Plasma and Fusion Research: Regular Articles

Volume 13, 3402115 (2018)

High-Field-Side RF Injection for Excitation ofElectron Bernstein Waves∗)
Ryota YONEDA, Kazuaki HANADA1) , Hatem ElSERAFY,
Nicola BERTELLI2) and Masayuki ONO2)
Interdisciplinary Graduate School of Engineering Sciences, Kyushu University, Kasuga 816-8580, Japan
1)
Research Institute for Applied Mechanics, Kyushu University, Kasuga 816-8580, Japan2)
Princeton Plasma Physics Laboratory, Princeton, New Jersey 08543, USA(Received 27 December 2017 / Accepted 2 July 2018)
An evaluation of high-field-side (HFS) X-mode injection for the electron-Bernstein-wave (EBW) scenario
is performed using the GENRAY ray-tracing code. In the early stage of low-density plasma start-up, when theelectron cyclotron resonance and upper hybrid resonance layers are close to each other, eﬃcient and localized
heating by the EBW is attainable. We show that, when the electron density rises, the HFS scenario spontaneously
shifts to current drive with successful electron heating. This shift can be explained as a change in heating mechanism from collisional to electron cyclotron damping. Also, we discuss a possible O-X-B scenario to continue theplasma current drive beyond the formation of an over-dense plasma.
c 2018 The Japan Society of Plasma Science and Nuclear Fusion Research

Keywords: electron Bernstein wave, electron cyclotron, high field side, plasma heating and current drive, mode
conversion
DOI: 10.1585/pfr.13.3402115

1. Introduction
Non-inductive current drive is one of the crucial topics in regard to spherical tokamak (ST), where space forthe central solenoid is technically limited [1]. Radiofrequency (RF) waves in the range of the electron cyclotronfrequency are commonly used in heating and current drivein STs [2–5]. In the initial phase of plasma build-up, thefirst pass absorption at the electron cyclotron resonance(ECR) layer is very small because the electron temperature T e and density ne are low, and multiple reflectionsof RF waves inside the vessel enable RF-induced breakdown [6–8].
The excitation of electron Bernstein waves (EBWs)
could result in highly eﬃcient heating of magnetized plasmas [9–12]. The significance of the EBW often arisesin the context of over-dense plasma, where the electron
plasma frequency ωpe is larger than the electron cyclotron
frequency Ωce (ωpe /Ωce > 1); therefore, the accessibility ofelectromagnetic electron cyclotron waves to the ECR layer
disappears. In contrast, the electrostatic EBW may propagate in the over-dense regime and be strongly damped
near the ECR layers. Also, in the initial discharge phase
where we have lower T e , eﬃcient collisional damping of
the EBW is expected because the group velocity of theEBW is comparable with electron thermal velocity. Thereare several ways to excite EBWs in a tokamak configuration but, in the initial low-density phase, where the electron
author’s e-mail: yoneda@triam.kyushu-u.ac.jp∗) This article is based on the presentation at the 26th International Toki
Conference (ITC26).

density is less than the cutoﬀ density, only the extraordinary mode (X-mode) injection from the high field side(HFS) is available. The other methods (O-X-B and X-XB) require an over-dense regime. Here, O and B stand forordinary mode and EBW, respectively. We expect the Xmode launched from the HFS to fully convert to the EBW
in the upper hybrid resonance (UHR) layer [13]. The diﬃculty of HFS injection lies in the engineering implementation; a waveguide at the HFS must cross the ECR layer andsuppressing RF breakdown inside the waveguide is necessary. In a laboratory test, we demonstrated the transmission of 20-kW RF power through the ECR layer inside awaveguide, which was filled with SF6 to suppress breakdown.
In this study, we investigated the feasibility of EBWs
in the low-density-phase for the initial tokamak plasma
start-up by RF injection from the HFS of the tokamak configuration. Adopting EBWs in the low-density regime hasa significant advantage when the ECRH is less eﬃcient.
The calculation of wave propagation and absorption wasperformed using GENRAY ray-tracing code [14, 15]. The
magnetic configuration used here is based on the experimental results of the QUEST spherical tokamak [16]. The
RF frequency and power are set at 8.2 GHz and 50 kW
to model the experimental set-up of the 8.2-GHz HFS Xmode in QUEST.

2. HFS Injection Scenarios for EBWsFirst, we confirmed the conditions right after breakdown when T e and ne are very low. Note that the O-3402115-1

c 2018 The Japan Society of Plasma
Science and Nuclear Fusion ResearchPlasma and Fusion Research: Regular Articles

Volume 13, 3402115 (2018)

Fig. 1 Low-density regime: (a) Poloidal view of ray-tracing.
Light blue dotted line is the 1st ECR, red dotted line is theRcutoﬀ, blue dotted line is the UHR and magenta line isthe lastclosed flux surface. The 1st ECR and UHR are located close to each other; (b) Toroidal view of ray-tracing.
Green dotted line is the magnetic axis. The X-mode isconverted to EBW at UHR and it starts to propagate inparallel direction; (c) Density ne profile. Rho is the minor radius defined by r/a; (d) RF power absorption withpoloidal projection of ray. Light blue dotted line is the 1stECR, where the X-mode passes through. The X-B mode
conversion (MC) point is also indicated.

