Improved performance of electron cyclotron
resonance heating by perpendicular injection in
the Large Helical Device
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言語: English
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公開日: 2021-12-23
キーワード (Ja):
キーワード (En):作成者: Tsujimura, Ii Toru, YANAI, Ryohma, MIZUNO,
Yoshinori, TANAKA, Kenji, YOSHIMURA, Yasuo,
TOKUZAWA, Tokihiko, NISHIURA, Masaki,
SAKAMOTO, Ryuichi, MOTOJIMA, Gen, KUBO, Shin,SHIMOZUMA, Takashi, IGAMI, Hiroe, TAKAHASHI,
Hiromi, YOSHINUMA, Mikiro, Ohshima, Shinsuke,
LHD, Experiment Group
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Improved performance of electron cyclotron
resonance heating by perpendicular injection in the
Large Helical Device
T. Ii Tsujimura1 , R. Yanai1 , Y. Mizuno1 , K. Tanaka1 ,Y. Yoshimura1 , T. Tokuzawa1,2 , M. Nishiura1 , R. Sakamoto1,2 ,G. Motojima1,2 , S. Kubo1 , T. Shimozuma1 , H. Igami1 ,H. Takahashi1,2 , M. Yoshinuma1 , S. Ohshima3 and the LHD
Experiment Group1
1

National Institute for Fusion Science, National Institutes of Natural Sciences, Toki,
Gifu 509-5292, Japan
2
The Graduate University for Advanced Studies, SOKENDAI, Toki, Gifu 509-5292,
Japan
3
Institute for Advanced Energy, Kyoto University, Uji, Kyoto 611-0011, Japan
E-mail: tsujimura.tohru@nifs.ac.jp
23 October 2020
Abstract. A real-time interlock system for power injection in electron cyclotron
resonance heating (ECRH) was developed to be applied to Large Helical Device (LHD)plasma. This system enabled perpendicular injection, thus improving the performanceof ECRH more than ever achieved before in LHD. Perpendicular propagation of theelectron cyclotron wave at 77 GHz became more insensitive to the eﬀect of refraction
in comparison to the conventional oblique propagation. The achieved central electron
temperature in the case of perpendicular injection was approximately 2 keV higher
than that in the case of standard oblique injection for a central electron density of
1 × 1019 m−3 by 1 MW injection. With such improved performance of ECRH, highdensity ECRH plasma of 8 × 1019 m−3 was successfully sustained after the injectionof multiple hydrogen ice pellets for the ﬁrst time in LHD.

1. Introduction
In magnetically-conﬁned fusion plasma, adjustments of launcher settings of electron
cyclotron resonance heating (ECRH) are necessary to produce high-performance plasma,
to realize desired power deposition proﬁles, to decrease the stray radiation level in thevessel, and to prevent damage of in-vessel components from unabsorbed power duringhigh-power long-pulse injection. Single-pass absorption must be maximized to fulﬁll
such requirements.
To obtain high single-pass absorption is strongly related to injection methods of
ECRH. In the Large Helical Device (LHD), high-power gyrotrons have been introducedImproved performance of ECRH by perpendicular injection in LHD

2

to extend the operational regime of high central electron temperature (Te0 ) and highcentral electron density (ne0 ) [1]. This operational regime can be extended not only by
the power increase of gyrotrons but also by adjustments of ECRH launcher settings.
Perpendicular injection to the ECR layer is expected to be more insensitive to the eﬀectof refraction. Historically, however, two kinds of injection methods of ECRH have been
adopted in the current LHD experiments for their speciﬁc purposes: (i) injection fromthe upper port on the vertically-elongated plasma cross section (U-port injection) and(ii) injection from the outer port on the horizontally-elongated plasma cross section(O-port injection) [1, 2]. The U-port injection is suitable for plasma startup, but it
is sensitive to refraction by high-ne plasma. A 77-GHz gyrotron has been used for
the U-port injection, which enables on-axis heating with the fundamental ordinary (O)mode in the standard magnetic conﬁguration of LHD with a magnetic ﬁeld strength of
2.75 T. The plasma cutoﬀ density is 7.4 × 1019 m−3 . Even in ne0 ∼ 1 × 1019 m−3 , theEC wave is easily refracted, so that tuning the launcher was performed with the raytracing code LHDGauss to obtain on-axis heating [3, 4]. The LHDGauss code runs on
the AutoAna system [5], which is helpful for analyzing experimental data immediately
after discharges on LHD. The ﬁne tuning of launchers along with predictions of power
deposition proﬁles by ray-tracing calculations contributed to the extension of the high-T
regime [6]. However, the sensitivity to refraction prevents eﬃcient heating in higher ne .
The cause of low heating performance is that the EC wave from the U port tangentiallyreaches the ECR layer. Most of the refracted wave cannot reach the ECR layer, whichtransmits over the plasma without absorption. The O-port injection improves theheating eﬃciency in high ne in comparison to the U-port injection because the EC
wave from the O-port injection can reach the ECR layer more perpendicularly. 77-GHz
and 154-GHz gyrotrons have been used for the O-port injection. As shown in Fig. 1, theﬁrst walls are reinforced with molybdenum (Mo) on the opposite side of the launcher
Zf (m)
0.5

