旋转圆柱等离子体中撕裂模和Kelvin-Helmholtz不稳定性的激发特性

毕海亮; 魏来; 范冬梅; 郑殊; 王正汹

doi:10.7498/aps.65.225201

摘要

采用约化的磁流体力学模型，数值研究了柱位形等离子体中q剖面和极向旋转剖面对q=1撕裂模不稳定性和Kelvin-Helmholtz（K-H）不稳定性的影响.随着旋转强度的增加，m/n=1/1模被逐渐抑制，而高阶谐波模式（如m/n=2/2，m/n=3/3等）会经历四个区间：撕裂模失稳区间、撕裂模致稳区间、稳定窗口区间和K-H不稳定性激发区间.更进一步，我们发现，m/n=1/1模的增长率随旋转强度的改变与剪切层所处位置有关，并且剪切层分布在有理面内外的结果基本一致；然而高阶谐波模式却没有此类现象.另外，有理面处磁剪切越小，撕裂模越容易被剪切流抑制，并且越容易激发K-H不稳定性.

关键词:

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:

作者及机构信息

1.
大连理工大学, 三束材料改性教育部重点实验室, 物理与光电工程学院, 大连 116024;

2.
中国航天系统科学与工程研究院, 北京 100048

通信作者: 魏来, laiwei@dlut.edu.cn;zxwang@dlut.edu.cn ; 王正汹, laiwei@dlut.edu.cn;zxwang@dlut.edu.cn

基金项目: 国家自然科学基金（批准号：11322549，11275043，11305027）、大连市杰出人才基金（批准号：2015R001）和中央高校基本科研业务费专项资金（批准号：DUT14RC（3）157，DUT15YQ103）资助的课题.

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).

参考文献

[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

施引文献

[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]	季梦, 尤云祥, 韩盼盼, 邱小平, 马乔, 吴凯健. 亚临界区圆柱绕流相干结构壁面模化混合RANS/LES模型. , 2024, 73(5): 054701. doi: 10.7498/aps.73.20231745
[2]	刘泰齐, 陈少永, 牟茂淋, 唐昌建. 超电阻对气球模线性不稳定性影响的理论研究. , 2023, 72(14): 145201. doi: 10.7498/aps.72.20230308
[3]	孙伟, 吕冲, 雷柱, 仲佳勇. 磁场对激光驱动Rayleigh-Taylor不稳定性影响的数值研究. , 2022, 71(15): 154701. doi: 10.7498/aps.71.20220362
[4]	曹义刚, 付萌萌, 杨喜昶, 李登峰, 王晓霞. 热传导对横截面不同的直管道中Kelvin-Helmholtz不稳定性的影响. , 2022, 71(9): 094701. doi: 10.7498/aps.71.20211155
[5]	石启陈, 赵志杰, 张焕好, 陈志华, 郑纯. 流向磁场抑制Kelvin-Helmholtz不稳定性机理研究. , 2021, 70(15): 154702. doi: 10.7498/aps.70.20202024
[6]	孙伟, 安维明, 仲佳勇. 磁场对激光驱动Kelvin-Helmholtz不稳定性影响的二维数值研究. , 2020, 69(24): 244701. doi: 10.7498/aps.69.20201167
[7]	刘迎, 陈志华, 郑纯. 黏性各向异性磁流体Kelvin-Helmholtz不稳定性: 二维数值研究. , 2019, 68(3): 035201. doi: 10.7498/aps.68.20181747
[8]	郑殊, 张甲鹏, 段萍, 魏来, 王先驱. 黏滞等离子体中双撕裂模不稳定性的数值模拟研究. , 2013, 62(2): 025205. doi: 10.7498/aps.62.025205
[9]	王立锋, 叶文华, 范征锋, 李英骏. 二维不可压流体Kelvin-Helmholtz不稳定性的弱非线性研究. , 2009, 58(7): 4787-4792. doi: 10.7498/aps.58.4787
[10]	王立锋, 滕爱萍, 叶文华, 范征锋, 陶烨晟, 林传栋, 李英骏. 超声速流体Kelvin-Helmholtz不稳定性速度梯度效应研究. , 2009, 58(12): 8426-8431. doi: 10.7498/aps.58.8426
[11]	王立锋, 叶文华, 范征锋, 孙彦乾, 郑炳松, 李英骏. 二维可压缩流体Kelvin-Helmholtz不稳定性. , 2009, 58(9): 6381-6386. doi: 10.7498/aps.58.6381
[12]	王立锋, 叶文华, 李英骏. 二维不可压缩流体Kelvin-Helmholtz不稳定性的二次谐波产生. , 2008, 57(5): 3038-3043. doi: 10.7498/aps.57.3038
[13]	庞晶, 陈小刚, 宋金宝. 有流存在时三层流体界面波的二阶Stokes波解. , 2007, 56(8): 4733-4741. doi: 10.7498/aps.56.4733
[14]	魏新华, 周国成, 曹晋滨, 李柳元. 无碰撞电流片低频电磁模不稳定性：MHD模型. , 2005, 54(7): 3228-3235. doi: 10.7498/aps.54.3228
[15]	李文飞, 张丰收. 非对称核物质的化学不稳定性与力学不稳定性. , 2001, 50(10): 1888-1895. doi: 10.7498/aps.50.1888
[16]	黄朝松, 李钧. 等离子体交换不稳定性的模耦合理论. , 1992, 41(5): 783-791. doi: 10.7498/aps.41.783
[17]	卞伯达, 林景, 郭世宠, 蔡诗东. 弱相对论捕获电子哨声模不稳定性. , 1990, 39(2): 218-224. doi: 10.7498/aps.39.218
[18]	顾永年. 小环径比锐边界等离子体的扭曲模不稳定性. , 1984, 33(4): 554-560. doi: 10.7498/aps.33.554
[19]	周玉美, 蔡诗东. 磁化等离子体里高频模和低频模耦合的参量不稳定性. , 1980, 29(7): 916-926. doi: 10.7498/aps.29.916
[20]	夏蒙棼, 周如玲. 逃逸电子不稳定性. , 1980, 29(6): 788-793. doi: 10.7498/aps.29.788

计量

文章访问数: 5973
PDF下载量: 157
被引次数: 0

姓名
邮箱
手机号码
标题
留言内容
验证码

搜索

留言板