Excitations of tearing mode and Kelvin-Helmholtz mode in rotating cylindrical plasmas

Bi Hai-Liang; Wei Lai; Fan Dong-Mei; Zheng Shu; Wang Zheng-Xiong

doi:10.7498/aps.65.225201

Abstract

The influences of safety factor q profile and poloidal rotation profile on the q=1 tearing and Kelvin-Helmholtz (K-H) instabilities are investigated numerically by using a magnetohydrodynamic model in cylindrical geometry. With increasing the poloidal rotation, the m/n=1/1 mode is suppressed, while four domains exist for the high-order harmonic modes (such as m/n=2/2, m/n=3/3):the destabilized tearing mode domain, stabilized tearing mode domain, stable-window domain, and unstable K-H mode domain. Further, we find that the growth rate of the m/n=1/1 mode is related to the location of shear layer. Roles of shear flow in the m/n=1/1 mode for the shear layer located t on both the inner and outer sides of rational surface are almost the same, which is different from the scenarios of high-order harmonic modes. In addition, the smaller the magnetic shear on the rational surface, the smaller the growth rate of tearing mode is, and the more easily the K-H instability is excited.

Keywords:

Authors and contacts

1.
Key Laboratory of Materials Modification by Laser, Ion, and Electron Beams(Ministry of Education), School of Physics and Optoelectronic Technology, Dalian University of Technology, Dalian 116024, China;
2.
China Aerospace Academy of Systems Science and Engineering, Beijing 100048, China

Corresponding author: Wei Lai, laiwei@dlut.edu.cn;zxwang@dlut.edu.cn ; Wang Zheng-Xiong, laiwei@dlut.edu.cn;zxwang@dlut.edu.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 11322549, 11275043, 11305027), Funds of Dalian Young Talents (Grant No. 2015R001), and the Fundamental Research Funds for the Central Universities, China (Grant Nos. DUT14RC(3)157, DUT15YQ103).

