Plasma and Fusion Research: Regular Articles

Volume 11, 2402095 (2016)

Development of Electron Bernstein Emission Diagnostic for
Heliotron J∗)
Kazunobu NAGASAKI, Yuji NAKAMURA1) , Sohei KAMIOKA1) , Hiroe IGAMI2) ,Francesco VOLPE3) , Torsten STANGE4) , Kinzo SAKAMOTO, Hiroyuki OKADA,Takashi MINAMI, Shinichiro KADO, Shinji KOBAYASHI, Satoshi YAMAMOTO,Shinsuke OHSHIMA, Gavin WEIR, Shigeru KONOSHIMA, Naoki KENMOCHI1) ,Yoshiaki OTANI1) , Yasuo YOSHIMURA2) , Nikolai MARUSHCHENKO4) and Tohru MIZUUCHI
Institute of Advanced Energy, Kyoto University, Gokasho, Uji 611-0011, Japan
Graduate School of Energy Science, Kyoto University, Gokasho, Uji 611-0011, Japan
2)
National Institute for Fusion Science, Toki 509-5292, Japan
3)
Applied Physics and Applied Mathematics, Columbia University, New York, USA
4)
Max-Planck-Institut für Plasmaphysik, IPP-EURATOM Association, D-17491, Greifswald, Germany
1)(Received 25 November 2015 / Accepted 6 May 2016)
Electron Bernstein Emission (EBE) diagnostic system using Ordinary (O) – eXtraordinary (X) - Bernstein(B) mode conversion process has been developed for determining electron temperature profiles at overdense
plasmas in a helical-axis heliotron device, Heliotron J. Ray-tracing calculation results show that the O-X mode
conversion window is accessible with a current ECH/ECCD launcher and transmission system. The EBW radiation from the core region is expected to be measurable by adjusting the magnetic field strength. Eﬀect of density
fluctuation on O-X mode conversion eﬃciency is also discussed. Based on the calculations, a multi-channel
radiometer of Ka-band range has been designed, assembled and tested.
c 2016 The Japan Society of Plasma Science and Nuclear Fusion Research

Keywords: electron Bernstein emission, diagnostic, ray tracing, radiometer, Heliotron J
DOI: 10.1585/pfr.11.2402095

1. Introduction
Electron cyclotron emission such as Ordinary (O) andeXtraordinary (X) modes are used for electron temperature
diagnostic in magnetic fusion devices. Although the ECE
diagnostic is reliable, there is an upper accessible density
limit so called cut-oﬀ density. Electron Bernstein Waves(EBWs) are electrostatic waves propagating in hot magnetized plasmas at densities where the O and X modes are notaccessible. The EBWs have advantage of no density limit
and high optical thickness even at low electron temperature. These aspects, along with high localization of theiremission, makes EBWs suitable for determining electron
temperature profiles and the pitch angle of magnetic fieldat overdense plasmas [1]. While the EBWs can exist only
in a plasma, they can be coupled to an external receiver bymeans of mode conversions. Of various schemes proposed,
the Bernstein (B)-X-O process is attractive since they canbe geometrically optimized by adopting a special line ofsight [2–4].
In this paper, we show recent progress on theoretical
study and diagnostic development for EBE measurement
in a helical-axis heliotron device, Heliotron J, aiming at
author’s e-mail: nakazaki.kazunobu.4x@kyoto-u.ac.jp∗) This article is based on the presentation at the 25th International Toki
Conference (ITC25).

measuring core electron temperature in overdense plasmas.
The theoretical study of mode conversion and radiation position is described in Sec. 2, and a radiometer system forEBE diagnostic is shown in Sec. 3. Summary is given inSec. 4.