2-OUR
C divertor tiles

Mo tiles0

0.5

Tf (m)

SS tilesFigure 1. A drawing viewed from the center of the ﬁnal mirror of the 2-OUR antenna(installed at the upper right side of the 2-O port) along with an imaginary target planewith a toroidally- and vertically-directed coordinate (Tf , Zf ) radially ﬁxed at Rf = 3.9
m. First walls are reinforced with Mo on the opposite side of the launcher.

Improved performance of ECRH by perpendicular injection in LHD

3on the 2-O port. Thus, the standard injection method from the O port is oblique
injection. Plasma startup can be also possible by the standard oblique injection. On
the other hand, since the carbon divertor tiles on the opposite side of the launcher are
fragile to transmitted high-power millimeter waves, perpendicular injection could not beapplied in LHD before without an interlock system for power injection. Oblique injection
contributes to EC current drive experiments as well [7]. Due to oblique propagationof the EC wave, however, the EC wave from the O-port injection is still sensitive torefraction in high ne . The heating eﬃciency is observed to decrease gradually as neincreases in the case of the standard oblique injection from the O port.
According to the current LHD project, there are strong needs for transport studies
for isotope eﬀects of high-ne plasma with high-power ECRH. In contrast to 154-GHz
ECRH, however, 77-GHz ECRH is rarely used for such transport studies at highne due to the eﬀect of refraction [8, 9, 10, 11]. A real-time control system of thedeposition location of ECRH was developed to mitigate the eﬀect of refraction [12, 13].
The deposition location was adjusted according to time-varying ne proﬁles. Higher
absorption was successfully maintained longer due to the real-time deposition location
control up to line-averaged density of ne,avg ∼ 3 × 1019 m−3 , where the deposition
location was kept in the plasma core region. However, the absorption power decreased
above 3 × 1019 m−3 even with the deposition location control. The eﬀect of multi-passabsorption is expected to be dominant.
This situation has led to the necessity of perpendicular injection (i.e., perpendicular
to the ECR layer) from the O port because it is expected to be more insensitive
to the eﬀect of refraction. The optical thickness for the fundamental O mode using
77 GHz increases as the propagation angle increases to reach 90◦ , i.e., perpendicularpropagation [2]. Here, the optical thickness is calculated by the non-relativistic theory
in a slab plasma [14, 15, 16]. Stronger absorption for the fundamental O modewith perpendicular propagation is expected. On the other hand, the fundamental
extraordinary (X) mode is reﬂected at the right-hand cutoﬀ layer located in front of
the ECR layer. Although the unabsorbed transmitted wave propagates to the divertor
region in LHD, as shown in Fig. 1, it is expected to be minute in principle. Figure 2
shows ray-tracing calculations in the cases of perpendicular injection and standard
oblique injection for ne,max = 3 × 1019 m−3 . The 77-GHz EC wave is launched fromthe 2-OUR antenna located at the upper right side of the 2-O port. Standard oblique
injection is sensitive to refraction by the high-ne plasma, which can decrease the ﬁrstpass absorption and achievable Te0 . On the other hand, perpendicular injection ismore insensitive to the eﬀect of refraction, which is veriﬁed with experiments and theresults of improved heating performance are presented in the following sections of thispaper. This perpendicular injection is a common similar heating method in tokamaks
and the W7-X stellarator [17, 18]. For tokamaks, the magnetic ﬁeld monotonicallydecreases with the major radius. Perpendicular injection from the low-ﬁeld side on apoloidal plane was utilized in plasma startup and heating of tokamaks such as DIIID [19], JT-60U [20], KSTAR [21], and TRIAM-1M [22]. However, for magnetic ﬁeld

Improved performance of ECRH by perpendicular injection in LHD
fce
reff/a99

fce = 77 GHz
2fce = 77 GHz

frc = 77 GHz
fuh = 77 GHz(a) Perpendicular injection

4
First wall
Ray(b) Standard oblique injection

Projected T − Tf (m)Z − Zf (m)

0.8
0.4
0
-0.4
-0.8
0.4
0
-0.4
-1

0
1
Projected R − Rf (m)

