Abstract
We investigate the influence of the finite extent of the computational domain and of specific boundary conditions on a theoretical model for solar eruptive processes originally proposed by Zwingmann (1987). In this model, the slow pre-onset time evolution of arcade-like solar coronal magnetic field structures is described by quasi-static equilibrium sequences. The magnetic field is represented by Euler potentials which allow for a realistic description of the photospheric boundary conditions, because the pressure and the magnetic footpoint displacement can be prescribed separately. We use an improved numerical method suitable for computing equilibrium sequences, allowing for larger domains and higher resolution than used in the previous work. With this method, we are able to show that, in contradiction to a supposition made by Zwingmann (1987), the results of the computations do strongly depend on the size of the computing domain. This has consequences for a possible physical interpretation of the model. We furthermore show that with the boundary conditions used in this model a shearing motion of the magnetic footpoints inevitably leads to the formation of singular current layers at the separatrix between field lines cutting the upper boundary (open field lines) and field lines which are only connected with the photosphere (closed field lines).
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Aly, J. J.: 1984,Astrophys. J. 283, 349.
Aly, J. J.: 1985,Astron. Astrophys. 143, 19.
Aly, J. J.: 1988,Astron. Astrophys. 203, 183.
Aly, J. J.: 1990a,Phys. Fluids B2, 1928.
Aly, J. J.: 1990b,Comp. Phys. Comm. 59, 13.
Aly. J. J.: 1992,Solar Phys. 138, 133.
Aly, J. J.: 1993,Phys. Fluids B 5, 151.
Athay, G.: 1976,The Solar Corona and Chromosphere: Quiet Sun, D. Reidel Publ. Co., Dordrecht, Holland.
Barnes, C. W. and Sturrock, P.: 1972,Astrophys. J. 174, 659.
Birn, J. and Schindler, K.: 1981, in E. R. Priest (ed.),Solar Flare Magnetohydrodynamics, Gordon and Breach, London, p. 337.
Birn, J., Goldstein, H., and Schindler, K.: 1978,Solar Phys. 57, 81.
Birn, J., Browning, P. K., Sakurai, T., Schindler, K., and Zwingmann, W.: 1984,Rapport d'active scientifique du CECAM 1984, CECAM workshop ‘Energy Conversion in Active Astrophysical Plasmas’, Paris, p. 52.
Biskamp, D. and Welter, H.: 1989,Solar Phys. 120, 49.
De Bruyne, P. and Hood, A.: 1989,Solar Phys. 119, 87.
Finn, J. M. and Lau, Y.-T.: 1991,Phys. Fluids B 3, 2675.
Forbes, T. G., and Isenberg, P. A.: 1991,Astrophys. J. 373, 294.
Hackbusch, W.: 1991,Iterative Lösungsverfahren großer schwach besetzter Gleichungssysteme, B. G. Teubner Verlag, Stuttgart.
Heyvaerts, J., Lasry, J. M., Schatzman, M., and Witomsky, G.: 1980,Springer Lecture Notes in Mathematics 782, 160.
Heyvaerts, J., Lasry, J. M., Schatzman, M., and Witomsky, G.: 1982,Astron. Astrophys. 111, 104.
Hood, A.: 1990,Comp. Phys. Rep. 12, 177.
Hood, A. and Anzer, U.: 1987,Solar Phys. 111, 333.
Hood, A. and Priest, E. R.: 1980,Solar Phys. 66, 113.
Inhester, B., Hesse, M., and Birn, J.: 1992,Solar Phys. 138, 257.
Jockers, K.: 1978,Solar Phys. 56, 37.
Keller, H. B.: 1977, in P. Rabinowitz (ed.),Applications of Bifurcation Theory, Academic Press, New York, p. 359.
Klimchuk, J. A. and Sturrock, P.: 1989,Astrophys. J. 345, 1034.
Kopp, R. A. and Pneumann, G. W.: 1976,Solar Phys. 50, 85.
Low, B. C.: 1977,Astrophys. J. 212, 234.
Low, B. C.: 1990,Annu. Rev. Astron. Astrophys. 28, 491.
Low, B. C. and Wolfson, R.: 1988,Astrophys. J. 324, 574.
Melville, J. P., Hood, A., and Priest, E. R.: 1983,Solar Phys. 87, 301.
Melville, J. P., Hood, A., and Priest, E. R.: 1984,Solar Phys. 92, 15.
Mikic, Z., Barnes, D. C., and Schnack, D. D.: 1988,Astrophys. J. 328, 830.
Parker, E. N.: 1972,Astrophys. J. 174, 499.
Parker, E. N.: 1979,Cosmical Magnetic Fields, Oxford University Press, Oxford.
Press, W. H., Flannery, B. P., Teukolsky, S. A., and Vetterling, W. T.: 1986,Numerical Recipes, Cambridge University Press, Cambridge.
Priest, E. R.: 1982,Solar Magnetohydrodynamics, D. Reidel Publ. Co., Dordrecht, Holland.
Roumeliotis, G.: 1993,Astrophys. J. 404, 781.
Sakurai, T.: 1989,Solar Phys. 121, 347.
Schindler, K.: 1985, in B. Buti (ed.),Advances in Space Plasma Physics, World Scientific Publ., Singapore, p. 142.
Schindler, K., Birn, J., and Janicke, L.: 1983,Solar Phys. 87, 103.
Stern, D. P.: 1976,Rev. Geophys. Space Sci 14, 199.
Švestka, Z.: 1981, in E. R. Priest (ed.),Solar Flare Magnetohydrodynamics, Gordon and Breach, London, p. 47.
Tandberg-Hanssen, E. and Emslie, A. G.: 1988,The Physics of Solar Flares, Cambridge Univ. Press, Cambridge.
Van Hoven, G., Anzer, U., Barbosa, D. D., Birn, J., Cheng, C.-C., Hansen, R. T., Jackson, B. V., Martin, S. F., McIntosh, P. S., Nakagawa, Y., Priest, E. R., Reeves, E. M., Reichmann, E. J., Schmahl, E. J., Smith, J. B., Solodyna, C. V., Thomas, R. J., Uchida, Y., and Walker, A. B. C.: 1980, in P. A. Sturrock (ed.),Solar Flares, Colorado Associated University Press, Boulder, p. 17.
Van Tend, W. and Kuperus, M.: 1978,Solar Phys. 59, 115.
Vekshtein, G. E. and Priest, E. R.: 1992,Astrophys. J. 384, 333.
Vekshtein, G. E. and Priest, E. R.: 1993,Solar Phys. 146, 119.
Wait, R. and Mitchell, A. R.: 1985,Finite Element Analysis and Applications, John Wiley and Sons, Chichester.
Zirin, H. and Tanaka, K.: 1973,Solar Phys. 32, 173.
Zwingmann, W.: 1987,Solar Physics 111, 309.
Zwingmann, W., Schindler, K., and Birn, J.: 1985,Solar Phys. 99, 31.
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Platt, U., Neukirch, T. Theoretical study of onset conditions for solar eruptive processes: Influence of the boundaries. Sol Phys 153, 287–306 (1994). https://doi.org/10.1007/BF00712507
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DOI: https://doi.org/10.1007/BF00712507