2. Ray Tracing Code for O-X-B Mode
Conversion in Heliotron JHeliotron J is a medium-sized stellarator/heliotron device [5]. The main device parameters are the plasma major radius R = 1.2 m, the averaged minor radius a = 0.1 0.2 m, the rotational transform ι/2π = 0.3 - 0.8, and themaximum magnetic field strength on magnetic axis, B =1.5 T. The coil system is composed of an L = 1, M = 4
helical coil, two types of toroidal coils A and B, and threepairs of vertical coils. Here L and M denote the poloidaland toroidal pitch numbers, respectively. Accessing thefundamental EBE by means of B-X-O conversion requires
the plasma densities over around 1 × 1019 m−3 , which areroutinely produced in the Heliotron J.
In toroidal geometries, an incident O-mode launchedfrom the low field side can be converted into a slow Xmode at the O-mode cut-oﬀ layer if the O-mode is injected
at the optimal angle oblique to the magnetic field. The
optimal angle at the O-mode cut-oﬀ is given by2402095-1

c 2016 The Japan Society of PlasmaScience and Nuclear Fusion ResearchPlasma and Fusion Research: Regular Articles
cos θopt=Y,
1+Y

Volume 11, 2402095 (2016)(1)

where θ is the angle that the magnetic field makes withthe wave vector, Y = ωce /ω, ωce is the electron cyclotron
angular frequency and ω is the wave angular frequency.
Before studying EBW, we investigate the viewing angle for O-X mode conversion by using a ray tracing code,
TRAVIS code [6]. The TRAVIS code was developed for
ECH/ECCD and ECE diagnostic in arbitrary 3D magnetic
configurations. The magnetic configuration is provided by
the 3D equilibrium code VMEC. The code is used throughan especially designed graphical user interface, which allows the preparation of input parameters and viewing results in convenient (2D and 3D) form. This interface makes
it rather easy to find out the parallel and perpendicular refractive indices at cut-oﬀ positions. The mode conversion
eﬃciency is given as
T (Ny , Nz ) =⎧⎫⎪⎪⎪⎪Y⎨22 ⎬exp ⎪,⎪−πk0 Ln 2 2(1 + Y)(Nz,opt − Nz ) + Ny ⎪⎪⎩⎭
(2)2= cos2 θopt = Y/(1 + Y), and Ln is the density
where Nz,opt

scale length [7]. Figure 1 illustrates the contour of O-X
mode conversion eﬃciency in viewing space for 35 GHz
frequency waves. The mode conversion window with morethan 50 % eﬃciency has an angle range of about 8 deg and3 deg in the toroidal and poloidal directions, respectively,
at electron density of ne = 2 × 1019 m−3 . Although theaccessible toroidal angle in the experiment is limited bysteering range of the antenna mirror and the port boundary,we expect that the conversion eﬃciency more than 50 % is
obtained at available viewing angles. As the mode conversion eﬃciency is a function of density scale length, the OX window is wider with an increase in electron density as
shown in Fig. 1 (b), which would be beneficial for searching the O-X conversion point.
A ray tracing code, KRAY, upgraded from B-RAY
code [8], has been developed to calculate the ray trajectory of O-mode, X-mode and EBW for Heliotron J. Newaspects on the KRAY code development, compared to theprevious B-RAY code is that the magnetic coordinates
given by the VMEC code were newly taken into consideration in the KRAY, while the magnetic field is given by filament coils and the flux surface is assumed elliptical in thepoloidal cross-section in the B-RAY code. Note that theO-X-B calculation is applicable to EBE measurement via
B-X-O mode conversion since the mode conversion process is reversible. The code solves the radiative transfer
equations under the geometrical optics approximation. To
calculate the ray trajectory, the three-dimensional magnetic
field structure and flux surfaces of Heliotron J is taken into
account, which are given by the VMEC code with finite
β. The dispersion relation for the electromagnetic waves isgiven by a cold plasma approximation, and the dispersion

Fig. 1 Contour of O-X mode conversion window at B = 1.22 T,(a) ne (0) = 2 × 1019 m−3 and (b) ne (0) = 3 × 1019 m−3 . The
white curved line denotes the port boundary.

