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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.
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Keywords:
- reversed magnetic shear /
- double tearing mode /
- plasma resistivity /
- plasma viscosity
[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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[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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