Nonlinear simulation of multiple toroidal Alfvén eigenmodes in tokamak plasmas

doi:10.1088/1674-1056/ab610e

Abstract Nonlinear evolution of multiple toroidal Alfvén eigenmodes (TAEs) driven by fast ions is self-consistently investigated by kinetic simulations in toroidal plasmas. To clearly identify the effect of nonlinear coupling on the beam ion loss, simulations over single-n modes are also carried out and compared with those over multiple-n modes, and the wave-particle resonance and particle trajectory of lost ions in phase space are analyzed in detail. It is found that in the multiple-n case, the resonance overlap occurs so that the fast ion loss level is rather higher than the sum loss level that represents the summation of loss over all single-n modes in the single-n case. Moreover, increasing fast ion beta β_h can not only significantly increase the loss level in the multiple-n case but also significantly increase the loss level increment between the single-n and multiple-n cases. For example, the loss level in the multiple-n case for β_h=6.0% can even reach 13% of the beam ions and is 44% higher than the sum loss level calculated from all individual single-n modes in the single-n case. On the other hand, when the closely spaced resonance overlap occurs in the multiple-n case, the release of mode energy is increased so that the widely spaced resonances can also take place. In addition, phase space characterization is obtained in both single-n and multiple-n cases.

Keywords: tokamak toroidal Alfvén eigenmode wave-particle interaction beam ion loss

Received: 18 November 2019
Revised: 09 December 2019
Accepted manuscript online:

PACS:	52.55.Fa	(Tokamaks, spherical tokamaks)
	52.35.Bj	(Magnetohydrodynamic waves (e.g., Alfven waves))
	94.20.wj	(Wave/particle interactions)
	52.55.Dy	(General theory and basic studies of plasma lifetime, particle and heat loss, energy balance, field structure, etc.)

Fund: Project supported by the National Key R&D Program of China (Grant No. 2017YFE0301900), the National Natural Science Foundation of China (Grant No. 11675083), and the Fundamental Research Funds for the Central Universities of China (Grant No. DUT18ZD101).

Corresponding Authors: Feng Wang, Zheng-Xiong Wang
E-mail: fengwang@dlut.edu.cn;zxwang@dlut.edu.cn

Cite this article:

Xiao-Long Zhu(朱霄龙), Feng Wang(王丰), Zheng-Xiong Wang(王正汹) Nonlinear simulation of multiple toroidal Alfvén eigenmodes in tokamak plasmas 2020 Chin. Phys. B 29 025201

