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HL-2A装置高能量离子驱动的比压阿尔芬本征模的扫频行为

侯玉梅 陈伟 邹云鹏 于利明 石中兵 段旭如

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HL-2A装置高能量离子驱动的比压阿尔芬本征模的扫频行为

侯玉梅, 陈伟, 邹云鹏, 于利明, 石中兵, 段旭如

Beta-induced Alfvén eigenmodes with frequency chirping driven by energetic ions in the HL-2A Tokamak

Hou Yu-Mei, Chen Wei, Zou Yun-Peng, Yu Li-Ming, Shi Zhong-Bing, Duan Xu-Ru
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  • 利用混合磁流体-动理学模拟程序MEGA对中国环流器二号装置观测到的具有频率啁啾行为的比压阿尔芬本征模进行分析. 区别于动理论方法Berk-Breizman模型, MEGA程序采用真实的实验参数, 如平衡位形、电子密度、电子温度和离子温度等, 再现了具有向上和向下扫频特性的比压阿尔芬本征模. 实验观测到下扫频行为出现时背景等离子体的参数和比压值相对更高. 据此设置MEGA程序的输入参数: 在下扫频行为模拟中, 高能量离子的螺矩角初始分布宽度和芯部比压值, 以及扩散系数均更高. 模拟结果显示快离子相空间的分布影响了扫频行为. 当上扫频行为占主导时, 平行于磁场的离子发挥主要作用; 而下扫频行为占主导时, 垂直于磁场的离子密度显著上升. 实验与模拟均表明: 下扫频行为占主导的比压阿尔芬本征模激发对比压值和高能量离子的密度要求更高, 这与之前的模拟分析得到的结论一致.
    The beta-induced Alfvén eigenmodes (BAEs) with frequency chirping, observed in the HL-2A Tokamak, are analysed by a MHD-kinetic hybrid code MEGA. Realistic parameters are applied to the code, such as equilibrium, electron density and temperature, ion temperature, which is different from the kinetic Berk-Breizman theory. The BAEs are observed by Mirnov probes and soft X-ray arrays. Toroidal and porloidal mode number are confirmed to be n/m = 2/3 by using the phase shift method with toroidal filtered Mirnov signal arrays. And the soft X-ray arrays’ signal shows that BAEs are located at the core of the plasma and they have a relatively broad mode structure. The BAEs with up- and down-chirping are reproduced with MEGA code. The simulation results of mode structure accord well with experimental observations. Compared with up-chirping BAEs, the down-chirping BAEs are excited with higher plasma parameters and beta value, thus the energetic ion distribution in pitch angle has a broader width, and the beta value of energetic ions in the core of plasma and diffusion value are higher in the down-chirping simulation. The simulation results show that the phase space distribution of energetic ions affects the wave chirping direction. The energetic ions parallel to the magnetic field drive the up-chirping behavior. When the down-chirping behavior dominates, the density of energetic ions perpendicular to the magnetic field increases significantly. It shows that the down-chirping BAEs require higher beta and energetic ion density, which is consistent with the previous simulation result.
      通信作者: 陈伟, chenw@swip.ac.cn
    • 基金项目: 国家磁约束核聚变发展研究(批准号: 2019YFE03020003, 2019YFE03010004)和国家自然科学基金(批准号: 12005054, 12125502, 12105084)资助的课题.
      Corresponding author: Chen Wei, chenw@swip.ac.cn
    • Funds: Project supported by the National Key R&D Program of China (Grant Nos. 2019YFE03020003, 2019YFE03010004) and the National Natural Science Foundation of China (Grant Nos. 12005054, 12125502, 12105084).
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    Wong K L 1999 Plasma Phys. Control. Fusion 41 R1Google Scholar

    [3]

    Heidbrink W W, Strait E J, Doyle E, et al. 1991 Nucl. Fusion 31 1635Google Scholar

    [4]

    Podestà M, Bell R E, Crocker N A, et al. 2011 Nucl. Fusion 51 063035Google Scholar

    [5]

    Wang X, Zonca F, Chen L 2010 Plasma Phys. Control. Fusion 52 115005Google Scholar

    [6]

    Qi L Y, Dong J Q, Bierwage A, et al. 2013 Phys. Plasmas 20 032505Google Scholar

    [7]

    Heidbrink W W, Strait E J, Chu M S, et al. 1993 Phys. Rev. Lett. 71 855Google Scholar

    [8]

    Chen W, Ding X T, Yang Q W, et al. 2010 Phys. Rev. Lett. 105 185004Google Scholar

    [9]

    Ding X T, Chen W 2018 Plasma Sci. Technol. 20 094008Google Scholar

    [10]

