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中国首台准环对称仿星器(CFQS)是目前世界上唯一在建的准环对称仿星器. 本文利用回旋弗拉索夫代码GKV开展了CFQS中离子温度梯度模(ITG)的模拟研究. 在静电绝热条件下, 模拟的结果给出了CFQS中纯的ITG与密度梯度和温度梯度间的依赖关系. ITG的激发存在温度梯度阈值, 此温度梯度阈值受到密度梯度的影响. ITG的增长率不仅与密度梯度的绝对值相关, 还取决于密度梯度的正负, 负密度梯度对ITG具有强的抑制作用. 非绝热的模拟结果表明, 捕获电子对ITG具有去稳作用, 电子温度梯度也对ITG具有去稳作用. 当考虑电磁条件时, 有限的等离子体比压会抑制ITG, 导致ITG向阿尔芬离子温度梯度模/动理学气球模(AITG/ KBM)的转化. 当密度和温度梯度都较大时, KBM的最大增长率与密度梯度和温度梯度近似成线性关系.
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关键词:
- 中国首台准环对称仿星器 /
- 离子温度梯度模 /
- 等离子体比压 /
- 动理学气球模
The Chinese First Quasi-axisymmetric Stellarator (CFQS) is now the only quasi-axisymmetric stellarator under construction in the world. In this work, ion temperature gradient (ITG) mode in CFQS is studied by using gyrokinetic Vlasov code GKV. The basic characteristics of the eletrtostatic ITG are separately given under the adiabatic condition and the non-adiabatic condition. There is a critical temperature gradient for ITG. The growth rate of ITG is proportional to the temperature gradient. Furthermore, the growth rate depends on not only the absolute value of density gradient, but also the plus or minus sign of the density gradient. The negative density gradient can strongly suppress the ITG. The kinetic electron can destabilize the ITG and the electron temperature gradient can also destabilize the ITG. For electromagnetic condition, the ITG modes can be suppressed by the finite plasma beta, and then a transition from ITG to Alfvenic ion temperature gradient mode/kinetic ballooning mode (AITG/KBM) comes into being. The maximum growth rate of KBM is linearly proportional to density gradient and temperature gradient when both gradients are large.-
Keywords:
- Chinese First Quasi-axisymmetric Stellarator /
- ion temperature gradient mode /
- plasma beta /
- kinetic ballooning mode
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图 1 不同密度梯度和温度梯度下绝热ITG的增长率波数谱 (a)
$ {R}_{0}/{L}_{n}=-2 $ ; (b)$ {R}_{0}/{L}_{n}=2 $ ; (c)$ {R}_{0}/{L}_{n}=8 $ Fig. 1. Growth rate spectra of ITG for different density gradients and temperature gradients: (a)
$ {R}_{0}/{L}_{n}=-2 $ ; (b)$ {R}_{0}/{L}_{n}=2 $ ; (c)$ {R}_{0}/{L}_{n}=8 $ .
图 2 不同密度梯度和温度梯度下绝热ITG的频率波数谱 (a)
$ {R}_{0}/{L}_{n}=-2 $ ; (b)$ {R}_{0}/{L}_{n}=2 $ ; (c)$ {R}_{0}/{L}_{n}=8 $ Fig. 2. Real frequency spectra of ITG for different density gradients and temperature gradients: (a)
$ {R}_{0}/{L}_{n}=-2 $ ; (b)$ {R}_{0}/{L}_{n}=2 $ ; (c)$ {R}_{0}/{L}_{n}=8 $ .
图 3 绝热ITG的最大增长率与密度梯度和温度梯度的关系
Fig. 3. Relationship of the maximum growth rate of adiabatic ITG to
$ {R}_{0}/{L}_{n} $ and$ {R}_{0}/{L}_{T} $ .
图 4 考虑捕获电子效应后ITG的增长率(a)和频率(b)波数谱, 其中
$ {R}_{0}/{L}_{n}=2 $ , 电子温度梯度标长和离子温度梯度标长相等, 即$ {R}_{0}/{L}_{{T}_{\mathrm{e}}}={R}_{0}/{L}_{{T}_{\mathrm{i}}} $ Fig. 4. Growth rate (a) and real frequency spectra (b) of kinetic ITG for
$ {R}_{0}/{L}_{n}=2 $ . Here,$ {R}_{0}/{L}_{{T}_{\mathrm{e}}}={R}_{0}/{L}_{{T}_{\mathrm{i}}} $ .
