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).

FullText HTML : translate this paragraph

References

[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

Cited By

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

[1]	Yang Guo, Shi Hong-Qiang, Li Xiao-Cong, Xiao Ru-Qi, Qi Shi-Shan, Wu Wen. Millimeter-Wave Frequency-Reconfigurable Filtering Antenna with High Frequency Turning Ratio. Acta Physica Sinica, 2025, 74(1): 1-11. doi: 10.7498/aps.74.20241494
[2]	Ma Rui-Rui, Chen Liu, Qiu Zhi-Yong. Theoretical studies of low-frequency shear Alfvén waves in reversed shear tokamak plasmas. Acta Physica Sinica, 2023, 72(21): 215207. doi: 10.7498/aps.72.20230255
[3]	Luo Xiao-Li, Gao Jian-Hua. Non-Abelian chiral kinetic equations in the Cartan-Weyl basis. Acta Physica Sinica, 2023, 72(11): 112503. doi: 10.7498/aps.72.20222471
[4]	Bao Jian, Zhang Wen-Lu, Li Ding. Global simulations of energetic electron excitation of beta-induced Alfvén eigenmodes. Acta Physica Sinica, 2023, 72(21): 215216. doi: 10.7498/aps.72.20230794
[5]	Xie Bai-Song, Li Lie-Juan, Melike Mohamedsedik, Wang Li. Enhancement effect of frequency chirp on vacuum electron-positron pair production in strong field. Acta Physica Sinica, 2022, 71(13): 131201. doi: 10.7498/aps.71.20220148
[6]	Zhou Xiao-Xi, Hu Chuan-Deng, Lu Wei-Xin, Lai Yun, Hou Bo. Numerical design of frequency-split Weyl points in Weyl metamaterial. Acta Physica Sinica, 2020, 69(15): 154204. doi: 10.7498/aps.69.20200195
[7]	Liu Xiong-Guo, Deng Li, Hu Ze-Hua, Li Rui, Fu Yuan-Guang, Li Gang, Wang Jia. Study of on-the-fly Doppler broadening in JMCT program. Acta Physica Sinica, 2016, 65(9): 092501. doi: 10.7498/aps.65.092501
[8]	Liu Ting-Yang, Zhang Fu-Min, Wu Han-Zhong, Li Jian-Shuang, Shi Yong-Qiang, Qu Xing-Hua. Absolute distance ranging by means of chirped pulse interferometry. Acta Physica Sinica, 2016, 65(2): 020601. doi: 10.7498/aps.65.020601
[9]	Luo Xiang-Yi, Ben Shuai, Ge Xin-Lei, Wang Qun, Guo Jing, Liu Xue-Shen. High-order harmonics and attosecond pulse generation of a He+ ion by a chirped two-color inhomogeneous laser field. Acta Physica Sinica, 2015, 64(19): 193201. doi: 10.7498/aps.64.193201
[10]	Chen Ji-Xiang, Zhou Shuo-Yao. Local atomic short-range-order features of NiZr, AlZr and BCr crystalline phases. Acta Physica Sinica, 2014, 63(6): 066101. doi: 10.7498/aps.63.066101
[11]	Wang Zhi-Guo, Long Xing-Wu, Wang Fei, Zhang Bin. Theoretical analysis of polarization eigenstate and magnetic sensitivity in a ring laser gyro. Acta Physica Sinica, 2013, 62(5): 054205. doi: 10.7498/aps.62.054205
[12]	Li Wei, Wang Guo-Li, Zhou Xiao-Xin. Single attosecond pulse generated by model helium atom exposed to the combined field of an intense few-cycle chirped laser pulse and a half cycle pulse. Acta Physica Sinica, 2011, 60(12): 123201. doi: 10.7498/aps.60.123201
[13]	Zhou Tie-Ge, Song Feng-Bin, Zuo Tao, Gu Jing, Xia Hou-Hai, Hu Ya-Ting, Zhao Xin-Jie, Fang Lan, Yan Shao-Lin. The model of capacitively coupled intrinsic Josephson junction array and its chaotic behavior. Acta Physica Sinica, 2007, 56(11): 6307-6314. doi: 10.7498/aps.56.6307
[14]	Jian Guang-De, Dong Jia-Qi. Numerical study of kinetic shear Alfvn instability in tokamak plasmas. Acta Physica Sinica, 2005, 54(4): 1641-1647. doi: 10.7498/aps.54.1641
[15]	Zhang Jie-Qiu, Liang Chang-Hong, Wang Geng-Guo, Zhu Jia-Zhen. Condition of Alfven Gauss wave-packet evolvement to solitons and criterion of Alfven wave modulation instability. Acta Physica Sinica, 2003, 52(4): 890-895. doi: 10.7498/aps.52.890
[16]	FU GANG, CHEN ZHI-XIONG, SHI BIN. INTRINSIC DEFECTS IN ZnO VARISTOR CERAMICS. Acta Physica Sinica, 1996, 45(5): 850-853. doi: 10.7498/aps.45.850
[17]	FU ZHUO-WU. THEORY OF N-COMPONENT DISORDER MATERIALS WITH SHORT-RANGE ORDER. Acta Physica Sinica, 1985, 34(4): 493-502. doi: 10.7498/aps.34.493
[18]	SHI CHANG-HE. THE NON-GEOMETRICAL OPTIC SOLUTION FOR THE ALFVEN WAVE IN DOUBLE PLASMA BEAM MODEL. Acta Physica Sinica, 1983, 32(1): 25-32. doi: 10.7498/aps.32.25
[19]	ZHANG CHENG-FU. THE EFFECT OF FINITE ION LARMOR RADIUS ON THE EIGENMODES OF DRIFT WAVE. Acta Physica Sinica, 1980, 29(6): 778-787. doi: 10.7498/aps.29.778
[20]	ZHANG CHENG-FU. THE EFFECT OF STOCHASTIC MAGNETIC FIELD ON THE EIGEN-MODES OF DRIFT WAVE. Acta Physica Sinica, 1980, 29(11): 1357-1366. doi: 10.7498/aps.29.1357

Catalog

Vol. 72, Issue 21 - 2023-11-05

Metrics

Abstract views: 2437
PDF Downloads: 49
Cited By: 0

姓名
邮箱
手机号码
标题
留言内容
验证码

Search

Article

留言板