[1]	Chen L 2008 Plasma Phys. Control. Fusion 50 124001
[2]	Chen L and Zonca F 2016 Rev. Mod. Phys. 88 015008
[3]	Todo Y 2019 Rev. Mod. Plasma Phys. 3 1
[4]	Aymar R, Chuyanov V A, Huguet M, Shimomura Y, ITER Joint Central Team and ITER Home Teams 2001 Nucl. Fusion 41 1301
[5]	Wan Y X, Li J G, Liu Y, Wang X L, Chan V, Chen C A, Duan X R, Fu P, Gao X, Feng K M, Liu S L, Song Y T, Wen P D, Wan B N, Wan F R, Wang H Y, Wu S T, Ye M Y, Yang Q W, Zheng G Y, Zhuang G, Li Q and Team CFETR 2017 Nucl. Fusion 57 102009
[6]	Fasoli A, Gormenzano C, Brek H L, Breizman B, Briguglio S, Darrow D S, Gorelenkov N, Heidbrink W W, Jaun A, Konovalov S V, Nazikian R, Noterdaeme J M, Sharapov S, Shinohara K, Testa D, Tobita K, Todo Y, Vlad G and Zonca F 2007 Nucl. Fusion 47 S264
[7]	Garcia-Munoz M, Hicks N, Van-Voomveld R, Classen I G J, Bilato R, Bobkov V, Bruedgam M, Fahrbach H U, Igochine V, Jaemsae S, Maraschek M, Sassenberg K and ASDEX Upgrade Team 2010 Phys. Rev. Lett. 104 185002
[8]	Podesta M, Heidbrink W W, Liu D, Ruskov E, Bell R E, Darrow D S, Fredrickson E D, Gorelenkov N N, Kramer G J, LeBlanc B P, Medley S S, Roquemore A L, Crocker N A, Kubota S and Yuh H 2009 Phys. Plasmas 16 056104
[9]	Nabais F, Kiptily V G, Pinches S D, Sharapov S E and contributors A 2010 Nucl. Fusion 50 084021
[10]	Duong H H, Heidbrink W W, Strait E J, Petrie T W, Lee R, Moyer R A and Watkins J G 1993 Nucl. Fusion 33 749
[11]	Collins C S, Heidbrink W W, Austin M E, Kramer G J, Pace D C, Petty C C, Stagner L, Van Zeeland M A, White R B, Zhu Y B and team DIII-D 2016 Phys. Rev. Lett. 116 095001
[12]	Heidbrink W W, Collins C S, Podesta M, Kramer G J, Pace D C, Petty C C, Stagner L, Van Zeeland M A, White R B and Zhu Y B 2017 Phys. Plasmas 24 056109
[13]	Bass E M and Waltz R E 2017 Phys. Plasmas 24 122302
[14]	Schneller M, Lauber Ph and Briguglio S 2016 Plasma Phys. Control. Fusion 58 014019
[15]	Chen L and Zonca F 2007 Nucl. Fusion 47 S727
[16]	Chen X, Heidbrink W W, Kramer G J, Van-Zeeland M A, Austin M E, Fisher R K, Nazikian R, Pace D C and Petty C C 2013 Nucl. Fusion 53 123019
[17]	White R B, Goldston R J, McGuire K, Boozer A H, Monticello D A and Park W 1983 Phys. Fluids 26 2958
[18]	Tobita K, Tani K, Nishitani T, Nagashima K and Kusama Y 1994 Nucl. Fusion 34 1097
[19]	Zhang R B, Fu G Y, White R B and Wang X G 2015 Nucl. Fusion 55 122002
[20]	Park W, Belova E V, Fu G Y, Tang X Z, Strauss H R and Sugiyama L E 1999 Phys. Plasmas 6 1796
[21]	Fu G Y, Park W, Strauss H R, Breslau J, Chen J, Jardin S and Sugiyama L E 2006 Phys. Plasmas 13 052517
[22]	Wang F, Fu G Y, Breslau J A, Tritz K and Liu J Y 2013 Phys. Plasmas 20 072506
[23]	Wang F, Fu G Y, Breslau J A and Liu J Y 2013 Phys. Plasmas 20 102506
[24]	Wang F, Fu G Y and Shen W 2017 Nucl. Fusion 57 016034
[25]	Shen W, Wang F, Fu G Y, Xu L Q, Li G Q and Liu C Y 2017 Nucl. Fusion 57 116035
[26]	Yang S X, Hao G Z, Liu Y Q, Wang Z X, Hu Y J, Zhu J X, He H D and Wang A K 2018 Nucl. Fusion 58 046016
[27]	Liu D, Fu G Y, Crocker N A, Podesta M, Breslau J A, Fredrickson E D and Kubota S 2015 Phys. Plasmas 22 042509
[28]	Ren Z Z, Wang F, Fu G Y, Shen W and Wang Z X 2017 Phys. Plasmas 24 052501
[29]	Shen W, Fu G Y, Sheng Z M, Breslau J A and Wang F 2014 Phys. Plasmas 21 092514
[30]	Shen W, Fu G Y, Tobias B, Van-Zeeland M, Wang F and Sheng Z M 2015 Phys. Plasmas 22 042510
[31]	Cai H S and Fu G Y 2012 Phys. Plasmas 19 072506
[32]	Hsu C T and Sigmar D J 1992 Phys. Fluids B 4 1492
[33]	Berk H L, Breizman B N and Ye H C 1992 Phys. Rev. Lett. 68 3563
[34]	Galdon-Quiroga J, Garcia-Munoz M, McClements K G, Nocente M, Hoelzl M, Jacobsen A S, Orain F, Rivero-Rodriguez J F, Salewski M, Sanchis-Sanchez L, Suttrop W, Viezzer E, the ASDEX Upgrade Team and the Eurofusion MST1 Team 2018 Phys. Rev. Lett. 121 025002
[35]	Chen Y, Parker S E, Lang J and Fu G Y 2010 Phys. Plasmas 17 102504

