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Exact equilibria for nonlinear force-free magnetic fields with its applications to astrophysics and fusion plasmas

Published online by Cambridge University Press:  15 January 2014

S. M. Moawad
S. M. Moawad*
Affiliation:
Department of Mathematics, Faculty of Science, Beni-Suef University, Beni-Suef, Egypt
*
†Email address for correspondence: [email protected]
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Abstract

Knowledge of the structure of coronal magnetic field originating from the photosphere is relevant to the understanding of many solar activity phenomena, e.g. flares, solar prominences, coronal loops, and coronal heating. In most of the existing literature, these loop-like magnetic structures are modeled as force-free magnetic fields (FFMF) without any plasma flow. In this paper, we present several exact solution classes for nonlinear FFMF, in both translational and axisymmetric geometries. The solutions are considered for their possible relevance to astrophysics and solar physics problems. These are used to illustrate arcade-type magnetic field structures of the photosphere and twisted magnetic flux ropes through the coronal mass ejections (CMEs), as well as magnetic confinement fusion plasmas.

Type
Papers
Information
Journal of Plasma Physics , Volume 80 , Issue 2 , April 2014 , pp. 173 - 195
Copyright
Copyright © Cambridge University Press 2014 

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References

REFERENCES

Alissandrakis, C. E. 1981 Astron. Astrophys. 100, 197.Google Scholar
Aly, J. J. 1985 Astron. Astrophys. 143, 19.Google Scholar
Bai-Song, X. 2006 Commun. Theor. Phys. 46, 735.Google Scholar
Bai-Song, X., Xin-Tao, Y. and Xia, L. 2006 Phys. Scr. 73, 655.Google Scholar
Bellan, P. M. and Hansen, J. F. 1998 Phys. Plasmas 5, 1991.Google Scholar
Biskamp, D. 1997 Nonlinear Magnetohydrodynamics. Cambridge, UK: Cambridge University Press.Google Scholar
Bogoyavlenskij, O. I. 2000 Phys. Rev. Lett. 84, 1914.CrossRefGoogle Scholar
Browning, P. K. 1988 Phys. Rep. 169, 329.CrossRefGoogle Scholar
Browning, P. K. and Priest, E. R. 1986 Astron. Astrophys. 159, 129.Google Scholar
Cargill, P. J. 2009 Space Sci. Rev. 144, 413.Google Scholar
Chandrasekhar, S. and Kendall, P. C. 1957 Astrophys. J. 126, 457.Google Scholar
Chiu, Y. T. and Hilton, H. H. 1977 Astrophys. J. 212, 873.CrossRefGoogle Scholar
Chou, Y. P. and Charbonneau, P. 1996 Solar Phys. 166, 333.Google Scholar
Cuperman, S. and Ditkowski, A. 1991 Astron. Astrophys. 241, 646.Google Scholar
Feynman, J. and Martin, S. F. 1995 J. Geophys. Res. 100, 3355.Google Scholar
Freidberg, J. P. 1982 Rev. Mod. Phys. 54, 801.Google Scholar
Freidberg, J. P. 1987 Ideal Magnetohydrodynamics. New York, NY: Plenum.Google Scholar
Gary, G. A. 1989 Astrophys. J. Suppl. Ser. 69, 323.Google Scholar
Gonzalez-Gascon, F. and Peralta-Salas, D. 2001 Phys. Lett. A 292, 75.Google Scholar
Guo, H. Y., Hoffman, A. L., Miller, K. E. and Steinhauer, L. C. 2004 Phys. Rev. Lett. 92, 245001.Google Scholar
Guo, H. Y., Hoffman, A. L., Steinhauer, L. C. and Miller, K. E. 2005 Phys. Rev. Lett. 95, 175001.CrossRefGoogle Scholar