    Yu L M, Chen W, Shi Z B, et al. 2021 Nucl. Fusion 61 026019Google Scholar

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    Shi P W, Chen W, Shi Z B, et al. 2019 Nucl. Fusion 59 066015Google Scholar

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    Xu M, Zhou T, Xu L Q, et al. 2018 Nucl. Fusion 58 124004Google Scholar

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    Heidbrink W W 1995 Plasma Phys. Control. Fusion 37 937Google Scholar

    [14]

    Shinohara K, Kusama Y, Takechi M, et al. 2001 Nucl. Fusion 41 603Google Scholar

    [15]

    Pinches S D, Berk H L, Gryaznevich M P, et al. 2004 Plasma Phys. Control. Fusion 46 S47Google Scholar

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    Fredrickson E D, Gorelenkov N N, Bell R E, et al. 2006 Nucl. Fusion 46 S926Google Scholar

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    Classen I G J, Lauber Ph, Curran D, et al. 2011 Plasma Phys. Control. Fusion 53 124018Google Scholar

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    Gryaznevich M P, Sharapov S E 2006 Nucl. Fusion 46 S942Google Scholar

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    Chen W, Yu L M, Liu Y, et al. 2014 Nucl. Fusion 54 104002Google Scholar

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    Berk H L, Breizman B N, Pekker M 1996 Phys. Rev. Lett. 76 1256Google Scholar

    [21]

    Berk H L, Breizman B N, Petviashvili N V 1997 Phys. Lett. A 234 213Google Scholar

    [22]

    Lilley M K, Breizman B N, Sharapov S E 2009 Phys. Rev. Lett. 102 195003Google Scholar

    [23]

    Lesur M, Idomura Y, Shinohara K, et al. 2010 Phys. Plasmas 17 122311Google Scholar

    [24]

    Zhang H S, Lin Z H, Holod I 2012 Phys. Rev. Lett. 109 025001Google Scholar

    [25]

    Zhu J, Ma Z W, Fu G Y 2014 Nucl. Fusion 54 123020Google Scholar

    [26]

    Wang X, Briguglio S, Chen L, et al. 2012 Phys. Rev. E 86 045401Google Scholar

    [27]

    Todo Y 2006 Phys. Plasmas 13 082503Google Scholar

    [28]

    Hou Y M, Chen W, Yu Y, et al. 2018 Nucl. Fusion 58 096028Google Scholar

    [29]

    Hou Y M, Chen W, Yu L M, et al. 2021 Chin. Phys. Lett. 38 045202Google Scholar

    [30]

    Wang X Q, Wang H, Todo Y, et al. 2021 Plasma Phys. Control. Fusion 63 015004Google Scholar

    [31]

    Bierwage A, Shinohara K, Todo Y, et al. 2017 Nucl. Fusion 57 016036Google Scholar

    [32]

    Shi Z B, Jiang M, Huang X L, et al. 2014 Rev. Sci. Instrum. 85 023510Google Scholar

    [33]

    Liu C H, Wang Y Q, Feng Z, et al. 2015 JINST 10 C12026Google Scholar

    [34]

    Li Y G, Zhou Y, Li Y, et al. 2017 Rev. Sci. Instrum. 88 083508Google Scholar

    [35]

    Yang Z C, Jiang M, Shi Z B, et al. 2021 JINST 16 P05020Google Scholar

    [36]

    Wei Y L, Yu D L, Liu L, et al. 2014 Rev. Sci. Instrum. 85 103503Google Scholar

    [37]

    Chen W, Ding X T, Liu Y, et al. 2010 Nucl. Fusion 50 084008Google Scholar

    [38]

    Yu L M, Chen W, Ji X Q, et al. 2021 Chin. Phy. Lett. 38 055202Google Scholar

    [39]

    Shi P W, Chen W, Shi Z B, et al. 2017 Phys. Plasmas 24 042509Google Scholar

    [40]

    Pei Y B, Xiang N, Hu Y J, et al. 2017 Phys. Plasmas 24 032507Google Scholar

    [41]

    Hou Y M, Zhou H Y, Chen W, et al. 2023 Rev. Sci. Instrum. 94 033508Google Scholar

  • 图 1  (a)电流和(b)中性束功率随时间的演化; (c) Mirnov探针的原始信号; (d)利用Mirnov探针信号进行傅里叶变换获得的BAEs的频谱图

    Fig. 1.  Evolution of (a) electric current and (b) the power of NBI; (c) the original signal of Mirnov probes; (d) the frequency spectrogram of BEAs obtained by using Fourier transform with Mirnov probes’ signal.