2

-1

0
1
Projected R − Rf (m)2

Figure 2. Ray-tracing calculations in the cases of (a) perpendicular injection and (b)standard oblique injection from the 2-OUR 77-GHz ECRH for ne,max = 3 × 1019
m−3 . The rays are projected onto two planes: (top) the plane consisting of two
orthogonal basis vectors, ez × (ez × einj ) and ez , and (bottom) the plane consisting of
etor ×(etor ×einj ) and etor , where ez , etor , and einj denote the unit vector in the verticaldirection, that in the toroidal direction at the 2-O port center, and that in the direction
from the launching antenna mirror center to the target point. The arrowheads denotethe target points. The contours of reﬀ /a99 and the electron cyclotron frequencies fce ,the lines of the right-hand cutoﬀ frequency frc , the upper hybrid resonance frequency
fuh , and fce for 77 GHz, and the ﬁrst walls are also superimposed on the planes.
Here, reﬀ /a99 denotes the eﬀective minor radius normalized by the minor radius
where 99% of the electron stored energy is conﬁned. The target positions are set
at (Rf , Tf , Zf ) = (3.9, 0, 0) m for (a) and at (Rf , Tf , Zf ) = (3.9, −0.5, 0.05) m for (b).
The magnetic ﬁeld strength is Bt = 2.85 T at the magnetic axis of Rax = 3.6 m.

conﬁgurations such as LHD, the magnetic ﬁeld is non-monotonic along the sight line
due to the presence of the saddle point in the magnetic ﬁeld isolines, as shown in Fig. 2,
which makes the ray trajectories divergent and the deposition proﬁle sensitive to theinjection angle. Perpendicular injection will be also applicable to FFHR-c1, a candidate
for helical DEMO reactors [23], along with the concept of a remote steering antenna [24],suitable for the blankets. When the 77-GHz EC wave is injected from the outside of thehorizontally-elongated cross section, on-axis ECRH with perpendicular propagation isavailable only in the magnetic ﬁeld increased with sub-cooled helical coils such as themagnetic ﬁeld strength of Bt = 2.85 T at the magnetic axis of Rax = 3.6 m [25]. In
contrast to the fundamental O-mode heating with 77 GHz, 154-GHz EC waves for thesecond-harmonic X-mode heating were obliquely injected as usual from the O port for
the experiments introduced in the following sections, because the eﬀect of refraction issmall in ne < 5 × 1019 m−3 . In addition, a portion of the incident wave at 154 GHz

Improved performance of ECRH by perpendicular injection in LHD

5couples to the second-harmonic O-mode wave even when the incident polarization iscontrolled to excite the pure X mode in the actual experiments. The second-harmonic
O-mode wave is in principle weakly absorbed, a part of which is transmitted to thedivertor region through the plasma.
2. Eﬀectiveness of perpendicular injection
The launching antenna 2-OUR for the fundamental O mode at 77 GHz was used toverify eﬀectiveness of perpendicular injection in ECRH on LHD. Figure 1 shows adrawing viewed from the center of the ﬁnal mirror of the 2-OUR antenna. In thedrawing, an imaginary grid target plane is shown with a toroidally- and verticallydirected coordinate (Tf , Zf ) radially ﬁxed at Rf = 3.9 m. The ﬁnal mirror of the
2-OUR antenna is steerable, so that the target position can be changed toroidally
and vertically. The target position was set at (Rf , Tf , Zf ) = (3.9, −0.5, 0.05) m forstandard oblique injection. The millimeter wave propagates into the ﬁrst wall with Mo
tiles under the vacuum condition. On the other hand, the target position was set at(Rf , Tf , Zf ) = (3.9, 0, 0) m for perpendicular injection. Each target position for each
injection was set so that the millimeter wave propagates to the magnetic axis on thevacuum magnetic surfaces, as shown in Fig. 2. The perpendicularly-injected millimeterwave propagates into the divertor region under the vacuum condition. The unabsorbed
transmitted EC wave can reach the divertor region when the O mode is less absorbed
under considerably low ne . Thus, ECRH with perpendicular injection cannot be used forplasma startup in LHD. Plasma must be sustained by other ECRH with oblique injection
from the O port. In order to prevent the unfavorable damage of the divertor region by
the transmitted wave, the interlock system for the power output from the gyrotron wasdeveloped. The interlock system constructed was based on the same system as realtime deposition location control of ECRH [12, 13]. This system was controlled withreal-time FPGA (ﬁeld programmable gate array) processing on a CompactRIO madeby National Instruments. For details, refer to the previous work [12, 13]. The real-time
acquisition was performed for ne,avg measured with the FIR laser interferometer and onechannel Te measured with the EC emission (ECE) diagnostic [26, 27]. The appropriate
threshold settings for the parameters guaranteed that conﬁned plasma was maintained
and perpendicular injection could be available.
With the system, the interlock for power injection only to plasma of ne,avg >0.5 × 1019 m−3 sustained by other ECRH functioned correctly to produce no unfavorable
sparks from the divertor region. Figure 3 shows a typical discharge of modulation
ECRH experiments to evaluate the heating performance. The plasma was sustainedby two 154-GHz gyrotrons. Then, the power of 2-OUR 77-GHz ECRH was modulated
at 11 Hz and was perpendicularly injected from the O port. The time evolution of
Te was measured with the Thomson scattering diagnostic [28]. As shown in Fig. 3(c),higher modulated Te in the case of perpendicular injection was observed than that in
the case of standard oblique injection. The measured point R = 3.646 m is close to theImproved performance of ECRH by perpendicular injection in LHD

