九州大学・応用力学研究所・教授

科学研究費助成事業　　研究成果報告書

様　式　Ｃ－１９、Ｆ－１９－１、Ｚ－１９ （共通）

機関番号：

研究種目：

課題番号：

研究課題名（和文）

研究代表者

研究課題名（英文）

交付決定額（研究期間全体）：（直接経費）

１７１０２

基盤研究(B)（一般）

2018～2015

先進核融合炉を指向した高強度ミリ波によるプラズマ電流立ち上げの研究

Non-inductive plasma start-up using intense millimeter-wave beam toward advanced tokamak reactor

７０２６００４９研究者番号：

出射　浩（Idei, Hiroshi）

研究期間：

１５Ｈ０４２３１

年 月 日現在 元 ６ ２１

円 12,400,000

研究成果の概要（和文）：28 GHz 新ランチャー・準光学偏波器システムを開発し、低電力試験装置、さらにQUEST 装置内で重ねて低電力で性能評価し、良好なビーム集束・入射角、偏波面制御性を確認した。斜め入射で93 kA (世界最高値)の非誘導電流立ち上げに成功した。共鳴条件検討で、斜め入射時に強い相対論効果、ドップラー拡がりで高速電子のアップシフト高調波共鳴が連続的に起きることを明らかにし、高効率電流駆動実現の可能性を示した。 垂直入射ではバルク電子吸収によって電子温度 200 eV、電子密度 5 x 10� m�(遮断密度近傍)の20-30 kA プラズマを生成し、0.2 秒程度、維持することに成功した。

研究成果の概要（英文）：New 28 GHz launcher and quasi-optical polarizer systems have been designed and developed, and its excellent beam focusing and steering, and polarization controllability were verified at a low power test-bench and also in the QUEST tokamak at a low power level. A world record of non-inductive plasma ramped current of 93 kA has been achieved in the oblique injection. The resonance region was remarkably shifted to high field side due to the relativistic mass effect, and was widely expanded due to Doppler shift effect for the energetic electrons. Up-shift resonance conditions on the higher harmonics were considered to be continuously satisfied for the 60 keV electrons in the low field side injection, indicating potential of realization of the highly efficient current drive. In the perpendicular injection, relatively high electron temperature(~200 eV) and density [~ 5x10� m� (almost cutoff) ] have been attained, and the non-inductive plasma current of 20-30 kA was sustained for 0.2 s.

研究分野： 核融合プラズマ理工学

キーワード： 電子サイクロトロン加熱電流駆動　トカマク　非誘導プラズマ電流立ち上げ

３版

令和

研究成果の学術的意義や社会的意義トカマク型炉で電流立ち上げ時にしか用いない中心ソレノイド(CS)コイル設置が、経済性や中性子問題と対峙することから、CS コイルを用いない非誘導電流立ち上げが重要課題となっている。本研究では、高強度ミリ波ビームを用いた高効率・非誘導プラズマ電流立ち上げのシナリオ検討、その実現を目的とする。高効率非誘導電流駆動には、入射ビームの一回通過吸収（局所加熱・電流駆動）が重要であり、ビーム集束・入射角制御、入射偏波面を実現する伝送・入射系を開発・実装した。電流駆動に関する理論解析的評価を加え、炉で切望されている非誘導プラズマ電流立ち上げを実証し、高効率化へのシナリオを提示した点で学術・社会的に意義深い。

ITER

ST

NSTX-U MAST-U X

ST JT-60SA JT-60SA

VECTOR VECTOR CS

JT-60SA SlimCS CS

CS CS ST CS

24NIFS NIFS 77/154GHz

1.5 MW QUEST

28 GHz8.2 GHz 28 GHz 66

kA

LATE QUEST 2.45 8.2 GHz VECTOR

4.3T 120 GHz MAST DIII-D

JT-60U JT-60U LATE decay index QUEST

QUEST −

CS

ST

STQUEST λ

λ

N//

v// N/

N//

28 GHz N//

/4 /8

1.5 m 0.32 m 1.2 m

0.22 m λ 0.05 m

0.05 m

0.05m

8.56 GHz

28 GHz

140 kW 70 kA

O

(a)HE11

HE11

28 GHz

偏波器偏波器ジャイロトロンアークセンサー

シングルディスクサファイヤ窓

２準光学鏡ランチャー

a (b) (c)

