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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.
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关键词:
- q剖面 /
- 旋转剖面 /
- 撕裂模不稳定性 /
- Kelvin-Helmholtz不稳定性
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.[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
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[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
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[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
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