黏滞等离子体中双撕裂模不稳定性的数值模拟研究

郑殊; 张甲鹏; 段萍; 魏来; 王先驱

doi:10.7498/aps.62.025205

摘要

本文采用磁流体力学模型, 数值研究了平板位形下双撕裂模线性增长率关于等离子体电阻η和黏滞ν的定标关系. 结果表明, 对于有理面间距较大的情况, 线性增长率关于电阻和黏滞的指数定标率随着黏滞的增加逐渐由γ∝η3/5ν0的定标变化到 γ∝η5/6ν-1/6的定标; 而对于有理面间距较小的情况, 其指数定标率随着黏性的增加从γ∝η1/3ν0的定标逐渐变化到γ∝η2/3ν-1/3 的定标. 本文还给出了初始阶段对称的双撕裂模的非线性演化, 发现在非线性阶段对称的双撕裂模将转化为反对称的双撕裂模, 并解释了相应的物理机理.

关键词:

Abstract

The scalings of double tearing mode (DTM) with various values of resistivity and viscosity have been investigated numerically by using a magneto hydrodynamic model in slab geometry. It is found that the growth rate changes from γ∝η3/5ν0 to γ∝η5/6ν-1/6 when the distance between two rational surfaces 2xs is sufficiently large. On the other hand, when the distance between two rational surfaces 2xs is very small, the scaling of γ and η and ν changes from γ∝η1/3ν0 to γ∝η2/3ν-1/3 as the viscosity increases. Moreover, the nonlinear evolution of symmetrical DTM is investigated in this paper. The study shows that the symmetrical DTM transforms to unsymmetrical DTM in the final phase.

Keywords:

作者及机构信息

1.
大连理工大学物理与光电工程学院, 大连 116024;

2.
大连海事大学物理系, 大连 116026

基金项目: 国家自然科学基金(批准号: 10975026, 11275034)、国家重点基础研究发展计划(973计划, ITER专项)(批准号: 2009GB105004, 2010GB106002, 2011GB107000)、中央高校基本科研业务费专项资金(批准号: DUT12ZD201)和辽宁省科技计划重点项目(批准号: 2011224007)资助的课题.

Authors and contacts

1.
School of Physics and Optoelectronic technology, Dalian University of Technology, Dalian 116024, China;

2.
Department of Physics, Dalian Maritime University, Dalian 116026, China

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 10975026, 11275034), the National Basic Research Program of China (Grant Nos. 2009GB105004, 2010GB106002, 2011GB107000), the Fundamental Research Funds for the Central Universities of Ministry of Education of China (Grant No. DUT12ZD201), and the Liaoning Province Science and Technology Key Project (Grant No. 2011224007).

参考文献

[1]	Furth H P, Killeen J, Rosenbluth M N 1963 Phys. Fluids 6 459
[2]	Rosenbluth M N, Dagazian R Y, Rutherford P H 1973 Phys. Fluids 16 1894
[3]	Ofman L, Chen X L, Morrison P J, Steinolfson R S 1991 Phys. Fluids B 3 1364
[4]	Chen X L, Morrison P J 1990 Phys. Fluids B 2 2575
[5]	Drake J F, Antonsen T M, Hassam A B 1983 Phys. Fluids 26 2509
[6]	Dobrowolny M, Veltri P, Mangeney A 1983 J. Plasma Phys. 29 393
[7]	Porcelli F 1987 Phys. Fluids 30 1734
[8]	Einaudi G, Rubini F 1986 Phys. Fluids 29 2563
[9]	Einaudi G, Rubini F 1989 Phys. Fluids B 1 2224
[10]	Shen C, Liu Z X 1996 Phys. Plasmas 3 4301
[11]	Pritchett P L, Lee Y C, Drake J F 1980 Phys. Fluids 23 1368
[12]	Dong J Q 1984 Acta Phys. Sin. 33 1341 (in Chinese) [董家齐 1984 33 1341]
[13]	Dong J Q, Mahajan S M, Horton W 2003 Phys. Plasmas 10 3151
[14]	Dong J Q, Mou Z Z, Long Y X, Mahajan S M 2004 Phys. Plasmas 11 5673
[15]	He Z X, Dong J Q, Long Y X, Mou Z Z, Gao Z, He H D, Liu F, Shen Y 2010 Phys. Plasmas 17 112102
[16]	He Z X, Dong J Q, He H D, Long Y X, Mou Z Z, Gao Z 2010 Phys. Scr. 82 065507
[17]	Wang Z X, Wang X G, Dong J Q, Lei Y A, Long Y X, Mou Z Z, Qu W X 2007 Phys. Rev. Lett. 99 185004
[18]	Wang Z X, Wang X G, Dong J Q, Kishimoto Y, Li J Q 2008 Phys. Plasmas 15 082109
[19]	Wang X Q, Wang X G, Xu W B, Wang Z X 2011 Phys. Plasmas 18 012102
[20]	Wei L, Wang Z X, Fan D M, Wang F, Liu Y 2011 Phys. Plasmas 18 042503
[21]	Wang Z X, Wei L, Wang X G, Zheng S, Liu Y 2011 Nucl. Fusion 51 033003
[22]	Wang X Q, Wang Z X, Wei L, Xu W B 2012 Phys. Lett. A 376 505
[23]	Zhang C L, Ma Z W, Dong J Q 2008 Plasma Sci. Technol. 10 407
[24]	Zhang C L, Ma Z W 2009 Phys. Plasmas 16 122113
[25]	Wang Z X, Wei L, Wang X G, Liu Y 2011 Phys. Plasmas 18 050701
[26]	Wei L, Wang Z X 2011 Nucl. Fusion 51 123005
[27]	Wang Z X, Li J Q, Dong J Q, Kishimoto Y 2009 Phys. Rev. Lett. 103 015004
[28]	Wang Z X, Li J Q, Kishimoto Y, Dong J Q 2009 Phys. Plasmas 16 060703
[29]	Wang Z X, Li J Q, Dong J Q, Kishimoto Y 2011 Phys. Plasmas 18 012110
[30]	Otto A, Birk G T 1992 Phys. Fluids B 4 3811
[31]	Yan M, Otto A, Muzzell D, Lee L C 1994 J. Geophys. Res. 99 8657
[32]	Shen C, Liu Z X 1998 Plasma Phys. and Control. Fusion 40 1
[33]	Shen C, Liu Z X 1998 Phys. Plasmas 5 2466
[34]	Strauss H R 1976 Phys. Fluids 19 134
[35]	Chang Z, Park W, Fredrickson E D, Batha S H, Bell M G, Bell R, Budny R V, Bush C E, Janos A, Levinton F M, McGuire K M, Park H, Sabbagh S A, Schmidt G L, Scott S D, Synakowski E J, Takahashi H, Taylor G, Zarnstorff M C 1996 Phys. Rev. Lett. 77 3553