References

[1]	Fu S Y, Pu Z Y, Liu Z X 1995J. Geophys. Res. 100 5657
[2]	Hasegawa H, Fujimoto M, Phan T D, Rème H, Balogh A, Dunlop M W, Hashimoto C, TanDokoro R 2004Nature 430 755
[3]	Li J H, Ma Z W 2010J. Geophys. Res. 115 A09216
[4]	Burrell K H 1997Phys. Plasmas 4 1499
[5]	Terry P W 2000Rev. Mod. Phys. 72 109
[6]	Lin Z, Hahm T S, Lee W W, Tang W M, White R B 1998Science 281 1835
[7]	Diamond P H, Itoh S I, Itoh K, Hahm T S 2005Plasma Phys. Controlled Fusion 47 R35
[8]	Gerhardt S P, Brenman D P, Buttery R, La Haye R J, Sabbagh S, Strait E, Bell M, Fredrickson E, Gates D, LeBlanc B, Menard J, Stutman D, Tritz K, Yuh H 2009Nucl. Fusion 49 032003
[9]	La Haye R J, Pretty C C, Politzer P A, DⅢ-D Team 2011Nucl. Fusion 51 053013
[10]	Chen X L, Morrison P J 1990Phys. Fluids B 2 495
[11]	Lau Y Y, Liu C S 1980Phys. Fluids 23 939
[12]	Miura A, Prichett P L 1982J. Geophys. Res. 87 7431
[13]	Chandrasekhar S 1961Hydrodynamic and Hydromagnetic Stability (Oxford:Clarendon)
[14]	Tatsuno T, Dorland W 2006Phys. Plasmas 13 092107
[15]	Takeji S, Tokuda S, Fujita T, Suzuki T, Isayama A, Ide S, Ishii Y, Kamada Y, Koide Y, Matsumoto T, Oikawa T, Ozeki T, Sakamoto Y, JT-60 Team 2002Nucl. Fusion 42 5
[16]	Chen W, Ding X T, Yang Q W, Liu Y, Ji X Q, Zhang Y P, Zhou J, Yuan G L, Sun H J, Li W, Zhou Y, Huang Y, Dong J Q, Feng B B, Song X M, Shi Z B, Liu Z T, Song X Y, Li L C, Duan X R, Liu Y, HL-2A Team 2010Phys. Rev. Lett. 105 185004
[17]	Edwards A W, Campbell D J, Engelhardt W W, Fahrbach H U, Gill R D, Granetz R S, Tsuji S, Tubbing B J D, Weller A, Wesson J, Zasche D 1986Phys. Rev. Lett. 57 210
[18]	Kadomtsev B B 1975Sov. J. Plasma Phys. 1 389
[19]	Wesson J A 1986Plasma Phys. Controlled Fusion 28 243
[20]	Hastie R J 1998Astrophys. Space Sci. 256 177
[21]	Aydemir A Y, Wiley J C, Ross D W 1989Phys. Fluids B 1 774
[22]	Lichtenberg A J, Itoh K, Itoh S I, Fukuyama A 1992Nucl. Fusion 32 495
[23]	Wang X, Bhattacharjee A 1993Phys. Rev. Lett. 70 1627
[24]	Qu Q 1995Nucl. Fusion 35 1012
[25]	Porcelli F, Boucher D, Rosenbluth M N 1996Plasma Phys. Controlled Fusion 38 2163
[26]	Matsumoto T, Tokuda S, Kishimoto Y, Takizuka T, Naitou H 1999J. Plasma Fusion Res. 75 1188
[27]	Chapman I T, Pinches S D, Graves J P, Akers R J, Appel L C, Budny R V, Coda S, Conway N J, de Bock M, Eriksson L G, Hastie R J, Hender T C, Huysmans G T A, Johnson T, Koslowski H R, Krämer-Flecken A, Lennholm M, Liang Y, Saarelma S, Sharapov S E, Voitsekhovitch I, MAST and TEXTOR Teams and JET EFDA Contributors 2007Plasma Phys. Controlled Fusion 49 B385
[28]	Halpern F D, Ltjens H, Luciani J F 2011Phys. Plasmas 18 102501
[29]	Nagayama Y, Taylor G, Yamada M, Fredrickson E D, Janos A C, McGuire K M 1996Nucl. Fusion 36 521
[30]	Yamaguchi S, Igami H, Tanaka H, Maekawa T 2004Plasma Phys. Controlled Fusion 46 1163
[31]	Chen W, Ding X T, Liu Yi, Yuan G L, Zhang Y P, Dong Y B, Song X Y, Zhou J, Song X M, Deng W, Yang Q W, Ji X Q, Duan X R, Liu Y, the HL-2A Team 2009Nucl. Fusion 49 075022
[32]	Igochine V, Dumbrajs O, Zohm H, Flaws A, ASDEX Upgrade Team 2007Nucl. Fusion 47 23
[33]	Sun Y, Wan B, Hu L, Chen K, Shen B, Mao J 2009Plasma Phys. Controlled Fusion 51 065001
[34]	Chen W, Ding X T, Yu L M, Ji X Q, Shi Z B, Zhang Y P, Zhong W L, Yuan G L, Dong J Q, Yang Q W, Liu Yi, Yan L W, Zhou Y, Jiang M, Li W, Song X M, Chen S Y, Duan X R, the HL-2A Team 2013Nucl. Fusion 53 113010
[35]	Chen W, Ding X T, Liu Yi, Yang Q W, Ji X Q, Isobe1 M, Yuan G L, Zhang Y P, Zhou Y, Song X Y, Dong Y B, Li W, Zhou J, Lei G J, Cao J Y, Deng W, Song X M, Duan X R, HL-2A Team 2010Nucl. Fusion 50 084008
[36]	Sauter O, Westerhof E, Mayoral M L, Alper B, Belo P A, Buttery R J, Gondhalekar A, Hellsten T, Hender T C, Howell D F, Johnson T, Lamalle P, Mantsinen M J, Milani F, Nave M F F, Nguyen F, Pecquet A L, Pinches S D, Podda S, Rapp J 2002Phys. Rev. Lett. 88 105001
[37]	Nave M F F, Lazzaro E, Coelho R, Belo P, Borba D, Buttery R J, Nowak S, Serra F, EFDA-JET Contributors 2003Nucl. Fusion 43 179
[38]	Furth H P, Killeen J, Rosenbluth M N 1963Phys. Fluids 6 459
[39]	Wang Z X, Wei L, Wang X 2012Phys. Plasmas 19 062108
[40]	Wei L, Wang Z X 2013Phys. Plasmas 20 012512
[41]	Fan D M, Wei L, Wang Z X, Zheng S, Duan P 2014Phys. Plasmas 21 092515
[42]	Bierwage A, Benkadda S, Hamaguchi S, Wakatani M 2005Phys. Plasmas 12 082504
[43]	Bierwage A, Yu Q, Gnter S 2007Phys. Plasmas 14 010704
[44]	Bell R E, Levinton F M, Batha S H, Synakowski E J, Zarnstorff M C 1998Phys. Rev. Lett. 81 1429

