elongation, triangularity, and aspect ratio were 1.53, 0.41, and 1.98, respectively. The divertor configuration with a high plasma
current (<∼25 kA) was also achieved during 17 s plasma
sustainment. High-density operation was conducted in helium and neon discharges as well as a hydrogen discharge.
A new operational window for sustained plasma current
was observed in the high-density plasma at the higher RF
incident power. High-power/frequency systems for use in
EBWH/CD experiments in high-density plasma were considered in the QUEST. The 8.56 GHz CW klystron and its
related components were prepared for the high-power experiments. The operating parameter region of the 28 GHz
gyrotron was surveyed in order to operate it within the limits of the Kyushu University power supply. CPD operationof the 28 GHz gyrotron was considered for joint operation
with the 8.56 GHz klystron. The gyrotron can be operated
at power levels of 500∼600 kW and 250∼300 kW without
and with the 8.56 GHz klystron operation in parallel, respectively. A long pulse of 1.8 s was attained at a power
level of 400 kW. The required anode voltage power supply,
a gyrotron tank, and an overcurrent detection system wereprepared for operation at Kyushu University.

Acknowledgments
This work was performed with the support andunder the auspices of the NIFS Collaboration Research Programs (NIFS09KUTR046/NIFS10KUTR048/NIFS11KUTR059/NIFS11KUTR069). This research waspartially supported by the Ministry of Education, Science, Sports and Culture, Grant-in-Aid for Sc. Res. (B)[21360452].
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