Proceedings of ITC/ISHW2007

Eﬃcient Heating at the Third Harmonic Electron Cyclotron
Resonance in Large Helical Device
Takashi SHIMOZUMA1) , Shin KUBO1) , Hiroe IGAMI1) , Yasuo YOSHIMURA1) , Takashi NOTAKE2) ,Nikolai B. MARUSHCHENKO3) , Yurij. TURKIN3) , Takashi MUTOH1) and LHD Experimental
Group1)
1)

2)

National Institute for Fusion Science, 322-6 Oroshi-cho, Toki 509-5292 Japan
University of Fukui, Research Center for Development of Far-Infrared Region, 3-9-1 Bunkyo, Fukui 910-8507 Japan
3)
Max-Plank-Institut für Plasmaphysik, EURATOM-Association, Greifswald, Germany(Received / Accepted )Eﬃcient heating at the third harmonic electron cyclotron resonance was attained by injection of millimeterwave power with 84 GHz frequency range at the magnetic ﬁeld strength of 1 T in LHD. The plasma center clearly
increased and the increment of the temperature reached 0.2 – 0.3 keV. Dependence of the power absorption rateon the antenna focal position was experimentally investigated, showing that the optimum position located in
the slightly high-ﬁeld side of the resonance layer. Ray-tracing calculation was performed in the realistic threedimensional magnetic conﬁguration. The results are compared with the experimental results.
Keywords: electron cyclotron resonance heating, gyrotron, harmonic resonance, quasi optical antenna, ray tracing
DOI: 10.1585/pfr.1.001

1.

Introduction
High harmonic heating of the electron cyclotron resonance (ECR) is an attractive method to extend a heating regime of plasma parameters by alleviating the density
limitation due to some cutoﬀs of the EC wave propagation. In the LHD launching geometry, the magnetic ﬁeld
strength is almost constant along the ray paths launchedfrom upper- and lower-port antennas which cross near themagnetic axis. Under this condition, the ray can keep resonant with the plasma over a considerable length. So goodabsorption is predicted over a wide density range even forthe 3rd harmonic heating by the linear theory [1].
Experimentally the 3rd harmonic heating was triedin Heliotron DR and eﬀective heating was observed [2].
In TCV tokamak, 3rd harmonic heating was carried out
with the 2nd harmonic heating by using two diﬀerent frequency gyrotrons such as 82.7 GHz for the 2nd harmonicand 118 GHz for the 3rd harmonic resonance. Hundred
percent absorption was attained on existence of high energy electrons produced by the 2nd harmonic resonanceheating [3, 4]. After that, the sophisticated feedback control of antenna focal position realized 100 % absorption
by only 3rd harmonic resonance heating [5]. In W7X, the 3rd harmonic heating is planned as a candidateof a normal heating scenario in the high density regime(0.6 − 2.0 × 1020 m−3 ) by using 140 GHz, 10 MW ECH
system [6].
Eﬀective 3rd harmonic heating has been alreadyachieved on the 2 T LHD plasma by injection of 168 GHz
millimeter wave power from upper-port antennas. In theauthor’s e-mail: shimozuma.takashi@LHD.nifs.ac.jp

experiments of the 3rd harmonic resonance heating, obvious heating of the bulk plasma (∆T e =0.2 keV) aroundthe plasma center by 340 kW power injection was observed [7].
Because ECH power of 84 GHz range has been upgraded up to 1.3 MW recently, we have tried the 3rdharmonic extraordinary(X)-mode heating by injection of84 GHz range power at the magnetic ﬁeld strength of 1 Twith the magnetic axis of 3.75 m. When the same frequency is used, a cutoﬀ density for the 3rd harmonic Xmode heating at 1 T becomes 4/3 higher than that for 2ndharmonic X-mode heating at 1.5 T. It is about 6 × 1019 m−3 .
2.

Experimental setup and results
The ECH system consists of 84 GHz range and 168
GHz gyrotrons, high voltage power supplies, long distance transmission lines, and in-vessel quasi-optical antennas. It has been improved step by step. At thelast campaign(2006) of LHD experiments ﬁve 84 GHz
range and three 168 GHz gyrotrons are operated and ECH
power could be injected from six antennas in the verticallyelongated cross section (upper-port and lower-port antennas) and two antennas in the horizontally elongated crosssection(outer-port antennas).
Two kinds of antenna systems for ECH are installedin the LHD vacuum vessel. The vertical injection antenna
system consists of four or two millimeter-wave focusingand steering mirrors. High power measurement of this system shows a good agreement with the designed beam-waist
size of 15 mm in radial and 50 mm in toroidal direction for
the upper-port antennas and of 30 mm for the lower-port

