Hostname: page-component-76fb5796d-vvkck Total loading time: 0 Render date: 2024-04-28T10:46:05.842Z Has data issue: false hasContentIssue false
  • English
  • Français

Numerical study of collisionless q = 1 double tearing instability in a cylindrical plasma

Published online by Cambridge University Press:  03 July 2012

LAI WEI ,
XUEFENG YANG ,
SHU ZHENG  and
YUE LIU
LAI WEI
Affiliation:
Key Laboratory of Materials Modification by Beams of the Ministry of Education, School of Physics and Optoelectronic Technology, Dalian University of Technology, Dalian 116024, China (zhengshu@dlut.edu.cn)
XUEFENG YANG
Affiliation:
School of Mathematical Science, Dalian University of Technology, Dalian 116024, China
SHU ZHENG
Affiliation:
Key Laboratory of Materials Modification by Beams of the Ministry of Education, School of Physics and Optoelectronic Technology, Dalian University of Technology, Dalian 116024, China (zhengshu@dlut.edu.cn)
YUE LIU
Affiliation:
Key Laboratory of Materials Modification by Beams of the Ministry of Education, School of Physics and Optoelectronic Technology, Dalian University of Technology, Dalian 116024, China (zhengshu@dlut.edu.cn)
Get access Rights & Permissions [Opens in a new window]

Abstract

The double tearing mode (DTM) instability with two qs = 1 rational surfaces is investigated by taking into account the collisionless effects, including electron inertia and electron viscosity in a cylindrical geometry. The calculations show that for q-profile with a small distance between two rational surfaces, Δrs, there exists a broad linear spectrum of collisionless DTMs. The collisionless effects not only can significantly increase the linear growth rate of DTMs but can also enlarge the width of spectrum of unstable modes. For the q-profile with fixed Δrs and fixed magnetic shears at two rational surfaces, the high-order harmonics with smaller wavelength, such as the m/n = 2/2, 3/3 and 4/4 modes, can be easily excited to have larger growth rates than the m/n = 1/1 mode by ‘lifting’ the safety factor value between two rational surfaces. The characteristics of eigenmode structures of the most unstable and secondly unstable DTMs with various mode numbers are analyzed in detail and the corresponding collisionless scalings are numerically obtained and verified theoretically based on the previous relevant analytical theories. In addition, the synergetic effects of plasma resistivity, electron inertia and electron viscosity on the linear growth rates of DTMs are analyzed.

Type
Papers
Information
Journal of Plasma Physics , Volume 78 , Issue 6 , December 2012 , pp. 663 - 672
Copyright
Copyright © Cambridge University Press 2012