    图 2  利用软X射线阵列信号得到的频谱图 (a) SX51, r = 2.5 cm, $ \rho \sim 0.065$; (b) SX49, r=–7.3 cm, $ \rho \sim -0.1825$; (c) SX53, r = 12 cm, $ \rho\sim $0.3; (d) SX54, r = 16.3 cm, $ \rho\sim $0.4075

    Fig. 2.  Frequency spectrogram obtained with soft X-ray arrays’ signal: (a) SX51, r = 2.5 cm, $ \rho\sim $0.065; (b) SX49, r=–7.3 cm, $ \rho\sim $–0.1825; (c) SX53, r = 12 cm, $ \rho\sim $0.3; (d) SX54, r = 16.3 cm, $ \rho\sim $0.4075.

    图 3  (a)环向和(b)极向磁探针信号. 可判断环向模数 n = 2, 极向模数 m = 3

    Fig. 3.  (a) Toroidal and (b) porloidal Mirnov probe signal. Toroidal and porloidal mode number are confirmed as n = 2 and m = 3 by using the phase shift method with toroidal filtered Mirnov signal arrays.

    图 4  (a) HL-2A装置第35491次放电实验, t = 908 ms对应的等离子体位形, 最外闭合磁面和q = 1.5面分别用红色、绿色线标注; (b) t = 908 ms与t = 920 ms时刻分别对应的总压强和q剖面分布

    Fig. 4.  (a) Magnetic surface shape of HL-2A discharge $ \# $35491 at 908 ms, the last-closed-flux-surface and q = 1.5 surface are indicated in red and green, respectively; (b) radial profiles of the total pressure and safety factor at t = 908 ms and t = 920 ms.

    图 5  HL-2A装置第35491次放电实验, t = 908 ms (红) 与t = 920 ms (蓝)两个时刻对应的等离子体参数剖面 (a)电子密度; (b)电子温度; (c)离子温度

    Fig. 5.  Profile of plasma parameters at t = 908 ms (red) and t = 920 ms (blue) in the shot $ \# $35491 of HL-2A Tokamak: (a) Electron density; (b) electron temperature; (c) ion temperature.

    图 6  利用MEGA程序模拟得到的具有上扫频特性的BAEs (a) 极向速度; (b) 频谱图

    Fig. 6.  (a) Poloidal velocity and (b) the frequency spectrogram of up-chirping BAEs obtained by MEGA code.

    图 7  图6两个时刻(a), (c) t = 0.122 ms (线性阶段), (b), (d) t = 0.166 ms (非线性阶段)分别对应的二维模结构与径向模结构

    Fig. 7.  The 2D mode structure and radial mode structure for different times of (a), (c) t = 0.122 ms (the linear growth phase) and (b), (d) t = 0.166 ms (the nonlinear phase) corresponding to Fig. 6.

    图 8  利用MEGA程序得到的下扫频BAEs (a)极向速度; (b)频谱图

    Fig. 8.  (a) Poloidal velocity and (b) the frequency spectrogram of down-chirping BAEs obtained by MEGA code.

    图 9  图8两个时刻(a), (c) t = 0.147 ms (线性阶段), (b), (d) t = 0.203 ms (非线性阶段)分别对应的二维模结构与径向模结构

    Fig. 9.  The 2D mode structure and radial mode structure for different times of (a), (c) t = 0.147 ms (the linear growth phase) and (b), (d) t = 0.203 ms (the nonlinear phase) corresponding to Fig. 8.

    图 10  (a)上扫频和(b)下扫频模拟时高能量离子的相空间初始分布

    Fig. 10.  Initial distribution of energetic ions in phase space, in the simulation of (a) the up- and (b) down-chirping, respectively.

  • [1]

    Chen L, Zonca F 2016 Rev. Mod. Phys. 88 015008Google Scholar

    [2]

    Wong K L 1999 Plasma Phys. Control. Fusion 41 R1Google Scholar

    [3]

    Heidbrink W W, Strait E J, Doyle E, et al. 1991 Nucl. Fusion 31 1635Google Scholar

    [4]

    Podestà M, Bell R E, Crocker N A, et al. 2011 Nucl. Fusion 51 063035Google Scholar

    [5]

    Wang X, Zonca F, Chen L 2010 Plasma Phys. Control. Fusion 52 115005Google Scholar

    [6]

    Qi L Y, Dong J Q, Bierwage A, et al. 2013 Phys. Plasmas 20 032505Google Scholar

    [7]

    Heidbrink W W, Strait E J, Chu M S, et al. 1993 Phys. Rev. Lett. 71 855Google Scholar

    [8]