6

PECRH (MW)

#157194, Rax = 3.6 m, Bt = 2.85 T
2-OUR, 77 GHz, Pin = 0.792 MW, 11 Hz modulation(a)2

Wp (MJ)00.2(b)Te (keV)05(c)

at R = 3.646 m

m )

-3

1

(10

19

ne,avg0

Oblique injection#157195

(d)

0
3

4

5
Time (s)6

Figure 3. Time evolution of (a) injection power of ECRH, (b) the plasma stored
energy Wp , (c) electron temperature Te at R = 3.646 m, and (d) ne,avg in the caseof perpendicular injection. Te in the case of oblique injection is also plotted forcomparison.

magnetic axis. In order to evaluate the radial proﬁle of modulated Te components, theconditional-averaging technique was applied to the Thomson scattering data during
the modulation ECRH [29]. The analysis was performed in the stationary period
during modulation, where ne,avg and the plasma stored energy Wp were almost constant.
Figures 4(a) and (b) show comparisons of the Te responses between perpendicular
injection and oblique injection in modulation ECRH. The perturbation amplitude of
Te0 in the case of perpendicular injection was higher than that in the case of oblique
injection. Perpendicular injection shows better central heating than oblique injection,although the absorption power was almost the same in both cases as shown in Fig. 6(c).
Figures 4(c) and (d) show the power spectral density (PSD) and the phase delay ofmodulated Te signals measured with the ECE diagnostic. The amplitude peak and thephase bottom could not be recognized in the case of ne,avg ≃ 1×1019 m−3 due to the lackof ECE channels near the magnetic axis. On the other hand, the amplitude peak and thephase bottom could be recognized at reﬀ /a99 ∼ 0.7 in the case of ne,avg ≃ 2 × 1019 m−3
and oblique injection. This suggests that the deposition shifted outward. Refraction and
Doppler-shifted absorption in oblique propagation of the EC wave caused broadening of
the deposition proﬁle, in particular, at higher ne . This eﬀect could not be compensatedwith the real-time deposition location control in high ne , which could only change theImproved performance of ECRH by perpendicular injection in LHD

7

Perpendicular injection
Standard oblique injection

6

Rax = 3.6 m, Bt = 2.85 T
2-OUR, 77 GHz, Pin = 792 kW, 11 Hz modulation(1) ne,avg ≈ 1 × 1019 m-3 (2) ne,avg ≈ 2 × 1019 m-3

Te,avg (keV)

(a1)

2

#157194#1571950δTe (keV)

(a2)

4

0.8

#157201#157200
(b1)

(b2)

(c1)

(c2)

(d1)

(d2)

0.4

Phase delay (ms)PSD (a.u.)

0
-4

10

10-5
40
20
0
0

0.5
reff/a99

0

0.5
reff/a99

Figure 4. Comparisons of radial proﬁles of (a) conditional-averaged Te and (b) its
perturbation δTe measured with the Thomson scattering diagnostic and (c) the power
spectral density (PSD) and (d) the phase delay of modulated Te signals measured
with the ECE diagnostic at the modulation frequency of 11 Hz in the cases of (1)ne,avg ≃ 1 × 1019 m−3 and (2) ne,avg ≃ 2 × 1019 m−3 .

deposition peak location. The deposition width could not be controlled. These results
clearly demonstrated that perpendicular injection is more insensitive to refraction and
Doppler eﬀects than oblique injection, as expected. Ray-tracing calculations by the
LHDGauss code, as shown in Fig. 5, also show better central heating in the case of
perpendicular injection and broader deposition in the case of oblique injection. Inﬂuenceof high energy electrons on power depositions can be negligible in n,avg ≳ 1 × 1019
m−3 [30]. Density scan in 1 × 1019 m−3 < ne,avg < 4 × 1019 m−3 was performedin modulation ECRH experiments, as shown in Fig. 6. The perturbation amplitudeof Te averaged inside reﬀ = 0.1 m decreased as ne,avg increased even in the case of
perpendicular injection due to the eﬀect of refraction. However, the absorption powerin the case of perpendicular injection was maintained higher than that in the case of
oblique injection for high density of ne,avg > 3 × 1019 m−3 . Better heating eﬃciency byImproved performance of ECRH by perpendicular injection in LHD

