Abstract
The stability of coronal magnetic loops is investigated with the influence of the dense photosphere (line-tying) included. The stability method, based on the Finite Fourier Series method developed by Einaudi and Van Hoven (1981, 1983), is applied to two different equilibria and the approximate critical conditions for the onset of different azimuthal instabilities are investigated. It is shown that, for nearly force-free loops, the extended Suydam criterion, obtained by De Bruyne and Hood (1989) for localized modes, predicts the existence of a global kink instability when a localized mode is just destabilized. For loops with substantial gas pressure gradients it is the localized modes that are destabilized first of all and the extended Suydam criterion gives the necessary and sufficient conditions for an instability. In this latter case, the instability threshold for the kink mode is quite close to the localized mode threshold. Finally, it is shown that the growth times of the instabilities are comparable to the Aflvén travel times along the loop when the extended Suydam criterion is violated.
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References
Anzer, U.: 1968, Solar Phys. 3, 298.
Bateman, G.: 1978, MHD Instabilities, MIT Press, Cambridge, Massachusetts.
Cargill, P. J., Hood, A. W., and Migliuolo, S.: 1986, Astrophys. J. 309, 402.
Chiuderi, C. and Einaudi, G.: 1981, Solar Phys. 73, 89.
Chiuderi, C., Einaudi, G., Ma, S. S., and Van Hoven, G.: 1980, J. Plasma Phys. 24, 39.
Craig, I. J. D., McClymont, A. N., and Sneyd, A. D.: 1988, Astrophys. J. 335, 441.
De Bruyne, P. and Hood, A. W.: 1989, Solar Phys. 119, 87.
Dewar, R. L., Manickam, J., Grimm, R. C., and Chance, M. S.: 1981, Nuclear Fusion 21, 493.
Einaudi, G. and Van Hoven, G.: 1981, Phys. Fluids 24, 1092.
Einaudi, G. and Van Hoven, G.: 1983, Solar Phys. 88, 163.
Foote, B. J. and Craig, I. J. D.: 1990, Astrophys. J. 350, 437.
Freidberg, J. P.: 1970, Phys. Fluids 13, 1812.
Freidberg, J. P.: 1982, Rev. Mod. Phys. 54, 801.
Gautschy, A. and Glatzel, W.: 1990, Monthly Notices Roy. Astron. Soc. 245, 154.
Giachetti, R., Van Hoven, G., and Chiuderi, C.: 1977, Solar Phys. 55, 371.
Goedbloed, J. P.: 1971a, Physica 53, 501.
Goedbloed, J. P.: 1971b, Physica 53, 535.
Goedbloed, J. P.: 1990, Comp. Phys. Comm. 59, 39.
Goedbloed, J. P. and Hagebeuk, H. J. L.: 1972, Phys. Fluids 15, 1090.
Goedbloed, J. P. and Sakanaka, P. H.: 1974, Phys. Fluids 17, 908.
Goedbloed, J. P. and Schuurman, W.: 1972, Plasma Phys. 14, 1.
Gold, T. and Hoyle, F.: 1960, Monthly Notices Roy. Astron. Soc. 120, 89.
Hood, A. W.: 1986a, Solar Phys. 103, 329.
Hood, A. W.: 1986b, Solar Phys. 105, 307.
Hood, A. W. and Priest, E. R.: 1979, Solar Phys. 64, 303.
Hood, A. W. and Priest, E. R.: 1981, Geophys. Astrophys. Fluid Dyn. 17, 297.
Hood, A. W., Van der Linden, R., and Goossens, M.: 1989, Solar Phys. 120, 261.
Kruskal, M. and Schwarzschild, M.: 1954, Proc. Roy. Soc. London A223, 348.
Lentini, M. and Pereyra, V.: 1977, SIAM J. Numer. Anal. 14, 91.
Lowder, R. S. and Thomassen, K. I.: 1973, Phys. Fluids 16, 1497.
Mikić, Z., Schnack, D. D., and Van Hoven, G.: 1990, Astrophys. J. 361, 690.
Newcomb, W. A.: 1960, Ann. Phys. 10, 232.
Press, W. H., Flannery, B. P., Teukolsky, S. A., and Vetterling, W. T.: 1987, Numerical Recipes, Cambridge University Press, Cambridge.
Priest, E. R.: 1982, Solar Magnetohydrodynamics, D. Reidel Publ. Co., Dordrecht, Holland.
Raadu, M. A.: 1972, Solar Phys. 22, 425.
Robinson, D. C.: 1971, Plasma Phys. 13, 439.
Rosner, R., Low, B. C., and Holzer, T. E.: 1986, in P. A. Sturrock, T. E. Holzer, D. M. Mihalas, and R. K. Ulrich (eds.), Physics of the Sun, D. Reidel Publ. Co., Dordrecht, Holland.
Shafranov, V. D.: 1970, Soviet Phys.-Tech. Phys. 15, 175.
Sneyd, A. D. and Craig, I. J. D.: 1989, Astrophys. Space Sci. 151, 265.
Suydam, B. R.: 1958, in Proc. Second United Nations Int. Conference on the Peaceful Uses of Atomic Energy, United Nations, Geneva, Vol. 31, p. 157.
Van der Linden, R. A. M., Goossens, M., and Kerner, W.: 1990, Comp. Phys. Comm. 59, 61.
Velli, M., Einaudi, G., and Hood, A. W.: 1990a, Astrophys. J. 350, 419.
Velli, M., Einaudi, G., and Hood, A. W.: 1990b, Astrophys. J. 350, 428.
von Hain, K. and Lüst, R.: 1958, Z. Naturforsch. 13a, 936.
Voslamber, D. and Callebaut, D. K.: 1962, Phys. Rev. (Ser. II) 128, 2016.
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De Bruyne, P., Hood, A.W. Stability of line-tied 1-d coronal loops: Significance of an extended Suydam criterion. Sol Phys 142, 87–111 (1992). https://doi.org/10.1007/BF00156635
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DOI: https://doi.org/10.1007/BF00156635