Fig. 2 Top view of ray trajectory in O-X-B mode conversion
process in the Heliotron J standard configuration.

relation for electrostatic waves is given by a hot plasma
approximation.
Figure 2 illustrates a top view of a ray trajectory inO-X-B mode conversion in the standard Heliotron J con-2402095-2

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Fig. 4 Calculated absorption radius against wave frequency atne (0) = 2 × 1019 m−3 .
Fig. 3 Refractive indices as a function of plasma radius.

figuration, and Fig. 3 shows the refractive indices along
the ray trajectory. In the KRAY code, the optimal viewing angle for O-X mode conversion is searched as well asthe TRAVIS code. We confirm that the O-X window region estimated in KRAY agrees with that by TRAVIS code.
The real part of perpendicular refractive index goes to zeroat the O-mode cut-oﬀ, and then the O-mode is converted
into the slow X-mode. After conversion, the X-mode
propagates toward high-density region until it turns backand propagates toward the upper hybrid resonance (UHR)
layer. When the X-mode approaches the UHR layer, theperpendicular component of the refractive index rapidly increases, resulting that the phase velocity of the wave slows
down. In this process, the electric field of the X-mode begins to lie parallel to the wave vector, that is, the wave turns
to be the EBW. The generated EBW propagates backward
into the high-density region, and the imaginary part of perpendicular refractive index rapidly increases at the position
where the Doppler shifted cyclotron resonance conditionis satisfied, resulting that the wave energy is transferred toelectrons. The EBW from the radiation position has thesign of N|| opposite to that of the EBW traced from theUHR. According to the Doppler-shifted resonance condition, ω(1 − N|| v|| /c) = ωce . the electrons with the opposite
sign of v|| resonate with the EBW when N|| is reversed, resulting that the deposition position is the same as the radiation position. If the velocity distribution is asymmetricwith v|| , the deposition position may be diﬀerent from theradiation position.
As shown in Fig. 4, the absorption position, which reflects the radiation position of the EBW, is located at coreregion if the magnetic field is properly chosen. As β increases, the magnetic axis is Shafranov-shifted outwardly,
aﬀecting the radiation position. The radiation frequency tomeasure the core electron temperature is 37 GHz at 1.20 T,
where the radiation position closest to the magnetic axis

is r/a = 0.1. In the calculation, the radiation position isdetermined by the ray with optimum launching condition.
Since the O-X window has a finite area, the radiation profile is broader when we include the ray trajectories with
non-optimum conditions. Accurate radiation profile will
be studied in future work.
Density fluctuation gives rise to beam divergence,
resulting in reduction in the O-X conversion eﬃciency.
Let us consider the fluctuation with a wave vector in thepoloidal direction. With a statistic description of the cutoﬀ surface roughness, the probability density function ofthe poloidal component Ny is given as⎫⎧⎪⎪⎪⎪
Ny2 λ2y⎪⎪λy−3/2⎬⎨p(Ny ) = √exp ⎪,−1 − Ny2⎪
⎪
⎪
⎪
⎪
22
⎩ 1 − Ny 2σ x ⎭2πσ x(3)where σ x is the the fluctuation amplitude standard deviation, σ x = Lñe /ne , λy is the poloidal correlation length [9].
The modified O-X conversion eﬃciency, T mod , including
density fluctuation eﬀect is written as 1T (Nz , Ny )p(Ny )dNy .
(4)
T mod (Nz ) =−1

Figure 5 shows the dependence of modified O-X mode
conversion eﬃciency, T mod , on the viewing angle. Here
we assume that ωce is equal to ω. The density fluctuation
reduces the mode conversion eﬃciency even at optimal angle considerably. Even though we do not have any experimental data on density fluctuation at the edge region inHeliotron J where the O-X mode conversion takes place,the calculation suggests that the density fluctuation of 8 %causes reduction in conversion eﬃciency by about 20 %.
The density fluctuation eﬀect is more significant as thedensity gradient is gentle, meaning that the steep density
gradient is favorable for high O-X mode conversion, which
is typically observed in ECH plasmas in helical devices.

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Fig. 5 Eﬀect of density fluctuation on O-X mode conversion efficiency.

Fig. 6 Schematic of EBE radiometer system.