    Chen W, Ding X T, Yang Q W, et al. 2010 Phys. Rev. Lett. 105 185004Google Scholar

    [9]

    Ding X T, Chen W 2018 Plasma Sci. Technol. 20 094008Google Scholar

    [10]

    Yu L M, Chen W, Shi Z B, et al. 2021 Nucl. Fusion 61 026019Google Scholar

    [11]

    Shi P W, Chen W, Shi Z B, et al. 2019 Nucl. Fusion 59 066015Google Scholar

    [12]

    Xu M, Zhou T, Xu L Q, et al. 2018 Nucl. Fusion 58 124004Google Scholar

    [13]

    Heidbrink W W 1995 Plasma Phys. Control. Fusion 37 937Google Scholar

    [14]

    Shinohara K, Kusama Y, Takechi M, et al. 2001 Nucl. Fusion 41 603Google Scholar

    [15]

    Pinches S D, Berk H L, Gryaznevich M P, et al. 2004 Plasma Phys. Control. Fusion 46 S47Google Scholar

    [16]

    Fredrickson E D, Gorelenkov N N, Bell R E, et al. 2006 Nucl. Fusion 46 S926Google Scholar

    [17]

    Classen I G J, Lauber Ph, Curran D, et al. 2011 Plasma Phys. Control. Fusion 53 124018Google Scholar

    [18]

    Gryaznevich M P, Sharapov S E 2006 Nucl. Fusion 46 S942Google Scholar

    [19]

    Chen W, Yu L M, Liu Y, et al. 2014 Nucl. Fusion 54 104002Google Scholar

    [20]

    Berk H L, Breizman B N, Pekker M 1996 Phys. Rev. Lett. 76 1256Google Scholar

    [21]

    Berk H L, Breizman B N, Petviashvili N V 1997 Phys. Lett. A 234 213Google Scholar

    [22]

    Lilley M K, Breizman B N, Sharapov S E 2009 Phys. Rev. Lett. 102 195003Google Scholar

    [23]

    Lesur M, Idomura Y, Shinohara K, et al. 2010 Phys. Plasmas 17 122311Google Scholar

    [24]

    Zhang H S, Lin Z H, Holod I 2012 Phys. Rev. Lett. 109 025001Google Scholar

    [25]

    Zhu J, Ma Z W, Fu G Y 2014 Nucl. Fusion 54 123020Google Scholar

    [26]

    Wang X, Briguglio S, Chen L, et al. 2012 Phys. Rev. E 86 045401Google Scholar

    [27]

    Todo Y 2006 Phys. Plasmas 13 082503Google Scholar

    [28]

    Hou Y M, Chen W, Yu Y, et al. 2018 Nucl. Fusion 58 096028Google Scholar

    [29]

    Hou Y M, Chen W, Yu L M, et al. 2021 Chin. Phys. Lett. 38 045202Google Scholar

    [30]

    Wang X Q, Wang H, Todo Y, et al. 2021 Plasma Phys. Control. Fusion 63 015004Google Scholar

    [31]

    Bierwage A, Shinohara K, Todo Y, et al. 2017 Nucl. Fusion 57 016036Google Scholar

    [32]

    Shi Z B, Jiang M, Huang X L, et al. 2014 Rev. Sci. Instrum. 85 023510Google Scholar

    [33]

    Liu C H, Wang Y Q, Feng Z, et al. 2015 JINST 10 C12026Google Scholar

    [34]

    Li Y G, Zhou Y, Li Y, et al. 2017 Rev. Sci. Instrum. 88 083508Google Scholar

    [35]

    Yang Z C, Jiang M, Shi Z B, et al. 2021 JINST 16 P05020Google Scholar

    [36]

    Wei Y L, Yu D L, Liu L, et al. 2014 Rev. Sci. Instrum. 85 103503Google Scholar

    [37]

    Chen W, Ding X T, Liu Y, et al. 2010 Nucl. Fusion 50 084008Google Scholar

    [38]

    Yu L M, Chen W, Ji X Q, et al. 2021 Chin. Phy. Lett. 38 055202Google Scholar

    [39]

    Shi P W, Chen W, Shi Z B, et al. 2017 Phys. Plasmas 24 042509Google Scholar

    [40]

    Pei Y B, Xiang N, Hu Y J, et al. 2017 Phys. Plasmas 24 032507Google Scholar

    [41]

    Hou Y M, Zhou H Y, Chen W, et al. 2023 Rev. Sci. Instrum. 94 033508Google Scholar

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出版历程
  • 收稿日期:  2023-05-04
  • 修回日期:  2023-07-07
  • 上网日期:  2023-09-05
  • 刊出日期:  2023-11-05

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