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Non-inductive current drive plays a crucial role in tokamak, especially for its steady state operations. Recently, the helicon wave (HW) has been regarded as a promising tool for driving off-axis plasma current in reactor-grade machine. The lower-hybrid wave (LHW) is the most effective radio-frequency current drive method, however, it has the drawback, which is limited by the conditions of wave accessibility in the high parameter tokamak, making the wave power usually damped at the plasma edge. HW can spiral towards the plasma centre directly under a high electron density. To obtain a long pulse steady state operation of reactor tokamak, the complementarity of HW and LHW in the aspect of driven current distribution in the high parameter tokamak is considered. The synergy current drive of the HW and the LHW is studied numerically in the steady-state scenario of HL-2M. According to the fast wave dispersion relation of plasma, the HW parameters, including its wave frequency and launched parallel refractive index, are obtained firstly. Results of GENRAY code simulation show that a single pass wave power absorption of the HW can be obtained generally through the electron Landau damping and transit time magnetic pumping effects. On the other hand, the LHW parameters are adopted from the equipped system on the machine. Results of single pass wave absorption are also obtained in the case of LHW. And then, the synergy effects of HW and LHW are studied numerically based on the GENRAY/CQL3D models. The cooperation of these two waves results in a broad plasma current distribution along the radial direction (
$\rho = $ 0.2－0.9) in the machine. Taking the electron distribution functions of these waves into account, it is clear that the electrons are accelerated by the HW in the parallel magnetic field direction, resulting in more electrons entering the region of LHW resonance area. As the consequence, a net plasma current appears. Furthermore, a fine-grained parametric scan is performed by changing the launched parallel refractive index of HW, and the results indicate that positive synergy effects can be generally observed once the related wave current drive profiles are overlapped. Finally, the synergy factor is shown to be proportional to this overlap and reaches its maximum value of 1.18 in HL-2M.-
Keywords:
- tokamaks /
- helicon wave /
- lower hybrid wave /
- synergy current drive
[1] Chiu S C, Chan V S, Harvey R W, Porkolab M 1989 Nucl. Fusion 29 2175
Google Scholar
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Google Scholar
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Google Scholar
[8] Prater R, Moeller C P, Pinsker R I, Porkolab M, Meneghini O, Vdovin V L 2014 Nucl. Fusion 54 083024
Google Scholar
[9] Vdovin V L 2013 Plasma Phys. Rep. 39 95
Google Scholar
[10] Van Compernolle B, Brookman M, Pinsker R, Moeller C, Squire J, Garofalo A M, Nagy A, Torrezan A, Ponce D, Pawley C, Chowdury S, Crocker N, Degrandchamp G, Hinson E, Lohr J, Marinoni A, Martin E, Petty C, Porkolab M, Rost C, Schmitz O, Thome K, Wang Q H, Watkins J, Zeller K 2021 63rd Annual Meeting of the APS Division of Plasma Physics Pittsburgh, November 8–12, 2021 UO07
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Google Scholar
[12] Fidone I, Giruzzi G, Granata G, Meyer R L 1984 Phys. Fluids. 27 2468
Google Scholar
[13] Kawashima H, Yamamoto T, Hoshino K, Uesugi Y, Mori M, Suzuki N 1991 Nucl. Fusion 31 495
Google Scholar
[14] Maekawa T, Maehara T, Minami T, Kishigami Y, Kishino T, Makino K, Hanada K, Nakamura M, Terumichi Y, Tanaka S 1993 Phys. Rev. Lett. 70 2561
Google Scholar
[15] Maehara T, Yoshimura S, Minami T, Hanada K, Nakamura M, Maekawa T, Terumichi Y 1998 Nucl. Fusion 38 39
Google Scholar
[16] Harvey R W, Chiu S C, McCoy M G, Kerbel G D, Smith G R, Mau T K 1991 Proc. of IAEA TCM on Fast Wave Current Drive in Reactor Scale Tokamaks Arles, France, September 23–25, 1991 p135
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Google Scholar
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Google Scholar
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Google Scholar
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[22] 刘祖光 2020 硕士学位论文 (衡阳: 南华大学)
Liu Z G 2020 M. S. Thesis (Hengyang: University of South China
[23] The GENRAY Ray Tracing Code, Smirnov A P, Harvey R W https://compxco.com/Genray_manual.pdf [2003-03-17
[24] Artaud J F, Imbeaux F, Garcia J, Giruzzi G, Aniel T, Basiuk V, Bécoulet A, Bourdelle C, Buravand Y, Decker J, Dumont R, Eriksson L G, Garbet X, Guirlet R, Hoang G T, Huynh P, Joffrin E, Litaudon X, Maget P, Moreau D, Nouailletas R, Pégourié B, Peysson Y, Schneider M, Urban J 2018 Nucl. Fusion 58 105001
Google Scholar
[25] 李新霞, 李国壮, 刘洪波 2020 物理学报 69 145201
Google Scholar
Li X X, Li G Z, Liu H B 2020 Acta Phys. Sin. 69 145201
Google Scholar
[26] 杨友磊, 胡业民, 项农 2017 物理学报 66 245202
Google Scholar
Yang Y L, Hu Y M, Xiang N 2017 Acta Phys. Sin. 66 245202
Google Scholar
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图 1 HL-2M装置稳态运行模式下的等离子体平衡参数 (a)电子温度和密度分布; (b)有效电荷和安全因子分布
Figure 1. Radial profiles of (a) electron temperature and density for the HL-2M steady-state scenario; radial profiles of (b) effective charge and safety factor for the HL-2M steady-state scenario.