He, J. H. and Abdou, M. A. 2007 Chaos Soliton. Fract. 34, 1421.Google Scholar
He, J. H. and Wu, X. H. 2006 Chaos Soliton. Fract. 30, 700.Google Scholar
Heyvaerts, J. and Priest, E. R. 1984 Astron. Astrophys. 137, 63.Google Scholar
Hu, Y. Q. 1995 Astrophys. J. 454, 480.Google Scholar
Low, B. C. 1975 Astrophys. J. 197, 251.Google Scholar
Low, B. C. 1977 Astrophys. J. 212, 234.Google Scholar
Low, B. C. 1980 Astrophys. J. 239, 377.Google Scholar
Low, B. C. 1981 Astrophys. J. 251, 352.Google Scholar
Low, B. C. 1993 Astrophys. J. 409, 798.Google Scholar
Low, B. C. and Nakagawa, Y. 1975 Astrophys. J. 199, 237.Google Scholar
Lynden-Bell, D. 1996 Mon. Not. R. Astron. Soc. 279, 389.Google Scholar
Macleod, M. A. 1995 J. Math. Phys. 36, 2951.CrossRefGoogle Scholar
Martynov, A. A. and Medvedev, S. Y. 2002 Plasma Phys. Rep. 28, 259.Google Scholar
Mogilevskii, E. I., Obridko, V. N. and Shilova, N. S. 2005 Astron. Astrophy. Trans. 24, 25.Google Scholar
Nakagawa, Y. and Raadu, M. A. 1972 Solar Phys. 25, 127.CrossRefGoogle Scholar
Nakagawa, Y., Raadu, M. A., Billings, D. E. and Harvey, J. W. 1973 Solar Phys. 30, 421.Google Scholar
Nakagawa, Y., Raadu, M. A., Billings, D. E. and McNamara, D. 1971 Solar Phys. 19, 72.Google Scholar
Poletto, G., Vaiana, G. S., Zomback, M. V., Krieger, A. S. and Timothy, A. F. 1975 Solar Phys. 44, 83.Google Scholar
Porter, L. J., Klimchuk, J. A. and Sturrock, P. A. 1992 Astrophys. J. 385, 738.Google Scholar
Priest, E. R. and Forbes, T. 1999 Magnetic Reconnection: MHD Theory and Applications. Cambridge, UK: Cambridge University Press.Google Scholar
Romashets, E. P. and Vandas, M. 2009 Astron. Astrophys. 499, 17.CrossRefGoogle Scholar
Sakurai, T. 1989 Space Sci. Rev. 51, 11.Google Scholar
Seehafer, N. 1978 Solar Phys. 58, 215.Google Scholar
Semel, M. 1988 Astron. Astrophys. 198, 293.Google Scholar
Steinhauer, L. C. and Ishida, A. 1997 Phys. Rev. Lett. 79, 3423.Google Scholar
Svestka, Z. 1976 Solar Flares. Dordrecht, Netherlands: D. Reidel, 300 pp.Google Scholar
Tang, X. Z. and Boozer, A. H. 2005 Phys. Rev. Lett. 94, 225004.Google Scholar
Taylor, J. B. 1974 Phys. Rev. Lett. 33, 1139.Google Scholar
Vaiana, G. S., Krieger, A. S. and Timothy, A. F. 1973 Solar Phys. 32, 81.Google Scholar
Vandas, M. and Romashets, E. P. 2003 Astron. Astrophys. 398, 801.Google Scholar
Vaiana, G. S. and Rosner, R. 1978 Ann. Rev. Astron. Astrophys. 16, 393.Google Scholar
Wheatland, M. S. 1999 Astrophys. J. 518, 948.CrossRefGoogle Scholar
Wiegelmann, T. and Neukirch, T. 2003 Nonlinear Proc. Geophys. 10, 313.Google Scholar
Yoshida, Z. and Mahajan, S. M. 2002 Phys. Rev. Lett. 88, 095001.Google Scholar
Zaghloul, H. and Barajas, O. 1990 Am. J. Phys. 58, 783.Google Scholar
Zaqarashvili, T. V., Kukhianidze, V. and Khodachenko, M. S. 2010a Month. Not. R. Astron. S. 404, L74.Google Scholar
Zaqarashvili, T. V., Murawski, K., Khodachenko, M. L., Kukhianidze, V. and Rucker, H. O. 2010b Proc. of the 7th International Workshop on Planetary, Solar and Heliospheric Radio Emissions (PRE VII), Graz, Austria, September 15–17, 2010. Vienna, Austria: Austrian Academy of Sciences Press, pp. 465–470.Google Scholar
Zirin, H. 1988 Astrophysics of the Sun. Cambridge, UK: Cambridge University Press.Google Scholar