全波解析：強度 [a.u.] 全波解析：位相 [rad.](c) 低電力試験：強度

(b)

N//= 0.78

80 kA λ 0.34 m

λ 60 keV

αQUEST

N//= 0.78

0.3 V 120 kW 93 kA

200 eV 5 x 1018 m-3 ~25kA

N//= 0.78

共鳴速度ピッチ[ v///v⊥] ��� ��� ���

相対論的シフトドップラー拡がり

オーバーラップ[3rd ‒ 4th ]

0.2 0.6 R [m]

(c)

時間 [秒]

プラズマ電流

[kA]

(a) (b)

Inte

nsity

[a.

u.]

Phas

e[d

eg]

(a) !" (b) !#

(c) $" (d) $#

Φ&/( [deg] Φ&/( [deg]

Φ &/)

[deg

]Φ &

/)[d

eg]

0.25

0.20

0

0.15

0.10

0.05

0

50

100

150

-50

-100

-150

Fig 6: Dependencies of measured (a)(b): amplitude ax,y and (c)(d): phase ✓x,yon rotation angles ��/4 and of ��/8 of �/4 and �/8 polarizer plates.

![d

eg]

(a) "#$% (b) "&'(

(c) )#$% (d) )&'(

Φ+/- [deg] Φ+/- [deg]

Φ +/.

[deg

]Φ +

/.[d

eg]

/[d

eg]

Fig 7: Dependencies of polarization parameters (a)(b): ↵exp, cal and (c)(d):�exp, cal, defined in Fig.6, on rotation angles ��/4 and of ��/8 of �/4 and �/8polarizer plates. The ↵exp and �exp are evaluated from the measured fields inFig. 7. The ↵cal and �cal were calculated by accounting phase delay at thecorrugated plates.

and the result is shown in Fig.8(a). The evaluated ⌘ is rela-tively high, however, it should be noted that ⌘ is significantlylow somewhere at the �/8-plate rotation-angle of -60 deg.

Figure 8(b) shows the parameter dependencies of ↵exp, cal and�exp, cal on the �/4-plate rotation-angle setting at �/8-plate set-ting of -60 deg. It seemed that the significantly low ⌘ came fromthe disagreement of �exp, cal. The small displacement of the an-tenna setting to measure Ex and Ey fields would a↵ect �exp. Theprecise antenna setting to measure the orthogonal fields is re-quired in future works.

Controllability of elliptical polarization would be discussedwith respect to ⌘max achieved experimentally. There were sim-ilar excited ↵ and � with various settings of polarizer angles asshown in Figs. 8. For target ↵0 and �0, a best polarizer settingcan be found to attain ⌘max as

⌘max = cos2(↵exp � ↵0) cos2(�exp � �0)+ sin2(↵exp � ↵0) sin2(�exp + �

0). (4)

(a) η (b)

(c) ηmax

Φ"/$ [deg]

Φ "/%

[deg

]

α’[deg]

β’ [d

eg]

Φ"/% [deg]

1.00

0.99

0.98

0.97

1.0

0.9

0.8

0.7

0.6

Fig 8: (a): Realized e�ciency ⌘ of polarization states defined in Eq. 3 onrotation angles ��/4 and of ��/8 of �/4 and �/8 polarizer plates. Dependencesof ↵exp, cal and �exp, cal, with ��/8= -60 degree, on ��/4 are plotted in (b). (c):Maximum e�ciency ⌘max for target polarization states (↵0, �0) by controllingthe polarizations.

through scanning of the corrugated-plate angles. Figure 8(c)shows the ⌘max on the target ↵0 and �0. The ⌘max higher than0.965 have been achieved for all target polarization states.

