Solar Physics

, Volume 245, Issue 2, pp 263–285 | Cite as

Magnetofrictional Extrapolations of Low and Lou’s Force-Free Equilibria

  • G. ValoriEmail author
  • B. Kliem
  • M. Fuhrmann


We present a careful investigation of the magnetofrictional relaxation and extrapolation technique applied to the reconstruction of two test fields. These fields are taken from the family of nonlinear force-free magnetic equilibria constructed by Low and Lou (Astrophys. J. 352, 343, 1990), which have emerged as standard tests for extrapolation techniques in recent years. For the practically relevant case that only the field values in the bottom plane of the considered volume (vector magnetogram) are used as input information (i.e., not including the knowledge about the test field at the side and top boundaries), the test field is reconstructed to a higher accuracy than obtained previously. Detailed diagnostics of the reconstruction accuracy show that the implementation of fourth-order spatial discretization was essential to reach this accuracy for the given test fields and to achieve near machine precision in satisfying the solenoidal condition. Different variants of boundary conditions are tested, which all yield comparable accuracy. In its present implementation, the technique yields a scaling of computing time with total number of grid points only slightly below N 5/3, which is too steep for applications to large (≥10242) magnetograms, except on supercomputers. Directions for improvement are outlined.


Magnetic fields MHD Methods: numerical Sun: corona 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Amari, T., Boulmezaoud, T.Z., Aly, J.J.: 2006, Astron. Astrophys. 446, 691. zbMATHCrossRefADSGoogle Scholar
  2. Chiu, Y.T., Hilton, H.H.: 1977, Astrophys. J. 212, 873. CrossRefADSGoogle Scholar
  3. Chodura, R., Schlüter, A.: 1981, J. Comput. Phys. 41, 68. zbMATHCrossRefADSGoogle Scholar
  4. Courant, R., Friedrichs, K.H., Lewy, H.: 1928, Math. Ann. 100, 32. CrossRefMathSciNetGoogle Scholar
  5. Craig, I.J.D., Sneyd, A.D.: 1986, Astrophys. J. 311, 451. CrossRefADSGoogle Scholar
  6. Dedner, A., Kemm, F., Kröner, D., Munz, C., Schnitzer, T., Wesenberg, M.: 2002, J. Comput. Phys. 175, 645. zbMATHCrossRefADSMathSciNetGoogle Scholar
  7. Low, B.C., Lou, Y.Q.: 1990, Astrophys. J. 352, 343. CrossRefADSGoogle Scholar
  8. Marder, B.: 1987, J. Comput. Phys. 131, 48. CrossRefADSGoogle Scholar
  9. McClymont, A.N., Jiao, L., Mikic, Z.: 1997, Solar Phys. 174, 191. CrossRefADSGoogle Scholar
  10. McClymont, A.N., Mikic, Z.: 1994, Astrophys. J. 422, 899. CrossRefADSGoogle Scholar
  11. Metcalf, T., DeRosa, M.L., Schrijver, C.J., Barnes, G., van Ballegooijen, A.A., Wiegelmann, T., Wheatland, M.S., Valori, G., McTiernan, J.: 2007, Solar Phys., submitted. Google Scholar
  12. Nakagawa, Y., Raadu, M.A.: 1972, Solar Phys. 25, 127. CrossRefADSGoogle Scholar
  13. Roumeliotis, G.: 1996, Astrophys. J. 473, 1095. CrossRefADSGoogle Scholar
  14. Sakurai, T.: 1981, Solar Phys. 69, 343. CrossRefADSGoogle Scholar
  15. Schrijver, C.J., DeRosa, M.L.: 2003, Solar Phys. 212, 165. CrossRefADSGoogle Scholar
  16. Schrijver, C.J., DeRosa, M.L., Metcalf, T.R., Liu, Y., McTiernan, J., Régnier, S., Valori, G., Wheatland, M.S., Wiegelmann, T.: 2006, Solar Phys. 235, 161 (Paper II). CrossRefADSGoogle Scholar
  17. Seehafer, N.: 1978, Solar Phys. 58, 215. CrossRefADSGoogle Scholar
  18. Song, M.T., Fang, C., Tang, Y.H., Wu, S.T., Zhang, Y.A.: 2006, Astrophys. J. 649, 1084. CrossRefADSGoogle Scholar
  19. Tóth, G., Keppens, R., Botchev, M.A.: 1998, Astron. Astrophys. 332, 1159. ADSGoogle Scholar
  20. Valori, G., Kliem, B., Keppens, R.: 2005, Astron. Astrophys. 433, 335 (Paper I). zbMATHCrossRefADSGoogle Scholar
  21. Wiegelmann, T.: 2004, Solar Phys. 219, 87. CrossRefADSGoogle Scholar
  22. Wiegelmann, T., Inhester, B., Kliem, B., Valori, G., Neukirch, T.: 2006, Astron. Astrophys. 453, 737. CrossRefADSGoogle Scholar
  23. Yang, W.H., Sturrock, P.A., Antiochos, S.K.: 1986, Astrophys. J. 309, 383. CrossRefADSGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2007

Authors and Affiliations

  1. 1.Astrophysikalisches Institut PotsdamPotsdamGermany
  2. 2.Kiepenheuer-Institut für SonnenphysikFreiburgGermany
  3. 3.Institut für PhysikUniversität PotsdamPotsdamGermany

Personalised recommendations