Cited By

[1]	Fu S Y, Pu Z Y, Liu Z X 1995J. Geophys. Res. 100 5657
[2]	Hasegawa H, Fujimoto M, Phan T D, Rème H, Balogh A, Dunlop M W, Hashimoto C, TanDokoro R 2004Nature 430 755
[3]	Li J H, Ma Z W 2010J. Geophys. Res. 115 A09216
[4]	Burrell K H 1997Phys. Plasmas 4 1499
[5]	Terry P W 2000Rev. Mod. Phys. 72 109
[6]	Lin Z, Hahm T S, Lee W W, Tang W M, White R B 1998Science 281 1835
[7]	Diamond P H, Itoh S I, Itoh K, Hahm T S 2005Plasma Phys. Controlled Fusion 47 R35
[8]	Gerhardt S P, Brenman D P, Buttery R, La Haye R J, Sabbagh S, Strait E, Bell M, Fredrickson E, Gates D, LeBlanc B, Menard J, Stutman D, Tritz K, Yuh H 2009Nucl. Fusion 49 032003
[9]	La Haye R J, Pretty C C, Politzer P A, DⅢ-D Team 2011Nucl. Fusion 51 053013
[10]	Chen X L, Morrison P J 1990Phys. Fluids B 2 495
[11]	Lau Y Y, Liu C S 1980Phys. Fluids 23 939
[12]	Miura A, Prichett P L 1982J. Geophys. Res. 87 7431
[13]	Chandrasekhar S 1961Hydrodynamic and Hydromagnetic Stability (Oxford:Clarendon)
[14]	Tatsuno T, Dorland W 2006Phys. Plasmas 13 092107
[15]	Takeji S, Tokuda S, Fujita T, Suzuki T, Isayama A, Ide S, Ishii Y, Kamada Y, Koide Y, Matsumoto T, Oikawa T, Ozeki T, Sakamoto Y, JT-60 Team 2002Nucl. Fusion 42 5
[16]	Chen W, Ding X T, Yang Q W, Liu Y, Ji X Q, Zhang Y P, Zhou J, Yuan G L, Sun H J, Li W, Zhou Y, Huang Y, Dong J Q, Feng B B, Song X M, Shi Z B, Liu Z T, Song X Y, Li L C, Duan X R, Liu Y, HL-2A Team 2010Phys. Rev. Lett. 105 185004
[17]	Edwards A W, Campbell D J, Engelhardt W W, Fahrbach H U, Gill R D, Granetz R S, Tsuji S, Tubbing B J D, Weller A, Wesson J, Zasche D 1986Phys. Rev. Lett. 57 210
[18]	Kadomtsev B B 1975Sov. J. Plasma Phys. 1 389
[19]	Wesson J A 1986Plasma Phys. Controlled Fusion 28 243
[20]	Hastie R J 1998Astrophys. Space Sci. 256 177
[21]	Aydemir A Y, Wiley J C, Ross D W 1989Phys. Fluids B 1 774
[22]	Lichtenberg A J, Itoh K, Itoh S I, Fukuyama A 1992Nucl. Fusion 32 495
[23]	Wang X, Bhattacharjee A 1993Phys. Rev. Lett. 70 1627
[24]	Qu Q 1995Nucl. Fusion 35 1012
[25]	Porcelli F, Boucher D, Rosenbluth M N 1996Plasma Phys. Controlled Fusion 38 2163
[26]	Matsumoto T, Tokuda S, Kishimoto Y, Takizuka T, Naitou H 1999J. Plasma Fusion Res. 75 1188