[1]	Gyrokinetic simulation of low-n Alfvénic modes in tokamak HL-2A plasmas Wen-Hao Lin(林文浩), Ji-Quan Li(李继全), J Garcia, and S Mazzi. Chin. Phys. B, 2023, 32(2): 025202.
[2]	Experimental investigation on divertor tungsten sputtering with neon seeding in ELMy H-mode plasma in EAST tokamak Dawei Ye(叶大为), Fang Ding(丁芳), Kedong Li(李克栋), Zhenhua Hu(胡振华), Ling Zhang(张凌), Xiahua Chen(陈夏华), Qing Zhang(张青), Pingan Zhao(赵平安), Tao He(贺涛), Lingyi Meng(孟令义), Kaixuan Ye(叶凯萱), Fubin Zhong(钟富彬), Yanmin Duan(段艳敏), Rui Ding(丁锐), Liang Wang(王亮), Guosheng Xu(徐国盛), Guangnan Luo(罗广南), and EAST team. Chin. Phys. B, 2022, 31(6): 065201.
[3]	Study on divertor plasma behavior through sweeping strike point in new lower divertor on EAST Yu-Qiang Tao(陶余强), Guo-Sheng Xu(徐国盛), Ling-Yi Meng(孟令义), Rui-Rong Liang(梁瑞荣), Lin Yu(余林), Xiang Liu(刘祥), Ning Yan(颜宁), Qing-Quan Yang(杨清泉), Xin Lin(林新), and Liang Wang(王亮). Chin. Phys. B, 2022, 31(6): 065204.
[4]	Observation of trapped and passing runaway electrons by infrared camera in the EAST tokamak Yong-Kuan Zhang(张永宽), Rui-Jie Zhou(周瑞杰), Li-Qun Hu(胡立群), Mei-Wen Chen(陈美文), Yan Chao(晁燕), Jia-Yuan Zhang(张家源), and Pan Li(李磐). Chin. Phys. B, 2021, 30(5): 055206.
[5]	Discharge simulation and volt-second consumption analysis during ramp-up on the CFETR tokamak Cheng-Yue Liu(刘成岳), Bin Wu(吴斌), Jin-Ping Qian(钱金平), Guo-Qiang Li(李国强), Ya-Wei Hou(侯雅巍), Wei Wei(韦维), Mei-Xia Chen(陈美霞), Ming-Zhun Lei(雷明准), Yong Guo(郭勇). Chin. Phys. B, 2020, 29(2): 025202.
[6]	Effect of edge transport barrier on required toroidal field for ignition of elongated tokamak Cui-Kun Yang(杨翠坤), Ming-Sheng Chu(朱名盛), Wen-Feng Guo(郭文峰). Chin. Phys. B, 2019, 28(4): 045202.
[7]	Observation of double pseudowaves in an ion-beam-plasma system Zi-An Wei(卫子安), Jin-Xiu Ma(马锦秀), Kai-Yang Yi(弋开阳). Chin. Phys. B, 2018, 27(8): 085201.
[8]	Synchrotron radiation intensity and energy of runaway electrons in EAST tokamak Y K Zhang(张永宽), R J Zhou(周瑞杰), L Q Hu(胡立群), M W Chen(陈美文), Y Chao(晁燕), EAST team. Chin. Phys. B, 2018, 27(5): 055206.
[9]	Fast parallel Grad-Shafranov solver for real-time equilibrium reconstruction in EAST tokamak using graphic processing unit Yao Huang(黄耀), Bing-Jia Xiao(肖炳甲), Zheng-Ping Luo(罗正平). Chin. Phys. B, 2017, 26(8): 085204.
[10]	Energetic-ion excited internal kink modes with weak magnetic shear in q₀ >1 tokamak plasmas Wen-Ming Chen(陈文明), Xiao-Gang Wang(王晓钢), Xian-Qu Wang(王先驱), Rui-Bin Zhang(张瑞斌). Chin. Phys. B, 2017, 26(8): 085201.
[11]	Simulations of the effects of density and temperature profile on SMBI penetration depth based on the HL-2A tokamak configuration Xueke Wu(吴雪科), Huidong Li(李会东), Zhanhui Wang(王占辉), Hao Feng(冯灏), Yulin Zhou(周雨林). Chin. Phys. B, 2017, 26(6): 065201.
[12]	North west cape-induced electron precipitation and theoretical simulation Zhen-xia Zhang(张振霞), Xin-qiao Li(李新乔), Chen-Yu Wang(王辰宇), Lun-Jin Chen. Chin. Phys. B, 2016, 25(11): 119401.
[13]	A divertor plasma configuration design method for tokamaks Yong Guo(郭勇), Bing-Jia Xiao(肖炳甲), Lei Liu(刘磊), Fei Yang(杨飞), Yuehang Wang(汪悦航), Qinglai Qiu (仇庆来). Chin. Phys. B, 2016, 25(11): 115201.
[14]	Effects of q-profiles of a weak magnetic shear on energetic ion excited q=1 mode in tokamak plasmas Ze-Yu Li(李泽宇), Xian-Qu Wang(王先驱), Xiao-Gang Wang(王晓钢). Chin. Phys. B, 2016, 25(1): 015203.
[15]	Start-up phase plasma discharge design of a tokamak via control parameterization method Guo Shan (郭珊), Xu Ke (许珂), Xu Chao (许超), Ren Zhi-Gang (任志刚), Xiao Bing-Jia (肖炳甲). Chin. Phys. B, 2015, 24(3): 035202.

No Suggested Reading articles found!

Viewed

Full text

Abstract

Cited

Metrics
Related Articles

Nonlinear simulation of multiple toroidal Alfvén eigenmodes in tokamak plasmas

Cite this article:

Online attention