图 2 在HL-2M装置放电条件下通过HW强阻尼条件求得的$ 2\overline {k_{ \bot {\text{I}}}^{(\rm e)}} a $值的等高线图 (a) ${\beta _{\text{e}}}\sim$2.0%时, $ 2\overline {k_{ \bot {\text{I}}}^{(\rm e)}} a $关于${\xi _{\text{e}}}$和$f$的等高线图; (b) $ {f_{{\text{HW}}}} = $0.6 GHz时, $ 2\overline {k_{ \bot {\text{I}}}^{(\rm e)}} a $关于${\xi _{\text{e}}}$和${\beta _{\text{e}}}$的等高线图
Figure 2. Contours of $ 2\overline {k_{ \bot {\text{I}}}^{(\rm e)}} a $ as a function of (a) ${\xi _{\text{e}}}$ and $f$ with ${\beta _{\text{e}}}\sim$2.0% for the strong damping condition of the HW of HL-2M; contours of $ 2\overline {k_{ \bot {\text{I}}}^{(\rm e)}} a $ as a function of (b) ${\xi _{\text{e}}}$ and ${\beta _{\text{e}}}$ with ${f_{{\text{HW}}}} = $0.6 GHz for the strong damping condition of the HW of HL-2M.
图 3 HL-2M装置LHW/HW波射线传播轨迹, 其中, ${f_{{\text{LH}}}} = $3.7 GHz, ${n_{{{/ /\rm LH}}}}$分别取2.2和2.6; ${f_{{\text{HW}}}} = $0.6 GHz, ${n_{{{/ / \rm HW}}}} = $3.7
Figure 3. Ray trajectories of the HW with ${f_{{\text{HW}}}} = $0.6 GHz and ${n_{{{/ / \rm HW}}}} = $3.7 in HL-2M, as well as the LHW with ${f_{{\text{LH}}}} = $3.7 GHz and ${n_{{{/ /\rm LH}}}}$ of 2.2 and 2.6 respectively.
图 4 HW, LHW和双波协同(HW+LH)驱动下的电流密度剖面
Figure 4. Driven current density profiles for the HW, the LHW, and the HW+ LHW.
图 5 (a)麦克斯韦(${D_{{\text{Maxwell}}}}$), HW(${D_{{\text{HW}}}}$), LHW(${D_{{\text{LH}}}}$)单独作用下和双波协同作用(${D_{{\text{HW}} + {\text{LH}}}}$)下的电子平行分布; (b) 图5(a)中黑色矩形框的放大区域
Figure 5. (a) Parallel electron distributions of the Maxwell, the HW, the LHW, and HW+LHW; (b) the enlarged area of the black rectangular box in Fig. 5(a).
图 6 波电场加速下的电子通量、波电场及碰撞作用下电子总通量的对数及射频波准线性扩散和碰撞作用下的电子分布 (a)—(c)分别为HW, LHW以及双波协同下的电子通量; (d)—(f) 分别为HW, LHW以及双波协同下的电子总通量的对数; (g)—(i)分别为HW, LHW以及双波协同下的电子分布
Figure 6. (a)–(c) Electron flux of the HW, the LHW, and the HW+LHW respectively; (d)–(f) the logarithms of the total electron fluxes for the case of Fig. 6(a)-(c); (g)–(i) contours of the electron distribution function for the case of Fig. 6(a)-(c).
表 1 不同HW平行折射率下的协同效果
Table 1. Synergistic effect in different HW parallel refractive indexes.