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Aydemir, A. Y. 1990 Phys. Fluids B 2, 2135.CrossRefGoogle Scholar
Aydemir, A. Y. 1992 Phys. Fluids B 4, 3469.CrossRefGoogle Scholar
Basu, B. and Coppi, B. 1981 Phys. Fluids 24, 465.CrossRefGoogle Scholar
Bhattacharjee, A., Germaschewski, K. and Ng, C. S. 2005 Phys. Plasmas 12, 042305.CrossRefGoogle Scholar
Bierwage, A., Benkadda, S., Hamaguchi, S. and Wakatani, M. 2005 Phys. Plasmas 12, 082504.CrossRefGoogle Scholar
Bierwage, A., Hamaguchi, S., Wakatani, M.Benkadda, S. and Leoncini, X. 2005 Phys. Rev. Lett. 94, 065001.CrossRefGoogle Scholar
Bierwage, A. and Yu, Q. 2007 Plasma Phys. Control. Fusion 49, 675.CrossRefGoogle Scholar
Bierwage, A., Yu, Q. and Günter, S. 2007 Phys. Plasmas 14, 010704.CrossRefGoogle Scholar
Birn, J., Drake, J. F., Shay, M. A., Rogers, B. N., Denton, R. E., Hesse, M., Kuznetsova, M., Ma, Z. W., Bhattacharjee, A., Otto, A.et al. 2001 J. Geophys. Res. 106, 3751.Google Scholar
Biskamp, D. 1993 Nonlinear Magnetohydrodynamics. Cambridge, UK: Cambridge University Press.CrossRefGoogle Scholar
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.et al. 1996 Phys. Rev. Lett. 77, 3553.CrossRefGoogle Scholar
Chapman, I. T., Hua, M. D., Pinches, S. D., Akers, R. J., Field, A. R., Graves, J. P., Hastie, R. J., Michael, C. A. and the MAST Team 2010 Nucl. Fusion 50, 045007.CrossRefGoogle Scholar
Charlton, L. A., Carreras, B. A., Holmes, J. A. and Lynch, V. E. 1988 Phys. Fluids 31, 347.CrossRefGoogle Scholar
Charlton, L. A., Hastie, R. J. and Hender, T. C. 1989 Phys. Fluids B 1, 798.CrossRefGoogle Scholar
Chen, X. L. and Morrison, P. J. 1990 Phys. Fluids B 2, 495.CrossRefGoogle Scholar
Coppi, B. 1964 Phys. Lett. 11, 226.CrossRefGoogle Scholar
Coppi, B., Mark, J. W.-K., Sugiyama, L. and Bertin, G. 1979 Phys. Rev. Lett. 42, 1058.CrossRefGoogle Scholar
Dong, J. Q., Mahajan, S. M. and Horton, W. 2003 Phys. Plasmas 10, 3151.CrossRefGoogle Scholar
Dong, J. Q., Mou, Z. Z., Long, Y. X. and Mahajan, S. M. 2004 Phys. Plasmas 11, 5673.CrossRefGoogle Scholar
Fredrickson, E., Bell, M., Budny, R. V. and Synakowski, E. 2000 Phys. Plasmas 7, 4112.CrossRefGoogle Scholar
Fujita, T., Ide, S., Shirai, H., Kikuchi, M., Naito, O., Koide, Y., Takeji, S., Kubo, H. and Ishida, S. 1997 Phys. Rev. Lett. 78, 2377.CrossRefGoogle Scholar
Furth, H. P., Killeen, J. and Rosenbluth, M. N. 1963 Phys. Fluids 6, 459.CrossRefGoogle Scholar
Furth, H. P., Rutherford, P. H. and Selberg, H. 1973 Phys. Fluids 16, 1054.CrossRefGoogle Scholar
Ganesh, R. and Vaclavik, J. 2005 Phys. Rev. Lett. 94, 145002.CrossRefGoogle Scholar
Halpern, F. D., Lütjens, H. and Luciani, J.-F. 2011 Phys. Plasmas 18, 102501.CrossRefGoogle Scholar
Hastie, R. J., Hender, T. C., Carreras, B. A., Charlton, L. A. and Holmes, J. A. 1987 Phys. Fluids 30, 1756.CrossRefGoogle Scholar
Hazeltine, R. D., Kotschenreuther, M. and Morrison, P. J. 1985 Phys. Fluids 28, 2466.CrossRefGoogle Scholar
He, Z., Dong, J. Q., Long, Y. X., Mou, Z. Z., Gao, Z., He, H. D., Liu, F. and Shen, Y. 2010 Phys. Plasmas 17, 112102.CrossRefGoogle Scholar
Ishii, Y., Azumi, M. and Kishimoto, Y. 2002 Phys. Rev. Lett. 89, 205002.CrossRefGoogle Scholar
Ishii, Y., Azumi, M., Kurita, G. and Tuda, T. 2000 Phys. Plasmas 7, 4477.CrossRefGoogle Scholar
Ishii, Y., Smolyakov, A. I. and Takechi, M. 2009 Nucl. Fusion 49, 085006.CrossRefGoogle Scholar
Ishizawa, A., Sato, M. and Wakatani, M. 2003 Phys. Plasmas 10, 3017.CrossRefGoogle Scholar
Janvier, M., Kishimoto, Y. and Li, J. Q. 2011 Phys. Rev. Lett. 107, 195001.CrossRefGoogle Scholar
Kadomtsev, B. B. and Pogutse, O. P. 1967 Sov. Phys. JETP 24, 1172.Google Scholar
Kaw, P. K., Valeo, E. J. and Rutherford, P. H. 1979 Phys. Rev. Lett. 43, 1398.CrossRefGoogle Scholar