[27]	Chapman I T, Pinches S D, Graves J P, Akers R J, Appel L C, Budny R V, Coda S, Conway N J, de Bock M, Eriksson L G, Hastie R J, Hender T C, Huysmans G T A, Johnson T, Koslowski H R, Krämer-Flecken A, Lennholm M, Liang Y, Saarelma S, Sharapov S E, Voitsekhovitch I, MAST and TEXTOR Teams and JET EFDA Contributors 2007Plasma Phys. Controlled Fusion 49 B385
[28]	Halpern F D, Ltjens H, Luciani J F 2011Phys. Plasmas 18 102501
[29]	Nagayama Y, Taylor G, Yamada M, Fredrickson E D, Janos A C, McGuire K M 1996Nucl. Fusion 36 521
[30]	Yamaguchi S, Igami H, Tanaka H, Maekawa T 2004Plasma Phys. Controlled Fusion 46 1163
[31]	Chen W, Ding X T, Liu Yi, Yuan G L, Zhang Y P, Dong Y B, Song X Y, Zhou J, Song X M, Deng W, Yang Q W, Ji X Q, Duan X R, Liu Y, the HL-2A Team 2009Nucl. Fusion 49 075022
[32]	Igochine V, Dumbrajs O, Zohm H, Flaws A, ASDEX Upgrade Team 2007Nucl. Fusion 47 23
[33]	Sun Y, Wan B, Hu L, Chen K, Shen B, Mao J 2009Plasma Phys. Controlled Fusion 51 065001
[34]	Chen W, Ding X T, Yu L M, Ji X Q, Shi Z B, Zhang Y P, Zhong W L, Yuan G L, Dong J Q, Yang Q W, Liu Yi, Yan L W, Zhou Y, Jiang M, Li W, Song X M, Chen S Y, Duan X R, the HL-2A Team 2013Nucl. Fusion 53 113010
[35]	Chen W, Ding X T, Liu Yi, Yang Q W, Ji X Q, Isobe1 M, Yuan G L, Zhang Y P, Zhou Y, Song X Y, Dong Y B, Li W, Zhou J, Lei G J, Cao J Y, Deng W, Song X M, Duan X R, HL-2A Team 2010Nucl. Fusion 50 084008
[36]	Sauter O, Westerhof E, Mayoral M L, Alper B, Belo P A, Buttery R J, Gondhalekar A, Hellsten T, Hender T C, Howell D F, Johnson T, Lamalle P, Mantsinen M J, Milani F, Nave M F F, Nguyen F, Pecquet A L, Pinches S D, Podda S, Rapp J 2002Phys. Rev. Lett. 88 105001
[37]	Nave M F F, Lazzaro E, Coelho R, Belo P, Borba D, Buttery R J, Nowak S, Serra F, EFDA-JET Contributors 2003Nucl. Fusion 43 179
[38]	Furth H P, Killeen J, Rosenbluth M N 1963Phys. Fluids 6 459
[39]	Wang Z X, Wei L, Wang X 2012Phys. Plasmas 19 062108
[40]	Wei L, Wang Z X 2013Phys. Plasmas 20 012512
[41]	Fan D M, Wei L, Wang Z X, Zheng S, Duan P 2014Phys. Plasmas 21 092515
[42]	Bierwage A, Benkadda S, Hamaguchi S, Wakatani M 2005Phys. Plasmas 12 082504
[43]	Bierwage A, Yu Q, Gnter S 2007Phys. Plasmas 14 010704
[44]	Bell R E, Levinton F M, Batha S H, Synakowski E J, Zarnstorff M C 1998Phys. Rev. Lett. 81 1429