施引文献

[1]	Furth H P, Killeen J, Rosenbluth M N 1963 Phys. Fluids 6 459
[2]	Rosenbluth M N, Dagazian R Y, Rutherford P H 1973 Phys. Fluids 16 1894
[3]	Ofman L, Chen X L, Morrison P J, Steinolfson R S 1991 Phys. Fluids B 3 1364
[4]	Chen X L, Morrison P J 1990 Phys. Fluids B 2 2575
[5]	Drake J F, Antonsen T M, Hassam A B 1983 Phys. Fluids 26 2509
[6]	Dobrowolny M, Veltri P, Mangeney A 1983 J. Plasma Phys. 29 393
[7]	Porcelli F 1987 Phys. Fluids 30 1734
[8]	Einaudi G, Rubini F 1986 Phys. Fluids 29 2563
[9]	Einaudi G, Rubini F 1989 Phys. Fluids B 1 2224
[10]	Shen C, Liu Z X 1996 Phys. Plasmas 3 4301
[11]	Pritchett P L, Lee Y C, Drake J F 1980 Phys. Fluids 23 1368
[12]	Dong J Q 1984 Acta Phys. Sin. 33 1341 (in Chinese) [董家齐 1984 33 1341]
[13]	Dong J Q, Mahajan S M, Horton W 2003 Phys. Plasmas 10 3151
[14]	Dong J Q, Mou Z Z, Long Y X, Mahajan S M 2004 Phys. Plasmas 11 5673
[15]	He Z X, Dong J Q, Long Y X, Mou Z Z, Gao Z, He H D, Liu F, Shen Y 2010 Phys. Plasmas 17 112102
[16]	He Z X, Dong J Q, He H D, Long Y X, Mou Z Z, Gao Z 2010 Phys. Scr. 82 065507
[17]	Wang Z X, Wang X G, Dong J Q, Lei Y A, Long Y X, Mou Z Z, Qu W X 2007 Phys. Rev. Lett. 99 185004
[18]	Wang Z X, Wang X G, Dong J Q, Kishimoto Y, Li J Q 2008 Phys. Plasmas 15 082109
[19]	Wang X Q, Wang X G, Xu W B, Wang Z X 2011 Phys. Plasmas 18 012102
[20]	Wei L, Wang Z X, Fan D M, Wang F, Liu Y 2011 Phys. Plasmas 18 042503
[21]	Wang Z X, Wei L, Wang X G, Zheng S, Liu Y 2011 Nucl. Fusion 51 033003
[22]	Wang X Q, Wang Z X, Wei L, Xu W B 2012 Phys. Lett. A 376 505
[23]	Zhang C L, Ma Z W, Dong J Q 2008 Plasma Sci. Technol. 10 407
[24]	Zhang C L, Ma Z W 2009 Phys. Plasmas 16 122113
[25]	Wang Z X, Wei L, Wang X G, Liu Y 2011 Phys. Plasmas 18 050701
[26]	Wei L, Wang Z X 2011 Nucl. Fusion 51 123005
[27]	Wang Z X, Li J Q, Dong J Q, Kishimoto Y 2009 Phys. Rev. Lett. 103 015004
[28]	Wang Z X, Li J Q, Kishimoto Y, Dong J Q 2009 Phys. Plasmas 16 060703
[29]	Wang Z X, Li J Q, Dong J Q, Kishimoto Y 2011 Phys. Plasmas 18 012110
[30]	Otto A, Birk G T 1992 Phys. Fluids B 4 3811
[31]	Yan M, Otto A, Muzzell D, Lee L C 1994 J. Geophys. Res. 99 8657
[32]	Shen C, Liu Z X 1998 Plasma Phys. and Control. Fusion 40 1
[33]	Shen C, Liu Z X 1998 Phys. Plasmas 5 2466
[34]	Strauss H R 1976 Phys. Fluids 19 134
[35]	Chang Z, Park W, Fredrickson E D, Batha S H, Bell M G, Bell R, Budny R V, Bush C E, Janos A, Levinton F M, McGuire K M, Park H, Sabbagh S A, Schmidt G L, Scott S D, Synakowski E J, Takahashi H, Taylor G, Zarnstorff M C 1996 Phys. Rev. Lett. 77 3553

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