Abstract
We present some preliminary results on different mathematical problems encountered in attempts to reconstruct the coronal magnetic field, assumed to be in a force-free state, from its values in the photosphere. We discuss the formulations associated with these problems, and some new numerical methods that can be used to get their approximate solutions. Both the linear constant-α and the nonlinear cases are considered. We also discuss the possible use of dynamical 3D MHD codes to construct approximate solutions of the equilibrium force-free equations, which are needed for testing numerical extrapolation schemes.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Alissandrakis, C. E.: 1981, Astron. Astrophys. 100, 197.
Aly, J. J.: 1987a, Solar Phys. 111, 287.
Aly, J. J.: 1987b, in R. Beck and R. Gräve (eds.), Interstellar Magnetic Fields, Springer-Verlag, Berlin, Heidelberg, New York, p. 240
Aly, J. J.: 1989, Solar Phys. 120, 19.
Aly, J. J.: 1991, Astrophys. J. 375, L61.
Amari, T.: 1991, in Advances in Solar System in E. R Priest and A. W. Hood (eds.), Magnetohydrodynamics, Cambridge University Press, Cambridge, p. 173.
Amari, T. and Aly, J. J.: 1989, Astron. Astrophys. 208, 261.
Amari, T. and Aly, J. J.: 1990, Astron. Astrophys. 231, 213.
Amari, T. and Démoulin, P. 1992, Proceedings of the Workshop ‘Méthodes de Détermination des Champs Magnétiques Solaires et Stellaires, Observatoire de Paris, p. 187.
Amari, T., Luciani, J. F., and Joly, P.: 1995, S.I.A.M. J., in press.
Amari, T., Luciani, J. F., Aly, J. J, and Tagger, M.: 1996, Astrophys. J., in press.
Anzer, U.: 1972, Solar Phys. 24, 324.
Barnes, C. W. and Sturrock, P. A.: 1972, Astrophys. J. 174, 659.
Bineau, M.: 1972, Comm. Pure Applied Math. 25, 77.
Chiu, Y. T. and Hilton, H. H.: 1977, Astrophys. J. 212, 873.
Cuperman, S. and Ditkowski, A.: 1991, Astron. Astrophys. 241, 646.
Cuperman, S., Ofman, L., and Semel, M.: 1990a, Astron. Astrophys. 227, 227.
Cuperman, S., Ofman, L., and Semel, M.: 1990b, Astron. Astrophys. 230, 193.
Cuperman, S., Démoulin, P., and Semel, M.: 1991, Astron. Astrophys. 245, 285.
Démoulin, P.: 1996, Solar Phys., presented at this Workshop.
Démoulin, P., Cuperman, S., and Semel, M.: 1992, Astron. Astrophys. 263, 351.
Gary, G. A.: 1989, Astrophys. J. 69, 323.
Gary, G. A.: 1990, in in G. Poletto (ed.), Memorie della Societa Astronomica Italiana.
Gary, G. A. and Hagyard, M. J.: 1990, Solar Phys. 126, 21.
Grad, H. and Rubin, H.: 1958, Proc. 2nd Int. Conf. on Peaceful Uses of Atomic Energy, Vol. 31, Geneva, United Nations, p. 190.
Hadamard, J.: 1932, Le Problème de Cauchy et les Equations aux Dérivées Partielles Linéaires Hyperboliques, Herman, Paris.
Hagyard, M. J.: 1988, Solar Phys. 115, 107.
Hagyard, M. J., Smith, J. B., Jr., Teuber, D., and West, E. A.: 1984, Solar Phys. 91, 115.
Hannakam, L., Gary, G. A., and Teuber, D.: 1984, Solar Phys. 94, 219.
Hofmann, A. and Kálmán, B.: 1991, Astron. Astrophys. 241, 203.
Jackson, J. D.: 1975, Classical Electrodynamics, John Wiley and Sons, New York.
Kress, R.: 1989, in B. Brosourski and E. Martensen (eds.), Methoden und Kerfahren der Mathematischem Physik, Problems of Applied Analysis.
Low, B. C.: 1982, Solar Phys. 77, 43.
Low, B. C. and Lou, Y. Q.: 1991, Astrophys. J. 352, 343.
Mandrini, C. H., Démoulin, P., Rovira, M. G., de la Beaujardière, J. F., and Hénoux, J. C.: 1995, Astron. Astrophys. 303, 927.
McClymont, A. N., Jiao, L., and Mikić, Z.: 1997, Solar Phys., this issue.
Mikic, Z. and McClymont, A. N.: 1994, in K. S. Balasubramaniam and G. Simon (eds.), Solar Active Region Evolution - Comparing Models with Observtions, ASP Conf Series.
Mikic, Z., Barnes, D. C., and Schnack, D. D.: 1988, Astrophys. J. 328, 830.
Mikic, Z., Linker, J. A., and Schnack, D. D.: 1996, Proceedings of the Sacramento Peak Workshop, Summer 1996, in press.
Mikic, Z., Schnack, D. D., and Van Hoven, G.: 1989, Astrophys. J. 338, 1148.
Nakagawa, Y., Raadu, M. A., and Harvey, J. W.: 1973, Solar Phys. 30, 421.
Pridmore-Brown, D.: 1981, Aerospace Report No. ATR-81(7813)-1, The Aerospace Corporation, El Sequndo, CA.
Sakurai, T.: 1981, Solar Phys. 69, 343.
Sakurai, T.: 1989, Space Sci. Rev. 51, 11.
Sakurai, T.: 1996, Solar Phys., presented at this Workshop.
Sakurai, T., Makita, M., and Shibasaki, K.: 1985, in H. U. Schmidt (ed.), Theoretical Problems in High Resolution Solar Physics, MPA-212, Max Planck-Institute, p. 312.
Schmidt, H. U.: 1964, in Physics of Solar Flares, NASA SP 50, p. 107.
Semel, M.: 1988, Astron. Astrophys. 198, 293.
Stenflo, J. O.: 1989, Astron. Astrophys. R1, 1.
Wu, S. T.: 1996, Solar Phys., presented at this Workshop.
Wu, S. T., Chang, H. M., and Hagyard, M. J.: 1985, in M. J. Hagyard (ed.), Measurement of Solar Vector Magnetic Fields, NASA Conf. Publ. 2374, Marshall Space Flight CenterWorkshop, p. 17.
Wu, S. T., Sun, M. T., Chang, H. M., Hagyard, M. J., and Gary, G. A.: 1990, Astrophys. J. 362, 698.
Yang, W. H., Sturrock, P. A., and Antiochos, S. K.: 1986, Astrophys. J. 309, 383.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Amari, T., Aly, J.J., Luciani, J.F. et al. RECONSTRUCTING THE SOLAR CORONAL MAGNETIC FIELD AS A FORCE-FREE MAGNETIC FIELD. Solar Physics 174, 129–149 (1997). https://doi.org/10.1023/A:1004966830232
Issue Date:
DOI: https://doi.org/10.1023/A:1004966830232