[1]	Ji Meng, You Yun-Xiang, Han Pan-Pan, Qiu Xiao-Ping, Ma Qiao, Wu Kai-Jian. A wall-modeled hybrid RANS/LES model for flow around circular cylinder with coherent structures in subcritical Reynolds number regions. Acta Physica Sinica, 2024, 73(5): 054701. doi: 10.7498/aps.73.20231745
[2]	Liu Tai-Qi, Chen Shao-Yong, Mou Mao-Lin, Tang Chang-Jian. Theoretical study of effect of hyper-resistivity on linear stability of ballooning mode. Acta Physica Sinica, 2023, 72(14): 145201. doi: 10.7498/aps.72.20230308
[3]	Sun Wei, Lü Chong, Lei Zhu, Zhong Jia-Yong. Numerical study of effect of magnetic field on laser-driven Rayleigh-Taylor instability. Acta Physica Sinica, 2022, 71(15): 154701. doi: 10.7498/aps.71.20220362
[4]	Cao Yi-Gang, Fu Meng-Meng, Yang Xi-Chang, Li Deng-Feng, Wang Xiao-Xia. Effect of thermal conduction on Kelvin-Helmholtz instability in straight pipe with different cross-sections. Acta Physica Sinica, 2022, 71(9): 094701. doi: 10.7498/aps.71.20211155
[5]	Shi Qi-Chen, Zhao Zhi-Jie, Zhang Huan-Hao, Chen Zhi-Hua, Zheng Chun. Mechanism of suppressing Kelvin-Helmholtz instability by flowing magnetic field. Acta Physica Sinica, 2021, 70(15): 154702. doi: 10.7498/aps.70.20202024
[6]	Sun Wei, An Wei-Ming, Zhong Jia-Yong. Two-dimensional numerical study of effect of magnetic field on laser-driven Kelvin-Helmholtz instability. Acta Physica Sinica, 2020, 69(24): 244701. doi: 10.7498/aps.69.20201167
[7]	Liu Ying, Chen Zhi-Hua, Zheng Chun. Kelvin-Helmholtz instability in anisotropic viscous magnetized fluid. Acta Physica Sinica, 2019, 68(3): 035201. doi: 10.7498/aps.68.20181747
[8]	Zheng Shu, Zhang Jia-Peng, Duan Ping, Wei Lai, Wang Xian-Qu. Numerical study of double tearing mode instability in viscous plasma. Acta Physica Sinica, 2013, 62(2): 025205. doi: 10.7498/aps.62.025205
[9]	Wang Li-Feng, Ye Wen-Hua, Fan Zheng-Feng, Li Ying-Jun. Study on the Kelvin-Helmholtz instability in two-dimensional incompressible fluid. Acta Physica Sinica, 2009, 58(7): 4787-4792. doi: 10.7498/aps.58.4787
[10]	Wang Li-Feng, Teng Ai-Ping, Ye Wen-Hua, Fan Zheng-Feng, Tao Ye-Sheng, Lin Chuan-Dong, Li Ying-Jun. Velocity gradient in Kelvin-Helmholtz instability for supersonic fluid. Acta Physica Sinica, 2009, 58(12): 8426-8431. doi: 10.7498/aps.58.8426
[11]	Wang Li-Feng, Ye Wen-Hua, Fan Zheng-Feng, Sun Yan-Qian, Zheng Bing-Song, Li Ying-Jun. Kelvin-Helmholtz instability in compressible fluids. Acta Physica Sinica, 2009, 58(9): 6381-6386. doi: 10.7498/aps.58.6381
[12]	Wang Li-Feng, Ye Wen-Hua, Li Ying-Jun. Second harmonic generation by the Kelvin-Helmholtz instability for two-dimensional incompressible fluid. Acta Physica Sinica, 2008, 57(5): 3038-3043. doi: 10.7498/aps.57.3038
[13]	Pang Jing, Chen Xiao-Gang, Song Jin-Bao. Second-order Stokes wave solutions for intefacial waves in three-layer stratified fluid with background current. Acta Physica Sinica, 2007, 56(8): 4733-4741. doi: 10.7498/aps.56.4733
[14]	Wei Xin-Hua, Zhou Guo-Cheng, Cao Jin-Bin, Li Liu-Yuan. Low-frequency electromagnetic instabilities in a collisionless current sheet:magnetohydrodynamic model. Acta Physica Sinica, 2005, 54(7): 3228-3235. doi: 10.7498/aps.54.3228
[15]	LI WEN-FEI, ZHANG FENG-SHOU. CHEMICAL INSTABILITY AND MECHANICAL INSTABILITY IN ASYMMETRIC NUCLEAR MATTER. Acta Physica Sinica, 2001, 50(10): 1888-1895. doi: 10.7498/aps.50.1888
[16]	HUANG CHAO-SONG, LI JUN. MODE COUPLING OF INTERCHANGE INSTABILITY IN PLASMAS. Acta Physica Sinica, 1992, 41(5): 783-791. doi: 10.7498/aps.41.783
[17]	BIAN BO-DA, LIN JING, GUO SHI-CHONG, CAI SHI-DONG. WHISTLER INSTABILITY WITH WEAKLY RELATIVISTIC TRAPPED ELECTRONS. Acta Physica Sinica, 1990, 39(2): 218-224. doi: 10.7498/aps.39.218
[18]	WU HAN-MING, PAN LIANG-RU. APPROXIMATE CALCULATION OF THE TILTING MODE INSTABILITY IN AN ELLIPTICAL SPHEROMAK BY VARIATIONAL METHOD. Acta Physica Sinica, 1984, 33(8): 1100-1111. doi: 10.7498/aps.33.1100
[19]	ZHOU YU-MEI, CAI SHI-DONG. PARAMETRIC INSTABILITIES WITH WELL SEPARATED FREQUENCIES IN MAGNETIZED PLASMA. Acta Physica Sinica, 1980, 29(7): 916-926. doi: 10.7498/aps.29.916
[20]	XIA MENG-FEN, ZHOU RU-LING. INSTABILITIES DUE TO RUNAWAY ELECTRONS. Acta Physica Sinica, 1980, 29(6): 788-793. doi: 10.7498/aps.29.788

Catalog

Vol. 65, Issue 22 - 2016-11-20

Metrics

Abstract views: 5996
PDF Downloads: 157
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