3. EBE Diagnostic for Heliotron JAn EBE diagnostic has been designed for HeliotronJ, based on the ray tracing calculation results. The designed EBE diagnostic consists of a steerable antenna, awaveguide transmission line and a heterodyne radiometer.
A launcher and transmission line of corrugated waveguides
for the existing 70 GHz ECRH/ECCD system is applied
for the EBE diagnostic instead of assembling a new independent system. A waveguide switch is installed 3 m
before the launcher, which manually switches from theECRH/ECCD to EBE measurement. A Gaussian-optics
antenna, which can measure two cross-polarizations, isused between the corrugated waveguide and the Ka-band(24 - 42 GHz) rectangular waveguide. A SPDT PIN switch
is set up in the Ka band rectangular waveguide line, which
selects the orthogonal field components in a plasma discharge by applying an external bias voltage.
The heterodyne radiometer system has been assem-Fig. 7 Calibration Results of heterodyne radiometer. The blackline denote the calibration results from a noise source,
the others denote those from a frequency scanning microwave source.

bled and tested before installation on the Heliotron J device. Figure 6 shows a schematic of the radiometer,
which covers Ka-band, corresponding to the cut-oﬀ density of 0.86 - 2.25 × 1019 m−3 . The radiometer consists ofa 24 GHz Gunn oscillator, a balanced mixer, a step attenuator, low-noise amplifiers, power dividers, band-pass filters, Shottky-barrier diodes. The band-pass filters of 1 GHzband width allow tuning 8 channels of the radiometers tofrequencies in the 26 - 41 GHz range. The center frequencies of bandpass filters are 2.5 GHz, 4.5 GHz, 6.5 GHz,
8.5 GHz, 10.5 GHz, 12.5 GHz, 14.5 GHz and 16.5 GHz.
Relative calibration has been performed with twokinds of microwaves sources as an input signal to theradiometer. One is a noise source of Ka-band (HewlettPackard R347B, 26.5 - 40 GHz) which radiates broadband
microwaves. The other is a frequency tunable microwave
source of 26 - 40 GHz frequency range, in which a powercalibrated microwaves of 12 - 20 GHz generated by a solidstate signal generator (Vaunix LMS-203, 10 - 20 GHz), aredoubled to 24 - 40 GHz with an active frequency doubler(SAGE SFA-282SF-S1, 26.5 - 40 GHz). For the former
source case, the radiometer output reflects the white broadband noise radiation input, and for the latter case, it reflects
the discrete frequency radiation. Figure 7 shows the relative calibration results. It can be seen that both calibration
results have the same tendency in output signal intensity,
but not exactly the same performance due to the diﬀerent characteristics between the two sources. Although thereason for fluctuations observed in the discrete frequency
source is not clear, it may be related to the characteristicsof the radiometer components such as mixer, low noise amplifiers, power splitter and band pass filter. The nW levelof input microwaves signal is possible to detect beyond
the noise level. Since the bandpass filters of 2.4 GHz and
4.5 GHz do not filter out high frequency components of
11 - 12 GHz and 13.5 - 15 GHz well, replacement into better ones is required.

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4. Summary
An EBE diagnostic system using B-X-O mode conversion process has been developed for determining electron temperature profiles at overdense plasmas in Heliotron
J. The calculation results using the ray tracing codes,
TRAVIS and KRAY, show that the current EC launcher antenna has an access window for the O-X conversion under
overdense plasma conditions. The ray tracing code, KRAY,
which considers the 3-D magnetic configuration with finite
beta, predicts that the radiation from the core region canbe detected through the B-X-O mode conversion process.
A multi-channel radiometer system has been designed, assembled and tested for EBE measurement. The EBE measurement in NBI plasmas will be performed in Heliotron Jin the near future. Application of this radiometer system tothe LHD device is also underway.

Acknowledgments
The authors are grateful to the Heliotron J staﬀ foruseful discussion. This work was performed with thesupport and under the auspices of the Collaboration Program of the Laboratory for Complex Energy Processes,
IAE, Kyoto University, and the NIFS Collaborative Research Program (NIFS10KUHL030, NIFS13KUHL059),
the NIFS/NINS project of Formation of International Network for Scientific Collaborations, and a Grant-in-Aid for
Scientific Research, MEXT.
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