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

doi:10.7498/aps.72.20230726

Abstract

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.

Keywords:

Authors and contacts

Southwestern Institute of Physics, Chengdu 610041, China

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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References

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

Figure 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.

DownLoad: Full-Size Img PowerPoint

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

Figure 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.

DownLoad: Full-Size Img PowerPoint

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

Figure 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.

DownLoad: Full-Size Img PowerPoint

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

Figure 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.

DownLoad: Full-Size Img PowerPoint

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

Figure 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.

DownLoad: Full-Size Img PowerPoint

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

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

DownLoad: Full-Size Img PowerPoint

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

Figure 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.

DownLoad: Full-Size Img PowerPoint

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

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

DownLoad: Full-Size Img PowerPoint

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

Figure 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.

DownLoad: Full-Size Img PowerPoint

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

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

DownLoad: Full-Size Img PowerPoint

[1]	Chen L, Zonca F 2016 Rev. Mod. Phys. 88 015008 Google Scholar
[2]	Wong K L 1999 Plasma Phys. Control. Fusion 41 R1 Google Scholar
[3]	Heidbrink W W, Strait E J, Doyle E, et al. 1991 Nucl. Fusion 31 1635 Google Scholar
[4]	Podestà M, Bell R E, Crocker N A, et al. 2011 Nucl. Fusion 51 063035 Google Scholar
[5]	Wang X, Zonca F, Chen L 2010 Plasma Phys. Control. Fusion 52 115005 Google Scholar
[6]	Qi L Y, Dong J Q, Bierwage A, et al. 2013 Phys. Plasmas 20 032505 Google Scholar
[7]	Heidbrink W W, Strait E J, Chu M S, et al. 1993 Phys. Rev. Lett. 71 855 Google Scholar
[8]	Chen W, Ding X T, Yang Q W, et al. 2010 Phys. Rev. Lett. 105 185004 Google Scholar
[9]	Ding X T, Chen W 2018 Plasma Sci. Technol. 20 094008 Google Scholar
[10]	Yu L M, Chen W, Shi Z B, et al. 2021 Nucl. Fusion 61 026019 Google Scholar
[11]	Shi P W, Chen W, Shi Z B, et al. 2019 Nucl. Fusion 59 066015 Google Scholar
[12]	Xu M, Zhou T, Xu L Q, et al. 2018 Nucl. Fusion 58 124004 Google Scholar
[13]	Heidbrink W W 1995 Plasma Phys. Control. Fusion 37 937 Google Scholar
[14]	Shinohara K, Kusama Y, Takechi M, et al. 2001 Nucl. Fusion 41 603 Google Scholar
[15]	Pinches S D, Berk H L, Gryaznevich M P, et al. 2004 Plasma Phys. Control. Fusion 46 S47 Google Scholar
[16]	Fredrickson E D, Gorelenkov N N, Bell R E, et al. 2006 Nucl. Fusion 46 S926 Google Scholar
[17]	Classen I G J, Lauber Ph, Curran D, et al. 2011 Plasma Phys. Control. Fusion 53 124018 Google Scholar
[18]	Gryaznevich M P, Sharapov S E 2006 Nucl. Fusion 46 S942 Google Scholar
[19]	Chen W, Yu L M, Liu Y, et al. 2014 Nucl. Fusion 54 104002 Google Scholar
[20]	Berk H L, Breizman B N, Pekker M 1996 Phys. Rev. Lett. 76 1256 Google Scholar
[21]	Berk H L, Breizman B N, Petviashvili N V 1997 Phys. Lett. A 234 213 Google Scholar
[22]	Lilley M K, Breizman B N, Sharapov S E 2009 Phys. Rev. Lett. 102 195003 Google Scholar
[23]	Lesur M, Idomura Y, Shinohara K, et al. 2010 Phys. Plasmas 17 122311 Google Scholar
[24]	Zhang H S, Lin Z H, Holod I 2012 Phys. Rev. Lett. 109 025001 Google Scholar
[25]	Zhu J, Ma Z W, Fu G Y 2014 Nucl. Fusion 54 123020 Google Scholar
[26]	Wang X, Briguglio S, Chen L, et al. 2012 Phys. Rev. E 86 045401 Google Scholar
[27]	Todo Y 2006 Phys. Plasmas 13 082503 Google Scholar
[28]	Hou Y M, Chen W, Yu Y, et al. 2018 Nucl. Fusion 58 096028 Google Scholar
[29]	Hou Y M, Chen W, Yu L M, et al. 2021 Chin. Phys. Lett. 38 045202 Google Scholar
[30]	Wang X Q, Wang H, Todo Y, et al. 2021 Plasma Phys. Control. Fusion 63 015004 Google Scholar
[31]	Bierwage A, Shinohara K, Todo Y, et al. 2017 Nucl. Fusion 57 016036 Google Scholar
[32]	Shi Z B, Jiang M, Huang X L, et al. 2014 Rev. Sci. Instrum. 85 023510 Google Scholar
[33]	Liu C H, Wang Y Q, Feng Z, et al. 2015 JINST 10 C12026 Google Scholar
[34]	Li Y G, Zhou Y, Li Y, et al. 2017 Rev. Sci. Instrum. 88 083508 Google Scholar
[35]	Yang Z C, Jiang M, Shi Z B, et al. 2021 JINST 16 P05020 Google Scholar
[36]	Wei Y L, Yu D L, Liu L, et al. 2014 Rev. Sci. Instrum. 85 103503 Google Scholar
[37]	Chen W, Ding X T, Liu Y, et al. 2010 Nucl. Fusion 50 084008 Google Scholar
[38]	Yu L M, Chen W, Ji X Q, et al. 2021 Chin. Phy. Lett. 38 055202 Google Scholar
[39]	Shi P W, Chen W, Shi Z B, et al. 2017 Phys. Plasmas 24 042509 Google Scholar
[40]	Pei Y B, Xiang N, Hu Y J, et al. 2017 Phys. Plasmas 24 032507 Google Scholar
[41]	Hou Y M, Zhou H Y, Chen W, et al. 2023 Rev. Sci. Instrum. 94 033508 Google Scholar

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