Kleva, R. G., Drake, J. F. and Waelbroeck, F. L. 1995 Phys. Plasmas 2, 23.CrossRefGoogle Scholar
Matsumoto, T., Naitou, H., Tokuda, S. and Kishimoto, Y. 2005, Nucl. Fusion 45, 1264.CrossRefGoogle Scholar
Matsumoto, T., Tokuda, S., Kishimoto, Y., Takizuka, T. and Naitou, H. 1999 J. Plasma Fusion Res. 75, 1188.CrossRefGoogle Scholar
Nave, M. F. F. and Wesson, J. 1988 Nucl. Fusion 28, 297.CrossRefGoogle Scholar
Ofman, L. 1992 Phys. Fluids B 4, 2751.CrossRefGoogle Scholar
Ofman, L., Chen, X. L., Morrison, P. J. and Steinolfson, R. S. 1991 Phys. Fluids B 3, 1364.CrossRefGoogle Scholar
Ottaviani, M. and Porcelli, F. 1993 Phys. Rev. Lett. 71, 3802.CrossRefGoogle Scholar
Ottaviani, M. and Porcelli, F. 1995 Phys. Plasmas 2, 4104.CrossRefGoogle Scholar
Papp, G., Pokol, G. I., Por, G., Magyarkuti, A., Lazányi, N., Horváth, L., Igochine, V., Maraschek, M. and ASDEX Upgrade Team 2011 Plasma Phys. Control. Fusion 53, 065007.CrossRefGoogle Scholar
Persson, M. 1991 Nucl. Fusion 31, 382.CrossRefGoogle Scholar
Persson, M. and Dewar, R. L. 1994 Phys. Plasmas 1, 1256.CrossRefGoogle Scholar
Porcelli, F. 1991 Phys. Rev. Lett. 66, 425.CrossRefGoogle Scholar
Pritchett, P. L., Lee, Y. C. and Drake, J. F. 1980 Phys. Fluids 23, 1368.CrossRefGoogle Scholar
Rosenbluth, M. N., Dagazian, R. Y. and Rutherford, P. H. 1973 Phys. Fluids 16, 1894.CrossRefGoogle Scholar
Rosenbluth, M. and Sloan, M. L. 1971 Phys. Fluids 14, 1725.CrossRefGoogle Scholar
Shen, C. and Liu, Z. X. 1998 Plasma Phys. Control. Fusion 40, 1.CrossRefGoogle Scholar
Strauss, H. R. 1976 Phys. Fluids 19, 134.CrossRefGoogle Scholar
Sun, Y., Wan, B., Hu, L., Chen, K., Shen, B. and Mao, J. 2009 Plasma Phys. Control. Fusion 51, 065001.CrossRefGoogle Scholar
Wang, X. and Bhattacharjee, A. 1993 Phys. Rev. Lett. 70, 1627.CrossRefGoogle Scholar
Wang, Z. X., Li, J., Dong, J. Q. and Kishimoto, Y. 2009 Phys. Rev. Lett. 103, 015004.CrossRefGoogle Scholar
Wang, Z. X., Li, J., Dong, J. Q. and Kishimoto, Y. 2011 Phys. Plasmas 18, 012110.CrossRefGoogle Scholar
Wang, Z. X., Li, J., Kishimoto, Y. and Dong, J. Q. 2009 Phys. Plasmas 16, 060703.CrossRefGoogle Scholar
Wang, Z. X., Wang, X. G., Dong, J. Q., Kishimoto, Y. and Li, J. Q. 2008 Phys. Plasmas 15, 082109.CrossRefGoogle Scholar
Wang, Z. X., Wang, X. G., Dong, J. Q., Lei, Y. A., Long, Y. X., Mou, Z. Z. and Qu, W. X. 2007 Phys. Rev. Lett. 99, 185004.CrossRefGoogle Scholar
Wang, Z. X., Wang, X. G., Dong, J. Q., Long, Y. X. and Mou, Z. Z. 2007 Plasma Science & Technology 9, 257.Google Scholar
Wang, X. Q., Wang, Z. X., Wei, L. and Xu, W. B. 2012 Phys. Lett. A 376, 505.CrossRefGoogle Scholar
Wang, X. Q., Wang, X., Xu, W. B. and Wang, Z. X. 2011a Phys. Plasmas, 18, 012102.CrossRefGoogle Scholar
Wang, Z. X., Wei, L., Wang, X. and Liu, Y. 2011b Phys. Plasmas 18, 050701.CrossRefGoogle Scholar
Wang, Z. X., Wei, L., Wang, X., Zheng, S. and Liu, Y. 2011c Nucl. Fusion 51, 033003.CrossRefGoogle Scholar
Wei, L. and Wang, Z. X. 2011 Nucl. Fusion 51, 123005.CrossRefGoogle Scholar
Wei, L., Wang, Z. X., Fan, D. M., Wang, F. and Liu, Y. 2011 Phys. Plasmas 18, 042503.CrossRefGoogle Scholar
Xu, X. Q., Dudson, B., Snyder, P. B., Umansky, M. V. and Wilson, H. 2010 Phys. Rev. Lett. 105, 175005.CrossRefGoogle Scholar
Yamada, M., Kulsrud, R. and Ji, H. 2010 Rev. Mod. Phys. 82, 603–664.CrossRefGoogle Scholar
Yu, Q. 1995 Nucl. Fusion 35, 1012.Google Scholar
Yu, Q. and Günter, S. 1999 Nucl. Fusion 39, 487.CrossRefGoogle Scholar
Yuh, H. Y.Kaye, S. M., Levinton, F. M., Mazzucato, E., Mikkelsen, D. R., Smith, D. R., Bell, R. E., Hosea, J. C., LeBlanc, B. P., Peterson, J. L.et al. 2011 Phys. Rev. Lett. 106, 055003.CrossRefGoogle Scholar
Zhang, C. L. and Ma, Z. W. 2009 Phys. Plasmas 16, 122113.Google Scholar
Zhao, X. M., Peng, X. D., Tang, C. J. and Qiu, X. M. 2011 Phys. Plasmas 18, 072506.CrossRefGoogle Scholar