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A New Method for Finding Topological Separators in a Magnetic Field

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Magnetic topology is a powerful tool for constraining certain physical properties of a given magnetic configuration, including the strengths and locations of current sheets, relative helicity and the magnetic free energy available for reconnection. A critical feature of magnetic topology is the separator, a field line bordering several different regions of connectivity. With existing methods, these field lines are at best computationally expensive and at worst impossible to find. A new method is presented for finding the Minimal Separator Set, all of the separators that necessarily exist in a configuration, and to use this information in combination with the optical analogy and a simulated annealing method to ‘cool’ an initial guess for each separator into a good approximation.

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  1. Aulanier, G., Pariat, E., and Démoulin, P.: 2005, Astron. Astrophys. 444, 961.

  2. Barnes, G., Longcope, D.W., and Leka, K.D.: 2005, Astrophys. J. 629, 561.

  3. Beveridge, C. and Longcope, D.W.: 2005, Solar Phys. 227, 193.

  4. Beveridge, C., Priest, E.R., and Brown, D.S.: 2004, Geophys. Astrophys. Fluid Dyn. 98, 429.

  5. Close, R.M., Parnell, C.E., and Priest, E.R.: 2004, Solar Phys. 225, 21.

  6. Démoulin, P., Hénoux, J.C., Priest, E.R., and Mandrini, C.H.: 1996a, Astron. Astrophys. 308, 643.

  7. Démoulin, P., Mandrini, C.H., Rovira, M.G., Hénoux, J.C., and Machado, M.G.: 1996b, Solar Phys. 150, 221.

  8. Galsgaard, K. and Nordlund, Å: 1997, J. Geophys. Res. 102, 231.

  9. Gorbachev, V.S., Kel'ner, S.R., Somov, B.V., and Schverts, A.S.: 1988, Sov. Astron. 32, 308.

  10. Greene, J.M.: 1988, J. Geophys. Res. 93, 8583.

  11. Lau, Y.-T. and Finn, J.M.: 1990, Astrophys. J. 350, 672.

  12. Longcope, D.W.: 1996, Solar Phys. 169, 91.

  13. Longcope, D.W. and Silva, A.V.R.: 1998, Solar Phys. 179, 349.

  14. Maclean, R., Beveridge, C., Hornig, G., and Priest, E.R.: 2006, Solar Phys. (in press).

  15. Maclean, R., Beveridge, C., Longcope, D.W., Brown, D.S., and Priest, E.R.: 2005b, Proc. Roy. Soc. London A461, 2009.

  16. Molodenskii, M.M. and Syrovatskii, S.I.: 1977, Sov. Astron. 21, 734.

  17. Parnell, C.E., Smith, J.M., Neukirch, T., and Priest, E.R.: 1996, Phys. Plasmas 3, 759.

  18. Parker, E.N.: 1991, Phys. Fluids B 3, 2652.

  19. Priest, E.R. and Titov, V.S.: 1996, Phil. Trans. Roy. Soc. London A354, 2951.

  20. Press, W.H., Flannery, B.P., Teukolsky, S.A., and Vetterling, W.T.: 1992, Numerical Recipes: The Art of Scientific Computing, Cambridge University Press, Cambridge (UK) and New York.

  21. Titov, V.S., Hornig, G., and Démoulin, P.: 2002, J. Geophys. Res. 107, SSH3-1.

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Correspondence to C. Beveridge.

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Beveridge, C. A New Method for Finding Topological Separators in a Magnetic Field. Sol Phys 236, 41–57 (2006). https://doi.org/10.1007/s11207-006-0124-3

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  • Initial Guess
  • Current Sheet
  • Solar Phys
  • Null Point
  • Minimal Separator