8

Pabs (MW) dPabs/dV (MW/m3)

Perpendicular injection
Oblique injection
10(1) ne,avg ≈ 1 × 1019 m-3(2) ne,avg ≈ 2 × 1019 m-3

(a1)

(a2)

(b1)

(b2)

1
0.1
0.01
0.8
0.4
0
0

0.5
reff/a99

0

0.5
reff/a99

Figure 5. Comparisons of radial proﬁles of (a) power deposition dPabs /dV and (b)integrated absorbed power Pabs calculated by the LHDGauss code for the discharges
shown in Fig. 4.

perpendicular injection can contribute to transport studies in ne < 5 × 1019 m−3 by gas
puﬃng [9, 10, 11].
In order to maximize single-pass absorption, optimization of the incident EC wave
polarization is important because the O-X mode coupling is aﬀected by the strong
magnetic shear and the ﬁnite plasma density at the peripheral region in LHD [31].
Polarization scan experiments were performed for relatively low-ne plasma. Figure 7
shows the results on absorption power as a function of polarization states. A polarization
state is represented by (α, β), where α and β denote the rotation angle and the ellipticityof the polarization ellipse. α = 0◦ is deﬁned as the toroidal direction [3]. The incident
millimeter wave couples to the EC waves with the O mode and the X mode under theirorthogonality. In this heating scenario, the pure O mode has to be excited to maximize
the single-pass absorption. The X mode is reﬂected at the right-hand cutoﬀ layer infront of the ECR layer, which causes the increase in multi-pass absorption. Each mode
purity ησ is represented byησ = cos2 (α − ασ ) cos2 (β − βσ ) + sin2 (α − ασ ) sin2 (β + βσ ), σ = O, X,
where (ασ , βσ ) is the optimum polarization state to excite each mode [3]. Then, theexperimental data were ﬁtted using the above equation, as shown in Fig. 7. These results
show that the linear polarization of (α, β) ≃ (45◦ , 0◦ ) is optimum to excite the pure O
mode in low-ne plasma of ∼ 1.5 × 1019 m−3 . The multi-pass absorption component isestimated to be 0.3 at the polarization state of (α, β) ≃ (−45◦ , 0◦ ), which is optimum
to excite the pure X mode for the ﬁrst path but relates to the stray radiation level inthe vessel. The optimum polarization states for each mode are also conﬁrmed from themode content analysis using the LHDGauss code [3].

Improved performance of ECRH by perpendicular injection in LHD

9Perpendicular injection
Oblique injection

Te (keV)6

Rax = 3.6 m, Bt = 2.85 T
2-OUR, 77 GHz, Pin = 0.792 MW(a)4
2
Averaged inside reff = 0.1 m

0δTe (keV)

0.8

(b)

0.4
0

Pabs (MW)

0.8 (c)0.4#157193 - #157225

0
0

1
2
3
ne,avg (× 1019 m-3)

4

Figure 6. Comparisons of (a) conditional-averaged Te and (b) its perturbation δTeaveraged inside reﬀ = 0.1 m and (c) absorption power Pabs as a function of ne,avg .
Pabs was experimentally evaluated from the response of the plasma stored energy tothe power modulation of 11 Hz.
77 GHz, 2-OUR, Pin = 0.792 MW

Pabs (MW)

0.6

4

2
Pabs = Pmax cos (α − αopt)
2+ γPmax sin (α − αopt)
Pmax = 0.71 MW
αopt = 43°
γ = 0.30

3

0.4

2

0.2
(a) Constant β = 0°
0
-90

-60

-30

0

α (°)

30

60

Pabs = Pmax cos2(β − βopt)+ γPmax sin2(β − βopt)
Pmax = 0.76 MW
βopt = 2°(b) Constant α = 45°
γ = 0.18

90 -45

-30

-15

0

15

30

1

ne,avg (1019 m-3)

0.8

0
45

β (°)

Figure 7. Absorption power Pabs as a function of (a) the polarization rotation angle
α and (b) the ellipticity β of the incident EC wave injected perpendicularly. Proﬁles
ﬁtted to the experimental data are also plotted.

