Proceedings of ITC/ISHW2007

Electron Bernstein Waves Simulation in Helical Systems
Sergi FERRANDO-MARGALET1) , Yasuo YOSHIMURA1) , Kazunobu NAGASAKI2) ,Chihiro SUZUKI1) , Shinji KOBAYASHI2) , Yasuhiro SUZUKI1) , Kazuo TOI1) , Shin KUBO1) ,Ryosuke IKEDA1) and Hiroe IGAMI1)
1)

2)

National Institute for Fusion Science,322-6 Oroshi-cho, Toki 509-5292, Japan
Institute of Advanced Energy, Kyoto University, Gokashou, Uji, Kyoto 611-0011, Japan

Following experimental results obtained in the CHS and the Heliotron-J devices concerning mode conversion
into and heating with Electron Bernstein Waves (EBWs), numerical simulations have been carried out involving
the ray-tracing, mode conversion and power deposition of EBWs for models of these experimental scenarios.
EBWs-based heating has been confirmed for all the cases studied so far as measured by the experiment. Further
investigation is being done to extend the range of the simulations and confirm more detailed issues like the power
deposition location.
Keywords: ray tracing, electron Bernstein waves, mode conversion, ECRH, numerical simulations.

1Introduction

Due to their electrostatic nature, Electron Bernstein Waves(EBWs) do not experience any density limit. This makes
them particularly useful to interact with over-dense plasmas. However, the ‘over-dense’ condition is not only
reached due to a very high plasma density. Propagation
cutoﬀs depend also on the frequency of the wave and thelocal magnetic field, therefore they can occur also in low
density-low field conditions. This makes EBWs a popular subject both in the tokamak and helical communities
for their ability to overcome the density limits and deposit
power in otherwise inaccessible regions of the plasma. The
study of EBWs and their applications is a matter of particular interest in Japanese helical devices. Experimental campaigns involving research on EBWs have been carried out
in the LHD and CHS experiments in NIFS as well as in theHeliotron-J in Kyoto University. In order to contrast theseexperimental results with the theory and to devise new experiments, numerical simulations of ray tracing, mode conversion and power deposition of EBWs are carried out withthe aid of the ART ray-tracing code [1] and the bundle ofcodes COBE [2].

2CHS - OXB

An increase of the plasma stored energy when ECH isswitched on is observed in CHS for a comparatively overdense plasma [3]. The core parameters are: n0 = 9.6
1019 m−3 , T0 = 0.4 keV, f0 = 54.5GHz, B 0 = 1.9T .
The density for this shot would block propagation of thelaunched O-mode waves: cutoﬀ density (f0 = 54.5GHz) =3.8 1019 m−3 . The increase of stored energy is thought tobe due to the absorption of EBW mode-converted from thelaunched O-mode wave (OXB) [see Fig. 1].
author’s e-mail: ferrando@nifs.ac.jp

Fig. 1 Experimental data from the shot 129213. It can be seen
an increase of the stored energy during the second ECRH
injection.

An estimated profile of the neutral beam driven current has been used to calculate the VMEC equilibrium withthe total measured current of -2.8kA. The evolution of theO-mode wave was simulated with the ART code. The numerical simulation show a clear OXB conversion in theevolution of the ray path. The power is absorbed betweens = 0.6 − 0.7 beyond the O-cutoﬀ (s ∼ 0.8).
The OXB conversion can be identified from the evolution of the perpendicular refractive index and the CMAdiagram. The O-mode wave propagates towards the coreof the plasma. Near the O-cutoﬀ region, it converts to Xmode (N⊥ goes to 0). The X-mode wave propagates backuntil it reaches the Upper Hybrid Layer (UHL). In the UHL
the X-mode is transformed to EBW (the N ⊥ increases drastically in a vertical line). Finally the B-mode wave propagates through the O-cutoﬀ where it is finally fully absorbed(see Fig. 2).

Proceedings of ITC/ISHW2007

Fig. 2 Numerical results of the OXB simulation for CHS shot
129213. Ray path in R-Z coordinates (top left), N⊥ (topright), normalised power deposition profile (bottom left)
and CMA diagram of the ray evolution (bottom right).
profile3