X-B mode conversion cannot be used at this low density
because there is no O-mode cutoﬀ. Ray-tracing results
by GENRAY are shown in Fig. 1. A spatially uniformT e = 5 eV and a ne of ne (0) = 2 × 1017 m−3 at the center
that is approximately 25% of the cutoﬀ density (ne_cut =8.3 × 1017 m−3 ) for 8.2 GHz electromagnetic waves, are set
up. To evaluate collisional damping, Zeﬀ is set to 3 for all
conditions presented in this study. The coeﬃcient of absorption associated with electron collisions with ions αcl[m−1 ] is expressed as
αcl = 2vei /vg ,3vei = 9.17 × 10−17 ne Zeﬀ ln Λ/T e2 (T e in keV),
where vei is the electron-ion collision rate, vg the group velocity of the waves, and ln Λ the Coulomb logarithm. InGENRAY, the calculation of αcl is taken along the ray’s
propagation path to estimate collisional damping. Because
the ECR and UHR gap is small [Fig. 1 (a)], we can expect
eﬃcient and localized absorption of the EBWs. GENRAY
can distinguish the damping mechanisms of the cyclotron
and collisional absorptions that contribute to both damping eﬀects and are comparable in this configuration with
low ne and T e . For cyclotron damping absorption, theDoppler-shifted resonance is included to evaluate the evolution of the parallel refractive index N for EBWs [17].

Fig. 2 Medium-density regime: (a) Poloidal view of ray-tracing,(b) Toroidal view of ray-tracing (for diﬀerent T e , ray trajectories are almost the same), (c) Parallel current density
driven by cyclotron damping with diﬀerent T e (note thatthe horizontal axis is zoomed in), and (d) RF power absorption with the poloidal projection of the rays for different T e .

In Fig. 1 (d), the power absorption of the perpendicular Xmode at the 1st ECR is included but is negligible with low
T e ; the EBW is rapidly damped right after the X-B mode
conversion. An important point to note is that the X-mode
should be launched oﬀ-mid-plane to control the current
drive direction [11].
Second, we consider the case when ne increases but
remains below the over-dense regime. To explore the effect of T e , we varied the value of T e from 5 eV to 100 eV.
Figure 2 shows results for center ne (0) set to 8.0 × 1017 m−3
and T e is spatially homogeneous. The current density andpower absorption profiles under cyclotron damping wereplotted [Figs. 2 (c) and (d)]. The contribution of cyclotron
damping clearly dominates relative to collisional damping at higher T e . Figure 2 (d) shows the diﬀerence inthe damping mechanism, in which plasma fully absorbs
the injected RF power. At T e = 5 eV, collisional damping of the EBW is dominant and the absorption is localized near the UHR layer. In contrast, as T e increases, thelocation of absorption moves closer to the ECR layer asexpected for cyclotron damping. As the toroidally propagating EBW [Fig. 2 (b)] can transfer wave momentum toexcite the driven current Icd , the current density increases
with higher T e [Fig. 2 (c)]. GENRAY evaluates the current drive generated by the injection of electron cyclotron
waves. In Fig. 3, the dependence of Icd with T e is shown.
With 50-kW injection, it suggests that Icd ∼ 20 kA is almost
possible. Moreover, cyclotron damping becomes dominant when T e ≥ 15 eV. If T e increases successfully with3402115-2

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Volume 13, 3402115 (2018)

Fig. 3 Dependence of the net current drive Icd on T e obtainedusing GENRAY.

Fig. 5 O-X-B scenario: (a) Poloidal view of ray-tracing. Greendotted line is the O-cutoﬀ and the black dotted line is theLcutoﬀ, (b) Toroidal view of ray-tracing, (c) ne profile,(d) T e profile, and (e) RF power absorption with poloidal
projection of the ray. O-X and X-B mode-conversion
points are specified.

no longer has to propagate the evanescent layer after reflections at the cutoﬀs or the vessel walls.

Fig. 4 Over-dense regime: (a) Poloidal view of ray-tracing.
Green dotted line is O-cutoﬀ, (b) Toroidal view of raytracing, (c) ne profile, and (d) RF power absorption withthe poloidal projection of the ray.

the injected RF power, then we can say that from the calculation the HFS X-mode scenario automatically shifts to
EBW current drive from heating.
Third, we examined the HFS X-mode scenario in theover-dense phase. In Fig. 4, we set ne at the center ne (0)= 1.5 × 1018 m−3 , which is about twice the cutoﬀ density (ne_cut = 8.3 × 1017 m−3 ) for 8.2 GHz. A temperatureof T e = 50 eV is assumed to be spatially uniform. With
increased ne , the X-mode starts to bend. In the calculations, the accessibility to the UHR layer disappears whenne (0) ∼ 2.0 × 1018 m−3 . Ray-tracing has been demonstrated
with a single ray but does not take into account multiplereflections. Even though the accessibility disappears forthe first pass, the reflected electromagnetic waves may stillreach the UHR as a X-mode and excite an EBW. The HFS
injection scenario has an advantage at this point in that it