Improved performance of ECRH by perpendicular injection in LHD

10

3. Improved performance of ECRH
Eﬀectiveness of perpendicular injection for 77 GHz is veriﬁed in the previous section.
With the improved performance of ECRH, achieved Te proﬁles were compared between
the two kinds of injection of 1 MW without modulation. Plasma was sustained by two
154-GHz gyrotrons with 1 MW injection power each. As shown in Fig. 8, Te0 increased
from 4 keV to over 6 keV by perpendicular injection for ne,avg ≃ 1 × 1019 m−3 . The
achieved Te0 was approximately 2 keV higher than that in the case of oblique injection
because the calculated deposition proﬁle for oblique injection is broader, as shown in
Fig. 9. The better central heating performance by perpendicular injection will contributeto extending the high-temperature regime in LHD [6].
Such an improved ECRH performance using perpendicular injection has opened up
a new operational region in LHD ECRH plasma with hydrogen ice pellet injection [32].
In these experiments, plasma was sustained by two 154-GHz gyrotrons and one 77GHz gyrotron. The 77-GHz EC wave was injected perpendicularly or obliquely forcomparison. As shown in Fig. 10 for the case of perpendicular injection, high-ne
ECRH plasma of ne0 ∼ 8 × 1019 m−3 was successfully sustained after injection of threeconsecutive hydrogen ice pellets for the ﬁrst time in LHD. Hollow ne proﬁles by gas
puﬃng changed to rather peaked proﬁles after the pellet injection. Equipartition heating
was signiﬁcant in the high-ne region: Ti0 ∼ Te0 ∼ 1 keV were obtained. On the other
hand, in the case of oblique injection, the high-ne plasma was radiatively collapsed after
the pellet injection due to the decreased absorption power. The diﬀerence of heating
Perpendicular injection (#156537)
Standard oblique injection (#156538)
2-OUR antenna, 77 GHz, Pin = 1.033 MW

ne (× 1019 m-3)

Te (keV)(1) Before injectiont = 3.47 s
8(a1)(2) During injectiont = 3.6 s
(a2)

6
4
2
0
2

(b1)

(b2)

1
0
0

0.5
reff / a99

1 0

0.5
reff / a99

1

Figure 8. Comparisons of radial proﬁles of (a) Te and (b) ne (1) before and (2) during
perpendicular/oblique injection.

Pabs (MW)dPabs/dV (MW/m3)

Improved performance of ECRH by perpendicular injection in LHD
10

11Perpendicular injection
Oblique injection

1
0.1

(a)

0.01
1
0.8
0.6
0.4
0.2
0

(b)
0

0.2

0.4
0.6
reff/a99

0.8

1Figure 9. Comparisons of radial proﬁles of (a) power deposition dPabs /dV and (b)integrated absorbed power Pabs calculated by the LHDGauss code for the discharges
shown in Fig. 8.

PECRH, Prad

(MW)
(1019 m-3)

Wp (MJ)T (keV)ne(1) Perpendicular injection (#160841)
Rax = 3.6 m, Bt = 2.85 T
2
1

Pin
Pabs
Prad

Pin
Pabs
Prad

(a1)

0
10

Pellets

5

ne,avg0
6
4
2
0(2) Oblique injection (#160844)
Rax = 3.6 m, Bt = 2.85 T

(b1)

(a2)

Pellets(b2)

ne,avg

ne0

ne0
(c1)

Ti0,crystal Te0(c2)
Ti0,crystal

Te0

(d1)

(d2)

0.5
0
3.5

4.0

4.5

5.0
Time (s)5.5

6.0

6.5 3.5

4.0

4.5Time (s)5.0

5.5

Figure 10. Comparisons of time evolution of (a) injection power Pin and absorption
power Pabs of ECRH, radiation power Prad , (b) ne,avg , ne0 , (c) Te0 , Ti0 measured
with the crystal spectrometer, and (d) Wp between (1) perpendicular injection and (2)oblique injection.

performance was conﬁrmed in the Hα emission from the ablating pellets as shown in
Fig. 11, which indicates the penetration depth of each pellet. The penetration depth
depends mainly on Te . Since Te0 in the case of oblique injection was lower than that

Improved performance of ECRH by perpendicular injection in LHD
Perpendicular injection (#160841)
Oblique injection (#160844)

Hα intensity (a.u.)