6. Summary

The QO polarizer, composed of two corrugated plates and aQO mirror, has been developed to avoid the arcing events for thehigher power transmission. The HE11 mode coupling with theQO mirror is limited at 88.3%. Improvement of the coupling isleft as a future work. The QO polarizer was tested with superheterodyne system to examine the QO characteristics and thedependencies of the polarization states on the two corrugatedplates rotation angles. The measured intensity and phase arereasonably in agreement with the calculation. The maximume�ciency ⌘max to realize a given polarization state (↵0, �0) forthe excited states was at rate of over 96.5%. Any polarizationstate can be generated through QO polarizer with no the gapbetween corrugated plate and the block.

Acknowledgments

This work was performed under the auspices and supportof the NIFS Collaboration Research Programs under GrantsNIFS13KUTR085 and NIFS17KUTR128. This research waspartially supported by Grant-in-Aid for Scientific Research (B)(JSPS KAKENHI Grant Number JP1504231)

References

[1] H. Idei, et al., Nucl. Fusion, 57 126045 (2017).[2] H. Idei, et al., Fusion Eng. Des., in submission.[3] T.li. Tsujimura, et al., Fusion Eng. Des., 114 97-101 (2017).[4] T. Ii, et al., Rev. Sci. Instrum., 86 023502 (2015) .[5] H. Idei, et al., J. Infrared Milli Terahz Waves, 36 662-674 (2015).[6] J. Doane, et al., J. Infrared Milli Terahz Waves, 13 1727 (1992).

4

(a) 準光学偏波器

準光学結合鏡

(b) 楕円パラメータコルゲート反射板回転角依存

α（実験）

β（実験）

α（理論）

β（理論）

Advanced Fusion Research Center

������./15M. Fukuyama et al.,

Fus. Eng. and Des. (2019)

$�#

�"

QUEST

λ/8���

λ/4���

�����#

�7;0

����

✅ λ/8: λ/4���, �)&��%486;0 [ α, β ],�� <�!�' α = π /2, β = 0 (

✅� �*+��%�,QUEST �����*��

E

B t2nd X7;2.39-

λ/8��� [deg.]

λ/8��� [ deg.]

λ/4���

[deg

.]λ/

4���

[deg

.]

- -90 0 90 -90 0 90λ/8板回転角（度）

λ/4板回転角（度）

-90 0 90 -90 0 90 90

0

-9045

0

-45

α（度）

β（度）

TASK-WR

3% (a) N//= 0.78β λ β

(b)

30-40 %

60 keV (c) N// RN// 60 keV

5 ①Y. Takase, A. Ejiri, T. Fujita, N. Fukumoto, A. Fukuyama, K. Hanada, H. Idei, et al Overview of spherical tokamak research in Japan Nuclear Fusion 57 102005 2017 DOI: 10.1088/ 1741-4326/aa62c1

H. Idei, T. Kariya, T. Imai, K. Mishra, T. Onchi, O. Watanabe, H. Zushi, K. Hanada, J. Qian, A. Ejiri, M.M. Alam, K. Nakamura, A. Fujisawa, Y. Nagashima, M. Hasegawa, K. Matsuoka, A. Fukuyama, S. Kubo, et al. Fully non-inductive second harmonic electron cyclotron plasma ramp-up in the QUEST spherical tokamak Nuclear Fusion 57 126045 2017 DOI: 10.1088/1741-4326/aa7c20

H. Idei, T. Onchi, M. Hasegawa, K. Nakamura, R. Ikezoe, O. Watanabe, K. Kuroda, K. Hanada, Y. Nagashima, A. Higashijima, T. Nagata, S. Shimabukuro, T. Kariya, T. Imai, T.I. Tsujimura, S. Kubo, et al.FULLY NON-INDUCTIVE 2ND HARMONIC ELECTRON CYCLOTRON CURRENT RAMP-UP WITH POLARIZED FOCUSING-BEAM IN THE QUEST SPHERICAL TOKAMAK Proceedings of the 27th IAEA Fusion Energy Conference (FEC 2018) 2018

H. Idei, T. Onchi, T. Kariya, T.I. Tsujimura, S. Kubo, et al. 28-GHz ECHCD system with beam focusing launcher on the QUEST spherical tokamak Fusion Engineering and Design 2019 DOI: 10.1016/j.fusengdes.2019.02.027