图 5 考虑捕获电子效应后ITG/TE-ITG最大增长率与密度梯度和温度梯度的关系, 其中
$ {R}_{0}/{L}_{{T}_{\mathrm{e}}}={R}_{0}/{L}_{{T}_{\mathrm{i}}} $ Fig. 5. Contour map of the maximum growth rate of kinetic ITG/TE-ITG mode vs.
$ {R}_{0}/{L}_{n} $ and$ {R}_{0}/{L}_{T} $ . Here,${R}_{0}/ {L}_{{T}_{\mathrm{e}}} $ $ ={R}_{0}/{L}_{{T}_{\mathrm{i}}}$ .
图 6 考虑捕获电子效应后ITG的增长率(a)和频率波数谱(b), 其中
$ {R}_{0}/{L}_{n}=2 $ ,$ {R}_{0}/{L}_{{T}_{\mathrm{e}}}=8 $ Fig. 6. Growth rate (a) and real frequency spectra (b) of kinetic ITG for
$ {R}_{0}/{L}_{n}=2 $ and$ {R}_{0}/{L}_{{T}_{\mathrm{e}}}=8 $ .
图 7 考虑捕获电子效应后ITG最大增长率与密度梯度和离子温度梯度的关系, 其中
$ {R}_{0}/{L}_{{T}_{\mathrm{e}}}=8 $ Fig. 7. Contour map of the maximum growth rate of kinetic ITG vs.
$ {R}_{0}/{L}_{n} $ and$ {R}_{0}/{L}_{{T}_{\mathrm{i}}} $ . Here,$ {R}_{0}/{L}_{{T}_{\mathrm{e}}}=8 $ .
图 8 当波数
$ {k}_{y}{\rho }_{\mathrm{i}}=1.0 $ 时增长率(a)与频率(b)随比压的变化(其中,$ {R}_{0}/{L}_{n}=2 $ ,$ {R}_{0}/{L}_{{T}_{\mathrm{e}}}={R}_{0}/{L}_{{T}_{\mathrm{i}}}=8 $ ), 图(a)中的箭头是从ITG转变为KBM的转变点Fig. 8. Growth rates (a) and real frequencies (b) vs.
$ \beta $ for$ {R}_{0}/{L}_{n}=2 $ and$ {R}_{0}/{L}_{{T}_{\mathrm{i}}}={R}_{0}/{{L}}_{{{T}}_{\mathrm{e}}}=8 $ at$ {k}_{y}{\rho }_{\mathrm{i}}=1.0 $ . The arrow is plotted in panel (a) to point the transition point from ITG to KBM.
图 9 取
$\beta =1{\text{%}}$ 时, KBM的增长率(a)和频率(b)波数谱, 其中$ {R}_{0}/{L}_{n}=2 $ ,$ {R}_{0}/{L}_{{T}_{\mathrm{e}}}=8 $ Fig. 9. Growth rate (a) and real frequency spectra (b) of KBM for
$ {R}_{0}/{L}_{n}=2 $ and$ {R}_{0}/{L}_{{T}_{\mathrm{e}}}=8 $ . Here,$\beta =1{\text{%}}$ . -
[1] Xu Y 2016 Matter Radiat. Extremes 1 192
Google Scholar
[2] Ho D D M 1987 Phys. Fluids 30 442
Google Scholar
[3] Boozer A H 1995 Plasma Phys. Controlled Fusion 37 A103
Google Scholar
[4] Subbotin A A, Mikhailov M I, Shafranov V D, Isaev M Yu, Nührenberg C, Nührenberg J, Zille R, Nemov V V, Kasilov SV, Kalyuzhnyj V N 2006 Nucl. Fusion 46 921
Google Scholar
[5] Garabedian P 1996 Phys. Plasmas 3 2483
Google Scholar
[6] Shimizu A, Liu H F, Isobe M, Okamura S, Nishimura S, Suzuki C, Xu Y, Zhang X, Liu B, Huang J, Wang X Q, Liu H, Tang C J, CFQS team 2018 Plasma Fusion Res. 13 3403123
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Google Scholar
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Google Scholar
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Google Scholar
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Luo Y M, Wang Z H, Chen J L, Wu X K, Fu C L, He X X, Liu L, Yang Z C, Li Y G, Gao J M, Du H R, Kulun Integrated Simulation and Design Group 2022 Acta Phys. Sin. 71 075201
Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Xie H S 2015 Ph. D. Dissertation (Hangzhou: Zhejiang University) (in Chinese)
[40] Aleynikova K, Zocco1 A, Xanthopoulos1 P, Helander1 P, Nührenberg C 2018 J. Plasma Phys. 84 745840602
Google Scholar
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