${n_{{{/ / \rm HW}}}}$ ${I_{{\text{HW}} + {\text{LH}}}}/{\text{kA}}$ ${I_{{\text{HW}}}}/{\text{kA}}$ ${I_{{\text{LH}}}}/{\text{kA}}$ ${F_{{\text{syn}}}}$ 3.3 1228.0 440.6 669.0 1.18 3.5 1211.1 433.3 669.0 1.16 3.7 1180.6 416.0 669.0 1.14 3.9 1151.6 396.5 669.0 1.13 4.1 1120.5 377.0 669.0 1.11 
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[1] Chiu S C, Chan V S, Harvey R W, Porkolab M 1989 Nucl. Fusion 29 2175
Google Scholar
[2] Peysson Y, Decker J, Nilsson E, Artaud J F, Ekedahl A, Goniche M, Hillairet J, Ding B, Li M, Bonoli P T, Shiraiwa S, Madi M 2016 Plasma Phys. Controlled Fusion 58 044008
Google Scholar
[3] Wang Z T, Long Y X, Dong J Q, He Z X 2013 Chin. Phys. B 22 095201
Google Scholar
[4] Phillips C K, Bell R E, Berry L A, Bonoli P T, Harvey R W, Hosea J C, Jaeger E F, LeBlanc B P, Ryan P M, Taylor G, Valeo E J, Wilgen J B, Wilson J R, Wright J C, Yuh H, NSTX Team 2009 Nucl. Fusion 49 075015
Google Scholar
[5] Huang C B, Gao X, Liu Z X, Han X, Zhang T, Wang Y M, Zang S B, Kong D F, EAST Team 2016 Plasma Phys. Controlled Fusion 58 075005
Google Scholar
[6] Duan X R, Ding X T, Dong J Q, Yan L W, Liu Y, Huang Y, Song X M, Zou X L, Xu M, Yang Q W, Liu D Q, Rao J, Xuan W M, Chen L Y, Mao W C, Wang Q M, Cao J Y, Lei G J, Zhang J H, Li X D, Chen W, Zhao K J, Xiao W W 2013 Nucl. Fusion 53 104009
Google Scholar
[7] Li X X, Xiang N, Gan C Y 2015 Chin. Phys. Lett. 32 035202
Google Scholar
[8] Prater R, Moeller C P, Pinsker R I, Porkolab M, Meneghini O, Vdovin V L 2014 Nucl. Fusion 54 083024
Google Scholar
[9] Vdovin V L 2013 Plasma Phys. Rep. 39 95
Google Scholar
[10] Van Compernolle B, Brookman M, Pinsker R, Moeller C, Squire J, Garofalo A M, Nagy A, Torrezan A, Ponce D, Pawley C, Chowdury S, Crocker N, Degrandchamp G, Hinson E, Lohr J, Marinoni A, Martin E, Petty C, Porkolab M, Rost C, Schmitz O, Thome K, Wang Q H, Watkins J, Zeller K 2021 63rd Annual Meeting of the APS Division of Plasma Physics Pittsburgh, November 8–12, 2021 UO07
[11] Liu H B, Liu G N, Sun A P, Xiao Z Y, Li X X 2022 J. Korean Phys. Soc. 81 397
Google Scholar
[12] Fidone I, Giruzzi G, Granata G, Meyer R L 1984 Phys. Fluids. 27 2468
Google Scholar
[13] Kawashima H, Yamamoto T, Hoshino K, Uesugi Y, Mori M, Suzuki N 1991 Nucl. Fusion 31 495
Google Scholar
[14] Maekawa T, Maehara T, Minami T, Kishigami Y, Kishino T, Makino K, Hanada K, Nakamura M, Terumichi Y, Tanaka S 1993 Phys. Rev. Lett. 70 2561
Google Scholar
[15] Maehara T, Yoshimura S, Minami T, Hanada K, Nakamura M, Maekawa T, Terumichi Y 1998 Nucl. Fusion 38 39
Google Scholar
[16] Harvey R W, Chiu S C, McCoy M G, Kerbel G D, Smith G R, Mau T K 1991 Proc. of IAEA TCM on Fast Wave Current Drive in Reactor Scale Tokamaks Arles, France, September 23–25, 1991 p135
[17] Yang Y L, Xiang N, Hu Y M 2017 Phys. Plasmas 24 032502
Google Scholar
[18] Yang Y L, Xiang N, Hu Y M 2017 Phys. Plasmas 24 082503
Google Scholar
[19] Yin L, Zheng P W, Gong X Y, Yang C, Yin X H, Song C Y, Huang Q H, Chen Y, Zhong Y J 2022 Nucl. Fusion 62 066023
Google Scholar
[20] Pinsker R I, Porkolab M, Petty C C, Prater R, Moeller C P 2015 AIP Conference Proceedings 1689 080012
Google Scholar
[21] Kennel C F, Engelmann F 1966 Phys. Fluids 9 2377
Google Scholar
[22] 刘祖光 2020 硕士学位论文 (衡阳: 南华大学)
Liu Z G 2020 M. S. Thesis (Hengyang: University of South China
[23] The GENRAY Ray Tracing Code, Smirnov A P, Harvey R W https://compxco.com/Genray_manual.pdf [2003-03-17
[24] Artaud J F, Imbeaux F, Garcia J, Giruzzi G, Aniel T, Basiuk V, Bécoulet A, Bourdelle C, Buravand Y, Decker J, Dumont R, Eriksson L G, Garbet X, Guirlet R, Hoang G T, Huynh P, Joffrin E, Litaudon X, Maget P, Moreau D, Nouailletas R, Pégourié B, Peysson Y, Schneider M, Urban J 2018 Nucl. Fusion 58 105001
Google Scholar
[25] 李新霞, 李国壮, 刘洪波 2020 物理学报 69 145201
Google Scholar
Li X X, Li G Z, Liu H B 2020 Acta Phys. Sin. 69 145201
Google Scholar
[26] 杨友磊, 胡业民, 项农 2017 物理学报 66 245202
Google Scholar
Yang Y L, Hu Y M, Xiang N 2017 Acta Phys. Sin. 66 245202
Google Scholar
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