M. Fukuyama, H. Idei, T.I. Tsujimura, S. Kubo, et al. Quasi-optical polarizer system for ECHCD experiments in the QUEST Fusion Engineering and Design 2019 DOI: 10.1016/ j.fusengdes.2019.02.099

11 QUEST ECH

2016 Y. Takase, A. Ejiri, T. Fujita, K. Hanada, H. Idei, M. Nagata, Y. Ono, H. Tanaka, A. Fukuyama, et al.

(a) β (b)

c

Advanced Fusion Research Center

������� [ N// ] ��

3rd

2nd

4th

3rd

2nd

4th

2 x 1018

3 x 1018

4 x 1018

5 x 1018

2 x 1018

3 x 1018

4 x 1018

5 x 1018

2 x 1018

3 x 1018

4 x 1018

5 x 1018

2 x 1018

3 x 1018

4 x 1018

5 x 1018

N// : 0.4

������� �������

H. Idei et al

7

[6, 21, 22]. The charge separation in a simple torus caused by drifts are cancelled through field connections by a moderate vertical magnetic field Bv, generating the initial PS current IPS. The initial toroidal IPS current can be estimated as [14],

IPS = 2⟨ p⟩S /(RBv), (1)

where ⟨ p⟩ is the spatially averaged plasma (electron) pressure, and S is a plasma cross section. The initial toroidal current is !3 kA, a small fraction of Ip at time frame (A) in figure 5(a). The bootstrap current is the same order as IPS, as estimated in [7]. An electron pressure of 10 Pa was assumed. The remaining vertical electric field E from the charge separation provides a E × B force to allow the plasma to expand throughout the torus. By time frame (C), the plasma has expanded outward somewhat, but it is still vertically elongated. The current spon-taneously jumps to the 20–25 kA level between frames (C) and (D) and the plasma expands to fill the vessel.

Specific electrons can be confined sufficiently well if the vertical motion from toroidal drift vd,t is cancelled by the ver-tical component of the parallel velocity v// (Bv/Bt) determined by the magnetic field pitch angle [23]. Here v// is the parallel

velocity to the filed line. The electrons under asymmetric con-finement contribute to the plasma current of the non-inductive startup plasma. In addition, banana orbits are possible even in open field lines with a magnetic mirror with M(> 1). A relatively high M(> 1) favors the confinement of energetic electrons generated in the electron cyclotron resonance (ECR) layers. The confined trapped electrons also contribute to cur-rent generation through precession in the toroidal direction. In the Ip startup period, the asymmetric structure on ± v// was grown up, and the plasma current was ramped up.

The deviation of the confined electron orbits between CW and CCW passing electrons is an aspect to consider the asymmetric structure on the ± v// after the closed magnetic flux formation. The major radius deviation ∆R of a guiding-center electron orbit was estimated at the inboard (high field side) midplane (Z = 0), when the electron orbit was stating at the outer (R ! 1) midplane (Z = 0). The ∆R between the 30 keV CW and CCW passing electrons was estimated to be about several centimeters. The deviation ∆R effect should be considered as an asymmetric structure on the ± v// for highly energetic electrons in the inner-limiter configuration.

4.2. The 28 GHz wave absorption and current drive mech anism

The incident 28 GHz O-mode wave is not effective for single-pass absorption in the 2nd harmonic ECR sce-nario. Doppler up-shifted fundamental ECR is first con-sidered for highly energetic electrons. The nth harmonic relativistic Doppler-shifted ECR condition for these electrons is expressed as γ[1 − N//(v///c)] = nfce/f with relativistic

factor γ = (1 + P2⊥ + P2

//)1/2, where P⊥ = mγv⊥/mc and

P//= mγv///mc are the normalized electron momenta in the perpendicular and parallel directions to the magnetic field. Here, f is the 28 GHz operating frequency, m is the electron rest mass, and c is the speed of light. The resonant electron energy can be explained with resonant ellipses described by the resonance condition in the normalized momentum spaces

Figure 11. Time evolution of (a) Ip and Bv, (b) loop voltage, and (c) nℓ in the 66 kA plasma ramped-up with the 28 GHz wave. The vertical field Bv is slowly ramped up to attain the 66 kA plasma current non-inductively. The line-integrated density evolution, in the pre-ionization and current-decay phases when the flux surfaces are not necessarily formed, is also shown in the figure, along with the nℓ evolution.