3. LFS Injection Scenarios for EBWs
Next, we evaluated a possible O-X-B mode conversion scenario after the formation of the over-dense plasma.
For this scenario, an O-mode launched from the low fieldside (LHS) must hit an optimized O-X conversion point
and then the X-mode excites the EBW at the UHR. GENRAY also can simulate an O-X-B scenario; see Fig. 5.
The ne and T e profiles [Figs. 5 (c) and (d)] are assumed
to be Gaussian-like distributions. After X-B conversion,
the EBW is gradually absorbed through collisional damping and is strongly damped near the ECR layer. Absorption is localized at the ECR layer but some power is absorbed prior to ECR [Fig. 5 (e)]. The net plasma current
driven by the EBW excited via the O-X-B mode conversion was evaluated, yielding Icd = 8.8 kA. This value does
not take into account the conversion loss during O-X-B
mode conversion. This scenario involves a triplet of resonances and cutoﬀs and hence its evaluation is more difficult compared with the HFS X-B scenario. In principle,
the O-X mode conversion eﬃciency cannot be calculated
directly by ray-tracing. A slight change from the optimum
launching for smooth O-X conversion in GENRAY may

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Volume 13, 3402115 (2018)

also allow an O-X mode conversion with less eﬃciency.
For waves that have a finite width and launched with anarbitrary angle, introducing a full wave calculation is required or a model which can restart the ray-tracing after transmission through the evanescent region to estimate
the characteristics of wave propagation including the O-X
mode conversion and the absorption [18]. Therefore, thepower of the waves launched with a finite width is expected
to be reduced to some extent after O-X mode conversion.
In contrast, the HFS X-mode scenario has an advantage inthat the launched waves can access the UHR without confronting the evanescent region and can be mode converted
fully to the EBW even if they have a finite width.
Another possible scenario from LFS is the direct X-B(X-X-B) conversion through the tunneling of the X-mode
at the R-cutoﬀ [19, 20]. With this direct X-mode scenario,
a precise handling of the launch angle is not required but isnecessary for O-X-B; here, the launched RF power should
be relatively larger to transport the injected X-mode beyond the R-cutoﬀ because reflections at the R-cutoﬀ are
not negligible [19].

4. Summary
In summary, an evaluation of HFS X-mode injection
for EBW heating and current drive has been performed using GENRAY. First, in the early stage of start-up, when
the ECR and UHR layers are close to each other, eﬃcient and localized heating by EBWs is attainable. Second, for increased ne , we showed that the HFS scenario
spontaneously shifts to current drive as T e increases. This
shift can be explained by the change in heating mechanism
from collisional to electron cyclotron damping. Third, weexplored the HFS X-mode in the over-dense regime. We
also considered a possible O-X-B scenario to continue theplasma current drive beyond the formation of the overdense plasma. All ray-tracing results presented are singleray analyses. To examine realistic experimental conditions, a multiple-ray analysis may be needed.

Acknowledgements
This work was supported by Japan/U.S. Cooperationin Fusion Research and Development in 2016 and 2017.
The Author (R.Y.) kindly acknowledges the financial support from Kyushu University Program for Leading Graduate Schools, Advanced Graduate Program in Global Strategy for Green Asia. We thank Richard Haase, Ph.D, fromEdanz Group for editing a draft of this manuscript.
[1] M. Ono and R. Kaita, Phys. Plasmas 22, 040501 (2015).
[2] H. Idei et al., Nucl. Fusion 57, 126045 (2017).
[3] T. Yoshinaga et al., Nucl. Fusion 47, 210 (2007).
[4] M. Ishiguro et al., Phys. Plasmas 19, 062508 (2012).
[5] S. Tashima et al., Nucl. Fusion 54, 23010 (2014).
[6] R. Yoneda et al., Phys. Plasmas 24, 062513 (2017).
[7] D.R. Whaley et al., Nucl. Fusion 32, 757 (1992).
[8] Y.H. An et al., Nucl. Fusion 57, 016001 (2017).
[9] A.K. Ram and S.D. Schultz, Phys. Plasmas 7, 4084 (2000).
[10] A.K. Ram et al., Phys. Plasmas 9, 409 (2002).
[11] C.B. Forest et al., Phys. Plasmas 7, 1352, (2000).
[12] V.F. Shevchenko et al., Nucl. Fusion 50, 22004 (2010).
[13] T. Maekawa et al., Phys. Rev. Lett. 86, 3783 (2001).
[14] A.P. Smirnov and R.W. Harvey, Bull. Am. Phys. Soc. 40,1837, abstract 8p35 (1995).
[15] E. Mazzucato et al., Phys. Fluids 30, 3745 (1987).
[16] K. Hanada et al., Nucl. Fusion 57, 126061 (2017).
[17] C.B. Forest et al., Nucl. Fusion 41, 619 (2001).
[18] H. Igami et al., Plasma Fusion Res. 11, 2403098 (2016).
[19] M. Ali Asgarian et al., Phys. Plasmas 21, 092516 (2014).
[20] J.G. Jo et al., Phys. Plasmas 24, 012103 (2017).

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