CHS - XBAn X-mode wave is launched from the top window anddirected with a steerable mirror in the outer part of the torus(see Fig.3) [4]. The relevant parameters for the simulation
are as follows: ECH power = 275kW, ECH frequency =54.5GHz, polarisations = X-mode, NBI power = 845kW,
Rax = 0.949m, Bax = 1.95T, plasma current = -11kA , β= 0.2. The magnetic geometry of CHS is such that thefundamental resonance reaches the magnetic axis but also
appears in the outer region of the torus near the mirror. Therays were launched with a fixed vertical angle aiming at
the fundamental resonance stripe (see Fig.4). A horizontal
angle scan was carried out detecting an increase of the coreelectron temperature.
The simulations show that conversion is achieved
when the wave is launched at towards the fundamental resonance region. However, the power is mainly absorbed
away from the core of the plasma. Nevertheless, deposition nearer to the axis region is obtained for high horizontal and vertical angles. More simulations are on theway to simulate the ray’s behaviour at wider horizontal angles > 20 Deg. The power deposition regions with respect
to horizontal and vertical toroidal angles are displayed inFig.5.

4Heliotron J - XB

The plasma conditions in Heliotron-J provide a low singlepass absorption, therefore reflexion in the vacuum vessel isexpected. The necessary conditions for an XB conversion
are achieved if waves are launched in such a way that thereflexion takes place in the inner part of the torus’ cornersection [5]. The rays reflected in the vacuum vessel aremodelled imposing the launching point in the inner part of
the torus and launching towards the outer region. Horizontal and vertical scans have been carried out to investigate the XB conversion and the core deposition of Bern-Fig. 3 CHS XB experiment launching scheme. The mirror isaimed at the region where the fundamental harmonic on
the last flux surface.

Fig. 4 CHS launching position and angles for the XB heatingexperiment. The scale of the magnetic field strength has
been reduced in order to highlight the fundamental resonance stripe on the las magnetic surface.

stein waves. Figure 6 shows the ray-path of three sample
rays directed respectively to clockwise, counter-clockwise
and downwards launching conditions, all with satisfactory
XB conversion. In Fig.7, the deposition location of theBernstein-transformed waves is shown with respect to thehorizontal launching angle. It is clear in this case that deposition takes place in the core region of the plasma as
expected from the experimental results.

5Conclusions

Helical devices with their complicated geometry oﬀer awide range of possibilities for mode conversion and powerdeposition. Ray tracing simulations for diﬀerent modeconversion scenarios leading to Bernstein wave heating inhelical systems have been performed by means of the ART
code.
OXB and XB simulations in CHS have been shown
to be in agreement with experimental results. The OXB
ray tracing calculations show a clear OXB conversion thatjustified the power deposition beyond the O-mode cutoﬀ
point. The XB simulations, show successful conversion

Proceedings of ITC/ISHW2007

Fig. 5 Table indicating the power deposition region with respect
to horizontal launching angle. The vertical angle of eachsimulation is also indicated. The thin lines represent
partial X-mode absorption and the thick lines indicatedBernstein wave absorption.

Fig. 7 Table indicating the power deposition region with respect
to horizontal launching angle for the Heliotron-J XB conversion experiment.

systems are presently being performed.
[1] F. Volpe, PhD Thesis, Max Planck Institute fuer Plasmaphysik, Greifswald, Germany (2003).
[2] S. Ferrando i Magalet, PhD Thesis, École PolytechniqueFédéral de Lausanne, Lausanne, Switzerland (2006).
[3] Y. Yoshimura et al, Fusion Science and Technology 52, 216(2007).
[4] Y. Yoshimura et al “Experimental conditions for electronBernstein heating by use of EC waves injected from the highfield side in CHS”, in these proceedings.
[5] K. Nagasaki et al “Electron Bernstein Wave Heating in Heliotron Systems”, Proc. 12th Joint Workshop on ECE &ECH, Aix-en-Provence, France, 2002, p. 317-322.
Fig. 6 Sample rays experiencing XB conversion when launchedfrom the inner side of the torus simulating evolution afterreflection in the inner wall. They represent reflections towards the clockwise, counter-clockwise and downwards
directions. The scale of the magnetic field strength has
been chosen to highlight the fundamental resonance region.

when the ray is directed towards the fundamental resonance stripe on the outer boundary and show that the power
deposition region tends to towards the core as the horizontal angle is widened. In this last case more calculations
are on the way for greater horizontal and vertical angles tobetter model the experimental results shown in [4].
In the Heliotron-J case, in order to model the trajectory of rays reflected on the vacuum vessel in the innerpart of the torus after being injected from the outer region
port, the launching point for the simulation has been imposed a few centimetres inwards from the inner boundaryof the plasma in the corner region. Vertical and horizontal angular scans have been carried out with the ART code
obtaining XB conversion in many cases. The deposition
profiles show that the energy absorbed from these rays isdeposited mainly in the core region in agreement with experimental measurements.
More simulations of EBW heating in Japanese helical