Figure 12. Resonant ellipse for relativistic Doppler-shifted fundamental ECR at R = 0.26 m. Momentum contours with 10 keV and 100 keV are also shown. Minimum parallel energy E min

// of

P min// is about 100 keV. Maximum parallel energy E max

// of P max

// and the energy Etop with P max

⊥ are also indicated. The energy Etop is 1.14 MeV.

Nucl. Fusion 57 (2017) 126045

Top View

1.0

0.5

0.00.0 R [m] 1.0 0.0 R [m] 1.0

-1.0 X [m] 1.0

-1.0

Y[m

]

1.0

(a)

(b)

Advanced Fusion Research Center

������� [ N// ] ��

3rd

2nd

4th

3rd

2nd

4th

2 x 1018

3 x 1018

4 x 1018

5 x 1018

2 x 1018

3 x 1018

4 x 1018

5 x 1018

2 x 1018

3 x 1018

4 x 1018

5 x 1018

2 x 1018

3 x 1018

4 x 1018

5 x 1018

N// : 0.4

������� �������

H. Idei et al

7

[6, 21, 22]. The charge separation in a simple torus caused by drifts are cancelled through field connections by a moderate vertical magnetic field Bv, generating the initial PS current IPS. The initial toroidal IPS current can be estimated as [14],

IPS = 2⟨ p⟩S /(RBv), (1)

where ⟨ p⟩ is the spatially averaged plasma (electron) pressure, and S is a plasma cross section. The initial toroidal current is !3 kA, a small fraction of Ip at time frame (A) in figure 5(a). The bootstrap current is the same order as IPS, as estimated in [7]. An electron pressure of 10 Pa was assumed. The remaining vertical electric field E from the charge separation provides a E × B force to allow the plasma to expand throughout the torus. By time frame (C), the plasma has expanded outward somewhat, but it is still vertically elongated. The current spon-taneously jumps to the 20–25 kA level between frames (C) and (D) and the plasma expands to fill the vessel.

Specific electrons can be confined sufficiently well if the vertical motion from toroidal drift vd,t is cancelled by the ver-tical component of the parallel velocity v// (Bv/Bt) determined by the magnetic field pitch angle [23]. Here v// is the parallel

velocity to the filed line. The electrons under asymmetric con-finement contribute to the plasma current of the non-inductive startup plasma. In addition, banana orbits are possible even in open field lines with a magnetic mirror with M(> 1). A relatively high M(> 1) favors the confinement of energetic electrons generated in the electron cyclotron resonance (ECR) layers. The confined trapped electrons also contribute to cur-rent generation through precession in the toroidal direction. In the Ip startup period, the asymmetric structure on ± v// was grown up, and the plasma current was ramped up.

The deviation of the confined electron orbits between CW and CCW passing electrons is an aspect to consider the asymmetric structure on the ± v// after the closed magnetic flux formation. The major radius deviation ∆R of a guiding-center electron orbit was estimated at the inboard (high field side) midplane (Z = 0), when the electron orbit was stating at the outer (R ! 1) midplane (Z = 0). The ∆R between the 30 keV CW and CCW passing electrons was estimated to be about several centimeters. The deviation ∆R effect should be considered as an asymmetric structure on the ± v// for highly energetic electrons in the inner-limiter configuration.

4.2. The 28 GHz wave absorption and current drive mech anism

The incident 28 GHz O-mode wave is not effective for single-pass absorption in the 2nd harmonic ECR sce-nario. Doppler up-shifted fundamental ECR is first con-sidered for highly energetic electrons. The nth harmonic relativistic Doppler-shifted ECR condition for these electrons is expressed as γ[1 − N//(v///c)] = nfce/f with relativistic

factor γ = (1 + P2⊥ + P2

//)1/2, where P⊥ = mγv⊥/mc and

P//= mγv///mc are the normalized electron momenta in the perpendicular and parallel directions to the magnetic field. Here, f is the 28 GHz operating frequency, m is the electron rest mass, and c is the speed of light. The resonant electron energy can be explained with resonant ellipses described by the resonance condition in the normalized momentum spaces

Figure 11. Time evolution of (a) Ip and Bv, (b) loop voltage, and (c) nℓ in the 66 kA plasma ramped-up with the 28 GHz wave. The vertical field Bv is slowly ramped up to attain the 66 kA plasma current non-inductively. The line-integrated density evolution, in the pre-ionization and current-decay phases when the flux surfaces are not necessarily formed, is also shown in the figure, along with the nℓ evolution.