6

12

1st pellet

2nd
4

3rd

2

0
0

0.2

0.4

0.6

0.8

1

reff/a99

Figure 11. Comparison of radial proﬁles of Hα intensity between perpendicular
injection and oblique injection during pellet injection for the discharges shown in
Fig. 10.

in the case of perpendicular injection, the penetration depth in the case of oblique
injection was deeper than that in the case of perpendicular injection especially for thesecond pellet injection. The better fueling eﬃciency and the decreased heating powerby oblique injection caused the increased ne0 and the radiative collapse.
The new launch scheme which makes possible an operation with high-ne in ECRH
plasma will promote comparative studies between devices. High-ne ECRH plasma
with Te0 ∼ Ti0 was compared with W7-X high-ne plasma for a reference to Fig. 2of [33]. Figure 12 shows an example of a typical discharge of high-ne ECRH plasmausing multiple pellet injection. When Wp reached a plateau at around 4.1 s, theplasma parameters were the following: Pin,ECRH = 2.79 MW, ne0 ∼ 7.5 × 1019 m−3 ,Ti0 ∼ 1 keV, Wp ∼ 0.6 MJ, the energy conﬁnement time τE ∼ 0.22 s, and the fusion
triple product ne0 τE Ti0 ∼ 1.6 × 1019 m−3 s keV, which resulted in (∼ 1/2) Pin,ECRH ,(∼ 1) ne0 , (∼ 1/3) Ti0 , (∼ 1/2) Wp , (∼ 1) τE , and (∼ 1/4) ne0 τE Ti0 of the W7-X reference
discharge. Accumulating a database of discharges with a wide range of heating powerand electron density will accelerate comparative studies in conﬁnement and transport
between diﬀerent devices.
The new launch scheme which makes possible an operation with high-ne in ECRH
plasma will also promote isotope eﬀect studies in LHD. Figure 13 shows an example ofcomparisons with the international stellarator scaling, ISS04 [34], in hydrogen plasmaand deuterium plasma. Here, in the hydrogen case, the plasma was started up withhydrogen gas puﬃng followed by injection of three consecutive hydrogen ice pellets.
In the deuterium case, the plasma was started up with deuterium gas puﬃng followed
by injection of three consecutive deuterium ice pellets. Dependence of Wp on ne,avg is
0.39
shown. Wp is normalized by Pin,ECRH, whose exponent is based on the scaling [34]. The
low-ne hydrogen plasma during gas puﬃng before pellet injection located almost along
the scaling. Then, the plasma behaved adiabatically during the ﬁrst pellet injectionImproved performance of ECRH by perpendicular injection in LHD

13

-3
19

(10

ne

T (keV)

6
Pin

2

Pabs

PNBI#4 (a)
3

Prad

1
0
10

0
Pellets

(b)

ne0

5

PNBI#4 (MW)

(MW)

3

m )

PECRH, Prad

#160940, Rax = 3.6 m, Bt = 2.85 T

ne,avg

0
6

(c)

Te0

4

Ti0,CXS

Ti0,crystal

2

Wp (MJ)

0
(d)
0.5

0
3.5

4.0

4.5
Time (s)5.0

5.5

Figure 12. Time evolution of (a) Pin and Pabs of ECRH, Prad , port-through powerof NBI#4 for Ti measurements, (b) ne,avg , ne0 , (c) Te0 , Ti0 measured with the crystal
spectrometer, Ti0 measured with the charge exchange spectroscopy, and (d) Wp .
Rax = 3.6 m, Bt = 2.85 T

0.39
Wp / Pin,ECRH

0.6

6.5

(b) D (#157256)

4
S0

4
S0

IS

IS

2nd
0.4

3rd

6.0
5.5

3rd

5.0

2nd
4.5

1st pellet

1st pellet

0.2

ne,SudoTime (s)(a) H (#160840)

4.0

ne,Sudo

0

3.5
0

2

4
6
ne,avg (1019 m-3)

8

0

2

4
6
ne,avg (1019 m-3)

8

Figure 13. Comparisons with the ISS04 scaling in (a) hydrogen plasma and (b)0.39
deuterium plasma sustained with multiple pellet injection. Wp normalized by Pinof ECRH is plotted as a function of ne,avg . Here, a99 = 0.63 m and ι-2/3 = 0.65 areassumed [34], where ι-2/3 denotes the rotational transform at reﬀ /a99 = 2/3.

and then relaxed to the state almost along the scaling after the pellet. The plasmatransiently exceeded the Sudo density limit [35] after the third pellet injection while theplasma relaxed to the state relatively beneath the scaling. In contrast, the normalizedImproved performance of ECRH by perpendicular injection in LHD

