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Topological stability of finite-length magnetic flux tubes

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Abstract

It has been suggested that the activity of cosmical magnetic fields is a consequence of a general topological nonequilibrium in the neighbourhood of magnetostatic equilibria. Evidence for this suggestion can be obtained from the Kolmogorov-Arnold-Moser theorem of classical mechanics, applied to the magnetic field line flow as a Hamiltonian system. A finite-length magnetic flux tube, however, always possesses two independent sets of flux surfaces - or, equivalently, the corresponding Hamiltonian system two independent first integrals - and is topologically stable if in the volume occupied by the tube there are no singular (null) points of the magnetic field and the normal field component does not change its sign on the end faces of the tube. Therefore, the concept of nonequilibrium due to flux surface destruction is not applicable to solar atmospheric loops with each end situated in the interior of one polarity of the photospheric normal field component. Further, it seems unlikely that the tearing-mode mechanism can play a role in such loops.

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References

  • An, C.-H.: 1984, Astrophys. J. 281, 419.

    Google Scholar 

  • Arnold, V. I.: 1973, Ordinary Differential Equations, MIT, Cambridge, Massachusetts.

    Google Scholar 

  • Arnold, V. I.: 1978, Mathematical Methods of Classical Mechanics, Springer-Verlag, New York.

    Google Scholar 

  • Bateman, G.: 1978, MHD Instabilities, MIT, Cambridge, Massachusetts.

    Google Scholar 

  • Bernardin, M. P. and Tataronis, J. A.: 1985, J. Math. Phys. 26, 2370.

    Google Scholar 

  • Berry, M. V.: 1978, in S. Jorna (ed.), Topics in Nonlinear Dynamics. A Tribute to Sir Edward Bullard, American Institute of Physics, New York.

    Google Scholar 

  • Boozer, A. H.: 1984, Report PPPL-2094, Princeton University.

  • Cary, J. R.: 1982, Phys. Rev. Letters 49, 276.

    Google Scholar 

  • Cary, J. R. and Littlejohn, R. G.: 1983, Ann. Phys. N.Y. 151, 1.

    Google Scholar 

  • Chow, S.-N. and Hale, J. K.: 1982, Methods of Bifurcation Theory, Springer-Verlag, New York.

    Google Scholar 

  • Dagazian, R. Y.: 1976, Phys. Fluids 19, 169.

    Google Scholar 

  • Doveil, F.: 1984, J. Physique 45, 703.

    Google Scholar 

  • Einaudi, G. and Van Hoven, G.: 1983, Solar Phys. 88, 163.

    Google Scholar 

  • Filonenko, N. N., Sagdeev, R. Z., and Zaslavsky, G. M.: 1967, Nucl. Fusion 7, 253.

    Google Scholar 

  • Furth, H. P., Killeen, J., and Rosenbluth, M. N.: 1963, Phys. Fluids 6, 459.

    Google Scholar 

  • Gibons, M. and Spicer, D. S.: 1981, Solar Phys. 69, 57.

    Google Scholar 

  • Hénon, M.: 1966, Compt. Rend. Acad. Sci. Paris A262, 312.

    Google Scholar 

  • Hood, A. W. and Priest, E. R.: 1979, Solar Phys. 64, 303.

    Google Scholar 

  • Hood, A. W. and Priest, E. R.: 1980, Solar Phys. 66, 113.

    Google Scholar 

  • Kruskal, M. D. and Kulsrud, R. M.: 1958, Phys. Fluids 1, 265.

    Google Scholar 

  • Kubiček, M. and Marek, M.: 1983, Computational Methods in Bifurcation Theory and Dissipative Structures, Springer-Verlag, New York.

    Google Scholar 

  • Low, B. C: 1985a, Astrophys. J. 293, 31.

    Google Scholar 

  • Low, B. C: 1985b, Solar Phys. 100, 309.

    Google Scholar 

  • Migliuolo, S. and Cargill, P. J.: 1983, Astrophys. J. 271, 820.

    Google Scholar 

  • Mok, Y. and Van Hoven, G.: 1982, Phys. Fluids 25, 636.

    Google Scholar 

  • Parker, E. N: 1972, Astrophys. J. 174, 499.

    Google Scholar 

  • Parker, E. N.: 1979, Cosmical Magnetic Fields, Clarendon Press, Oxford, Chapter 14.

    Google Scholar 

  • Priest, E. R.: 1982, Solar Magnetohydrodynamics, D. Reidel Publ. Co., Dordrecht, Holland.

    Google Scholar 

  • Raadu, M. A.: 1972, Solar Phys. 22, 425.

    Google Scholar 

  • Roberts, K. V. and Taylor, J. B.: 1965, Phys. Fluids 8, 315.

    Google Scholar 

  • Roberts, P. H.: 1967, An Introduction to Magnetohydrodynamics, Longmans, London.

    Google Scholar 

  • Salat, A.: 1985, Z. Naturforsch. 40a, 959.

    Google Scholar 

  • Seehafer, N.: 1986, Astrophys. Space Sci. 122, 247.

    Google Scholar 

  • Spicer, D. S.: 1976, Report 8036, Naval Research Laboratory, Washington, D.C.

    Google Scholar 

  • Spicer, D. S.: 1977, Solar Phys. 53, 305.

    Google Scholar 

  • Thyagaraja, A. and Haas, F. A.: 1985, Phys. Fluids 28, 1005.

    Google Scholar 

  • Tsinganos, K. C., Distler, J., and Rosner, R.: 1984, Astrophys. J. 278, 409.

    Google Scholar 

  • Turner, L.: 1985, J. Math. Phys. 26, 991.

    Google Scholar 

  • Van Hoven, G.: 1979, Astrophys. J. 232, 572.

    Google Scholar 

  • Van Hoven, G.: 1981, in E. R. Priest (ed.), Solar Flare Magnetohydrodynamics, Gordon and Breach, New York, p. 217.

    Google Scholar 

  • White, R. B.: 1983, in A. A. Galeev and R. N. Sudan (eds.), Basic Plasma Physics I, Volume I of Handbook of Plasma Physics, North-Holland, Amsterdam, p. 611.

    Google Scholar 

  • Whiteman, K. J.: 1977, Rep. Progr. Phys. 40, 1033.

    Google Scholar 

  • Yu, G.: 1973, Astrophys. J. 181, 1003.

    Google Scholar 

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  1. Zentralinstitut für Astrophysik, Telegrafenberg, 1500, Potsdam, G.D.R.

    N. Seehafer

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  1. N. Seehafer
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Seehafer, N. Topological stability of finite-length magnetic flux tubes. Sol Phys 107, 73–81 (1986). https://doi.org/10.1007/BF00155343

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  • DOI: https://doi.org/10.1007/BF00155343

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