Figure 12. Resonant ellipse for relativistic Doppler-shifted fundamental ECR at R = 0.26 m. Momentum contours with 10 keV and 100 keV are also shown. Minimum parallel energy E min

// of

P min// is about 100 keV. Maximum parallel energy E max

// of P max

// and the energy Etop with P max

⊥ are also indicated. The energy Etop is 1.14 MeV.

Nucl. Fusion 57 (2017) 126045

Top View

1.0

0.5

0.00.0 R [m] 1.0 0.0 R [m] 1.0

-1.0 X [m] 1.0

-1.0

Y[m

]

1.0

(a)

(b)

共鳴速度ピッチ[ v///v⊥] ��� ��� ���

相対論的シフトドップラー拡がり

オーバーラップ[3rd ‒ 4th ]

0.2 0.6 R [m]

(c)

Overview of Spherical Tokamak Research in Japan 26th IAEA Fusion Energy Conference2016

H. Idei, T. Onchi, T. Kariya, K. Hanada, T. Imai, A. Ejiri, O. Watanabe, K. Mishra,K. Nakamura, M. Hasegawa, S. Kawasaki, H. Nakashima, A. Higashijima, H. Zushi, Y. Takase, and A. Fukuyama, et al. Non-inductive Electron Cyclotron Heating and Current Drive with Dual Frequency (8.2{28 GHz) Waves in QUEST 26th IAEA Fusion Energy Conference 2016

H.Idei, T.Onchi, T.Kariya, M.Hasegawa, K.Nakamura, A.Ejiri, N. Matsumoyo, Y.Kawamata, K. Mishura, M.Fukuyama, M.Yunoki, S.Kojima, K.Kuroda, O.Wanatabe, K.Hanada, T.I.Tsujimura, S. Kubo, et al. Fully non-inductive electron cyclotron plasma ramp-up with focusing mirror launcher system in the QUEST spherical tokamak Plasma Conference 2017 2017

K. Mishra

QUEST 28 GHz 2018

M. Fukuyama, H. Idei, T. Tsujimura, S. Kubo, et al. Quasi-optical polarizer system for ECH/ECCD experiments in the QUEST spherical tokamak 30th Symposium on Fusion Technology (SOFT 2018)

2018 H. Idei, A. Higashijima, A. Ejiri, A. Fukuyama, G. Taylor, K. Hanada, K. Nakamura, K. Nagata, K.

Kuroda, K. Mishra, M. Hasegawa, M Fukuyama, M. Ono, M. Yunoki, N. Matsumoto, N. Bertelli, O. Watanabe, R. Yoneda, S. Murakami, S. Kobayashi, S. Kubo, et al Fully Non-inductive 2nd Harmonic Electron Cyclotron Current Ramp-up with Focused Polarized Beams in the QUEST Spherical Tokamak27th IAEA Fusion Energy Conference (FEC 2018) 2018

H. Idei, T. Onchi, T. Kariya, T.I. Tsujimura, S. Kubo, et al. (AAPPS-DPP2018)2018

QUEST ECH/CD 35

2018 H. Idei, T. Onchi, T. Kariya, T. Tsujimura, S. Kubo, et al. System of 28GHz ECHCD with beam

focusing launcher on the QUEST spherical tokamak 30th Symposium on Fusion Technology (SOFT 2018)2018

QUEST74 2019

0

○ 0 ○ 0

https://www.triam.kyushu-u.ac.jp/ideiken/index.html

(1) −

Atushi Fukuyama

8 60116499

Shin Kubo

8 80170025

(2)