Abstract
Using the MHD energy principle of Bernstein et al. (1958) we develop a formalism in order to analyze the stability properties of two-dimensional magnetostatic plasma equilibria. We apply this to four models of quiescent prominences, namely those of Menzel (1951), Dungey (1953), Kippenhahn and Schlüter (1957), and finally Lerche and Low (1980). For the observed parameter range, all models are stable and they explain reasonably well the reported flare-initiated oscillations in quiescent prominences. We also investigate other parameters regions, which may be relevant in some stellar atmospheres. It is found that, with the exception of the Kippenhahn and Schlüter model, all models become unstable. The instabilities that occur show simultaneously several features of well-known MHD-instabilities. However, an unequivocal assignment of the instabilities to specific instability prototypes is not possible. Our formalism allows one to investigate not only more realistic prominence equilibria, but also arbitrary one- and two-dimensional static ideal MHD-equilibria.
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References
Anzer, U.: 1969, Solar Phys. 8, 37.
Bashkirtsev, V. S. and Mashnich, G. P.: 1984, Solar Phys. 91, 93.
Bernstein, I. B., Frieman, E. A., Kruskal, M. D., and Kulsrud, R. M.: 1958, Proc. Roy. Soc. London A244, 17.
Brown, A.: 1958, Astrophys. J. 128, 646.
Dungey, J. W.: 1953, Monthly Notices Roy. Astron. Soc. 113, 180.
Galindo, T. J. and Schindler, K.: 1984, Astrophys. J. 277, 422.
Hain, K., Lüst, R., and Schlüter, A.: 1957, Z. Astrophys. 43, 36.
Jefferies, J. T. and Orrall, F. Q.: 1963, Astrophys. J. 137, 1232.
Kippenhahn, R. and Schlüter, A.: 1957, Z. Astrophys. 43, 36.
Kleczek, J. and Kuperus, M.: 1969, Solar Phys. 6, 72.
Laval, G., Mercier, C., and Pellat, R.: 1965, Nucl. Fusion 5, 156.
Lerche, I. and Low, B. C.: 1980, Solar Phys. 67, 229.
Leroy, J. L.: 1977, Astron. Astrophys. 60, 79.
Leroy, J. L.: 1978, Astron. Astrophys. 64, 247.
Low, B. C.: 1975, Astrophys. J. 197, 251.
Low, B. C.: 1981, Astrophys. J. 246, 538.
Low, B. C. and Wu, S. T.: 1981, Astrophys. J. 248, 335.
Low, B. C., Hundhausen, A. J., and Zweibel, E. G.: 1983, Phys. Fluids 26, 2731.
Malville, J. P., Hood, A. W., and Priest, E. R.: 1984, Solar Phys. 92, 15.
Menzel, D. H.: 1951, Proc. Conf. on Dynamics of Ionised Media, London.
Migliuolo, S.: 1982, J. Geophys. Res. 81, 3462.
Mikhailovskii, A. B.: 1974, Theory of Plasma Instabilities, Volume 2, Consultants B, New York.
Nakagawa, Y. and Mc Kim Malville, J.: 1969, Solar Phys. 9, 102.
Osherovich, V. A.: 1983, Astrophys. J. 271, 847.
Osherovich, V. A.: 1985, Astrophys. J. 297, 314.
Ramsey, H. E. and Smith, S. F.: 1966, Astron. J. 71, 197.
Sakai, J. and Nishikawa, K.-L: 1983, Solar Phys. 88, 241.
Schindler, K., Birn, J., and Janicke, I.: 1983, Solar Phys. 87, 103.
Schuurman, W., Bobeldijk, C., and de Vries, R. F.: 1969, Plasma Phys. 11, 495.
Shafranov, V. D.: 1957, J. Nucl. Energy II 5, 86.
Shafranov, V. D.: 1959, Plasma Physics and the Problem of Controlled Thermonuclear Reactions, Vol. II, p. 197.
Spicer, D. S.: 1978, ‘Physics of Solar Prominences’, IAU Colloq. 44, 307.
Tayler, R. J.: 1957a, Proc. Phys. Soc. London B70, 31.
Tayler, R. J.: 1957b, Proc. Phys. Soc. London B70, 1049.
Van Kampen, N. G. and Felderhof, B. U.: 1967, Theoretical Methods in Plasma Physics, North-Holland Publ. Co., Amsterdam.
Wiehr, E., Stellmacher, G., and Balthasar, H.: 1984, Solar Phys. 94, 285.
Zienkiewicz, O. C.: 1977, The Finite Element Method in Engineering Science, London.
Zweibel, E. G.: 1982, Astrophys. J. 258, L53.
Zweibel, E. G. and Hundhausen, A. J.: 1982, Solar Phys. 76, 261.
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Trejo, J.G. Stability analysis of two-dimensional models of quiescent prominences. Sol Phys 108, 265–313 (1987). https://doi.org/10.1007/BF00214166
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DOI: https://doi.org/10.1007/BF00214166