Proceedings of ITC/ISHW2007
antennas. The direction of the beam can be steered radially and toroidally. The injected millimeter-wave beams
from these antennas consequently have a grazing incidence
angle to the cyclotron resonance and continues to interact
along a long ray-path. For horizontal injection, the antenna
system consists of 2 mirrors, one is ﬁxed and another issteerable. Movable range covers the whole plasma crosssection for perpendicular injection and can change about±30 degrees toroidally. In this case, the injected beams
perpendicularly pass through the ECR layer with the shortest gradient length.

increment of the temperature reached 0.2 – 0.3 keV.

Fig. 2 Electron temperature proﬁles just before (t=1.37sec) andduring (t=1.57sec) ECH. ρ is the normalized minor radius.

Fig. 1 Wave form of NBI power, ECH timing, stored energy W pand line-averaged density from top to bottom.

A magnetic conﬁguration was chosen such that the 3rd
harmonic electron cyclotron resonance located on the magnetic axis for both in the vertically and horizontally elongated cross sections, because microwave beams from allantennas could access almost perpendicularly to the magnetic ﬁeld line of force. So the magnetic ﬁeld strength of
1 T on the magnetic axis placed on Rax = 3.75 m wasadopted.
In the experiments, target plasmas were produced andsustained by only NBI power. The electron temperatureof a target plasma was about 1 keV and the line-averaged
density was 0.6 × 1019 m−3 at the center. ECH power(1.3 MW) was injected from t=1.4 sec and 1.5 sec stairlikely as shown in Fig. 1. The ECH pulse which has alonger pulse width corresponds to 84 GHz power from theouter-port antenna. The ECH pulse with a shorter pulse
width is 82.7 GHz from top-antennas and 84 GHz frombottom-antennas. The absorption rate for the diﬀerent wayof resonance can be discriminated independently and effectively by the stair-like injection. Obvious increase of
the stored energy was observed during both the ﬁrst andsecond ECH pulses, while there was no change in the density.
Figure 2 shows electron temperature proﬁles just before (t=1.37 sec) and during (t=1.57sec) ECH power injection. The plasma center was eﬃciently heated, and theAbsorbed power was estimated by the increment of
the plasma stored energy dW p /dt before and after ECH
on-timing, assuming that the other plasma parameters did
not change so much. The dependence on the focal point
R f oc of the upper-port antennas (82.7 GHz) was examinedin special(Fig. 3). The maximum absorption rate was obtained on the antenna focal position R f oc =3.7m, which wasslightly smaller than the 3rd harmonic ECR layer (3.75m).
The absorption rate, however, is rather low, because thetemperature and density of the target plasma was fairly low.
The absorption rate for the other antennas were estimatedto be about 8 %.
Detailed calculations by ray-tracing in the LHD magnetic conﬁguration is required to discuss the absorption
rate and its dependence on the antenna focal point.

Fig. 3 Eﬃciency of absorbed power for 82.7GHz antenna wasestimated by change of dW p /dt at ECH on-timing. Antenna focal point on the equatorial plane R f oc dependence
is shown.

Proceedings of ITC/ISHW2007
3.

Preliminary ray-trace calculation in LHD magnetic conﬁguration
In order to estimate the absorption rate, ray trace calculation was carried out for a given electron temperatureand density proﬁles in the LHD magnetic ﬁeld conﬁguration.
The ray-tracing code, ”TRAVIS (IPP)”, has been developed for ECH/ECCD and ECE studies in an arbitrary
three-dimensional magnetic conﬁguration [8, 9]. The basic ray-tracing equations include weakly relativistic formulation for Hamiltonian with taking into account possible anomalous dispersion eﬀects. Gaussian power distribution of an injected beam is assumed and the beam crosssection is discretized by the arbitrary number of radial andazimuthal points. The wave absorption can be calculated infully relativistic formulation. The power deposition is decomposed for passing and trapped electrons contributions.

part of the power is absorbed by the passing electrons near
the magnetic axis. A small fraction is absorbed by thetrapped electrons within ρ ∼ 0.2 and around ρ ∼ 0.4 − 0.5.
The integrated absorbed power is shown in Fig. 5 (b). Total amount of the absorption power reaches 0.6 MW for
1.3 MW injection. Maximum absorption rate is about
50 %.

