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Numerical study of double tearing mode instability in viscous plasma

Zheng Shu Zhang Jia-Peng Duan Ping Wei Lai Wang Xian-Qu

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Numerical study of double tearing mode instability in viscous plasma

Zheng Shu, Zhang Jia-Peng, Duan Ping, Wei Lai, Wang Xian-Qu
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  • 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.
    • 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).
    [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

  • [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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Publishing process
  • Received Date:  24 June 2012
  • Accepted Date:  20 August 2012
  • Published Online:  05 January 2013

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