14

Wp in the deuterium plasma was relatively larger than that in the hydrogen plasma
after the third pellet injection although the injection power of ECRH was the same
between the two discharges. The deuterium plasma relaxed to the state almost along
the scaling even in high ne . The conﬁnement properties depending on the isotope masscannot be concluded yet only with this example. Isotope eﬀects on energy, particle
transport and turbulence have been discussed in relatively low-ne ECRH plasma withgas puﬃng [10, 11]. Experiment data in a wide range of ne and ECRH power will be
accumulated in order to discuss the isotope eﬀect in high-ne ECRH plasma with pellet
injection as a future work.
4. Summary and outlook
A method of perpendicular injection from the O port was developed in order for theEC wave to be more insensitive to the eﬀect of refraction in LHD. The achieved Te0 in
the case of perpendicular injection was approximately 2 keV higher than that in thecase of oblique injection for ne0 ∼ 1 × 1019 m−3 by 1 MW injection. With such an
improved performance of ECRH, high-density ECRH plasma of ne0 ∼ 8 × 1019 m−3 was
successfully sustained after multiple hydrogen pellet injections. This method as well as
the real-time deposition location control for eﬃcient ﬁrst-pass absorption in the plasmacore region are beneﬁcial not only for preventing damage of in-vessel components duringlong-pulse operations but also for extending high-temperature operational regimes andconducting precise transport studies.
For a future outlook, further improvement of ECRH performance up to plasma
cutoﬀ density is envisaged by proposing the fundamental O-mode perpendicular
injection on the vertically-elongated cross section in LHD. Figure 14 shows comparisonsof ray trajectories for four diﬀerent injection methods in ne0 = 7 × 1019 m−3 . The
calculations were performed with the TRAVIS code [36], whose specially designed
graphical user interface (GUI) is easy to use in order to study and design the newlaunch scheme by graphically changing the launching angle, the launching position, or
plasma parameters. The newly-proposed perpendicular injection shown in Fig. 14(d)can be eﬃcient in heating up to the plasma cutoﬀ density of 7.4 × 1019 m−3 because
the propagation path is shorter than that in the case of perpendicular injection fromthe O port on the horizontally-elongated cross section, whose heating performance ispresented in this paper. Peripheral heating by the obliquely-injected X mode can bealso expected up to the left-hand cutoﬀ density if the ﬁnal mirror is steerable. The
launched millimeter wave from corrugated waveguides at a U port should be reﬂected
at the ﬁnal mirror installed outside on the equatorial plane of the vertically-elongatedcross section. A feasible launcher is under development.

Improved performance of ECRH by perpendicular injection in LHD

15(a) Pabs/Pin = 17.1%(d) Pabs/Pin = 99.4%(Pp/Pabs = 86%, Pt/Pabs = 14%)C(3.98, 0, 1.67) m
T(3.6, 0, 0) m(b) Pabs/Pin = 1.6% (Pp/Pabs = 93%, Pt/Pabs = 7%)
0.35

C(6.55, 0, 0) m
T(3.9, -0.5, 0) m

1.3

Z (m)

(Pp/Pabs = 98%, Pt/Pabs = 2%)
0.9

0

0.45

-0.35

C(4.2, 0, 0) m
T(3.5, 0, 0) m

0.65

3.6

Z (m)

5.4

4.5

6.3

R (m)

Z (m)

0

(c) Pabs/Pin = 56.9% (Pp/Pabs = 67%, Pt/Pabs = 33%)

0

C(6.55, 0, 0) m
T(3.9, 0, 0) m

0.25
Z (m)
-0.65

-0.45

0

-0.25
3.5 3.75 4
R (m)

2.85

3.8

4.75
R (m)

5.7

-0.9
3.5

3.75
R (m)

4

Figure 14. Ray trajectories of the fundamental O mode for (a) the conventional
U-port injection, (b) the conventional O-port oblique injection, (c) the O-port
perpendicular injection on the horizontally-elongated cross section, and (d) the U-port
perpendicular injection on the vertically-elongated cross section. Magnetic surfaces
and isolines of magnetic ﬁeld strength are also shown. The resonance line at B = 2.75
T is shown in thick violet lines. The center of each ﬁnal mirror and the target position
are shown by C(R, T , Z) and T(R, T , Z), respectively. The incident millimeterwave is represented by a cylinder with a radius of 50 mm at the electric ﬁeld strengthof 1/e. The magnetic ﬁeld conﬁguration is Rax = 3.6 m, Bt = 2.81 T, and theplasma beta β = 0.44%. Proﬁles of ne and Te are given by ne = ne0 (1 − ρ8 ) and2
Te = Te0 [0.8 + 0.2(1 − ρ4 )1.1 − 0.7(1 − e−(ρ/0.5) )], where ρ = reﬀ /a99 , ne0 = 7 × 1019
m−3 , and Te0 = 2.5 keV. The absorption power Pabs is normalized by the injection
power Pin . The contributions to Pabs from passing electrons (Pp ) and trapped electrons
Pt are evaluated.

Acknowledgments
This work was supported in part by National Institute for Fusion Science under grants
ULRR027 and KLPH038, and by JSPS KAKENHI Grant Numbers JP16K18338 and
JP19K14687.
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