Fig. 5 Power deposition. (a) Deposited power density is plotted
as a function of normalized minor radius and (b) integral
value of absorbed power along the ray path. Total amountis decomposed into each component absorbed by passing
and trapped electrons.

4.

Fig. 4 Ray trace calculation together with mod-B contours andﬂux surfaces.

An X-mode is assumed to be perpendicularly injectedfrom the lower-port antenna focused on the magnetic axis.
In Fig. 4, the conﬁguration of calculation is illustrated with
mod-B counters, ﬂux surfaces and wave rays. The 3rd
harmonic electron cyclotron resonance is also depicted.
Calculated rays from the lower-port antenna are typicallyshown. The proﬁle of the electron temperature is assumed(T e0 − T ea ) × (1 − ρ3 )1.5 + T ea with T e0 =1.3 keV, whereρ = r/a is a normalized minor radius, and T e0 and T ea are
the electron temperature at the plasma center and the edge,respectively. The central electron density ne0 is assumed
to be 1 × 1019 m−3 . The proﬁle of the electron density was
assumed the same as the electron temperature.
The power absorption is localized near the 3rd harmonic resonance (B = 1 T) and the deposition is almost
limited within ρ ∼ 0.2, which is shown in Fig. 5 (a). Most

Discussion and summary
The experimental results show the eﬃcient heating at
the 3rd harmonic resonance even in the fairly low electron temperature (∼ 1 keV) and low electron density (∼0.6 × 1019 m−3 ). However experimentally obtained absorption rate of about 20 % is lower than that expected by theray-tracing calculation, which was carried out in the realistic three-dimensional magnetic conﬁguration of LHD. One
possible reason of the discrepancy seems to be the diﬀerences of values and proﬁles of the temperature and density
for between the actual plasma and the modeled one. Because the optical thickness scales as τ ∼ ne · T e2 , a littletemperature change possibly leads to fairly large diﬀerenceof the absorption rate. Figure 6 shows a contour-plot of thesingle-pass absorption rate in the electron temperature anddensity space for the injection from the upper-port antenna
with R f oc = 3.7 m. In these calculations the dispersion relation of a cold plasma was assumed for ray calculationand the weekly relativistic eﬀect were included for the absorption [10]. The proﬁles of the electron temperature anddensity are assumed to have the same ones such as (1−ρ2 )2 .

Proceedings of ITC/ISHW2007
heating and diagnostic devices. They also thank Professors A. Komori, S. Sudo and O. Motojima for their continuous guidance and encouragement. This work has been
supported by NIFS under NIFS06ULRR501,502,503.

Fig. 6 Single-pass absorption rate for the injection from upperport antenna is contour-plotted in the electron temperature and density space.

The values of temperature, T e , and density, ne , in the ﬁgure
represent the values in the center. The ﬁgure clearly shows
almost 100 % absorption is expected in the high temperature (& 3 keV) and high density (1 − 4 × 1019 m−3 ) region
up to the right-hand cut-oﬀ density. However in the lowtemperature (.1 keV) and low density (. 1 × 1019 m−3 ),the absorption rate can change from several percent to several tens percent according to the small change of plasma
parameters.
Another possible reason is the production of suprathermal electrons by the 3rd harmonic ECR, which could
be drifting out from a plasma quickly before thermalization and do not contribute to the increment of diamagnetic
energy of the plasma. These facts can partly explain thediscrepancy between the values of the single-pass absorption calculated by the ray-tracing and the absorption rateevaluated from the temporal change of dW p /dt.
In summary, the 3rd harmonic electron cyclotron resonance heating experiments were performed. Especially,
because of the upgrade of 84 GHz gyrotrons and transmission line, the eﬃcient heating results were obtained evenfor the 3rd harmonic resonance. During the ECH pulse of
0.4 sec. stored energy of the plasma increased several percents. The central electron temperature raised about 0.2 –0.3 keV. Dependence of the absorption rate on the antenna
focal position shows the maximum at a slightly higher-ﬁeld
side of the resonance position. Preliminary calculation using ray-tracing code ”TRAVIS”, which has been developedin IPP Greifswald (Germany), was successfully carried out
in the three-dimensional magnetic conﬁguration of LHD.
In order to discuss a detailed quantitative comparison
is required between experimental and calculated results forthe optimization of the heating eﬃciency in view of injection conﬁguration. These works are under way.
Acknowledgment
The authors gratefully acknowledge the LHD technical group for their sophisticated operation of LHD, and the[1] U. Gasparino, H. Idei, S. Kubo, et al., Nuclear Fusion,
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