Coronal Magnetic Structure: the Role of Ideal MHD Invariants

  • Mitchell A. Berger
Conference paper


Magnetic helicity measures properties of field lines such as linking, knotting, and twisting. Severe bounds can be placed on its dissipation in a highly conducting plasma. Motions of field line endpoints at the photosphere inject helicity into the corona. An associated invariant is the net twist between two neighboring field lines. Random photospheric motions should twist neighboring lines through a few turns in one day. The current associated with this twist is small, suggesting that most coronal current resides in sheets. Other ideal invariants can be defined which measure the mutual braiding of three or more field lines. Coronal heating models which rely on the buildup of helicity and braiding will be reviewed.


Field Line Current Sheet Flux Tube Magnetic Helicity Coronal Magnetic Field 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. Aly J J.: 1990, in The numerical modelling of Solar and Stellar MED, NATO Advanced Research Workshop, Spitzingsee (FRG), to appearGoogle Scholar
  2. Antiochos S.: 1987, Astrophysical. J. 312, 886CrossRefADSGoogle Scholar
  3. Barnes C., Fernandez J, Henins I, Jarboe T, Knox S, Marklin G, and McKenna K: 1986, Physics of Fluids 29, 3415CrossRefADSGoogle Scholar
  4. Berger M A and Field G B: 1984, J. Fluid Mechanics 147, 133MathSciNetCrossRefADSGoogle Scholar
  5. Berger M A: 1984, Geophysical and Astrophysical Fluid Dynamics 30, 79CrossRefADSGoogle Scholar
  6. Berger M A: 1985, Astrophysical J. Supplement 59, 433CrossRefADSGoogle Scholar
  7. Berger M A: 1988, Astronomy and Astrophysics 201, 355MathSciNetMATHADSGoogle Scholar
  8. Berger M A: 1990, Astronomy and Astrophysics, (submitted)Google Scholar
  9. Berger M A: 1990b, in Topological Fluid Mechanics H K Moffatt and A Tsinober, eds. (Cambridge University Press) p. 440Google Scholar
  10. Berger M A: 1990c, in Physics of Magnetic Flux Ropes C Russell, E Priest, and L C Lee, eds. (AGU) p. 251CrossRefGoogle Scholar
  11. Bhattacharjee A, Dewar R L, and Monticello D: 1982, Physics of Fluids 25, 887MathSciNetMATHCrossRefADSGoogle Scholar
  12. Browning P K, Sakurai T, and Priest E R: 1986, Astronomy and Astrophysics 158, 217ADSGoogle Scholar
  13. Chandrasekhar S: 1961, Hydrodynamic and Hydromagnetic Stability (Oxford: Clarendon)MATHGoogle Scholar
  14. Choudhuri A R: 1986, in Coronal and Prominence Plasmas A I Poland, ed. (NASA CP 2442) p. 451Google Scholar
  15. Choudhuri A R and Königl A: 1986, Astrophysical J. 310, 96CrossRefADSGoogle Scholar
  16. Dixon A, Berger M A, Browning P, and Priest E R: 1989, Astronomy and Astrophysics 225, 156MathSciNetADSGoogle Scholar
  17. Finn J H and Antonsen T M: 1985, Comments on Plasma Physics and Controlled Fusion 9, 111Google Scholar
  18. Frazer E N and Stenflo J O: 1972, Soiar Physics 27, 330ADSGoogle Scholar
  19. Glencross W M: 1975, Astrophysical J. 199, L53CrossRefADSGoogle Scholar
  20. Hameiri E and Bhattacharjee A: 1987, Physics of Fluids 30, 1743MATHCrossRefADSGoogle Scholar
  21. Heyvaerts J and Priest E R: 1985, Astronomy and Astrophysics 137, 63ADSGoogle Scholar
  22. Jensen T H and Chu M S: 1984, Physics of Fluids 27, 281CrossRefGoogle Scholar
  23. Mikic Z, Schnack D D, and Van Hoven G: 1989, Astrophysical J. 338, 1148CrossRefADSGoogle Scholar
  24. Moffatt H K: 1969, J. Fluid Mechanics 35, 117MATHCrossRefADSGoogle Scholar
  25. Moffatt H K: 1985, J. Fluid Mechanics 159, 359MathSciNetMATHCrossRefADSGoogle Scholar
  26. Molodensky M M: 1974, Solar Physics 39, 393CrossRefADSGoogle Scholar
  27. Parker E N: 1983, Astrophysical J. 264, 642CrossRefADSGoogle Scholar
  28. Parker E N: 1987, Astrophysical J. 318, 876CrossRefADSGoogle Scholar
  29. Parker E N: 1989, Geophysical and Astrophysical Fluid Dynamics 45, 159CrossRefADSGoogle Scholar
  30. Parker E N: 1990, Geophysical and Astrophysical Fluid Dynamics 52, 183CrossRefADSGoogle Scholar
  31. Reiman A: 1980, Physics of Fluids 23, 230MathSciNetCrossRefADSGoogle Scholar
  32. Rosner R, Low B C., Tsinganos K, and Berger M A: 1989, Geophysical and Astrophysical Fluid Dynamics 48, 251MATHCrossRefADSGoogle Scholar
  33. Sakai J: 1990, Astrophysical J. Supplement 73, 321CrossRefADSGoogle Scholar
  34. Song Y and Lysak R L: 1989, J. Geophysical Research 94, 5273CrossRefADSGoogle Scholar
  35. Sturrock P A and Uchida Y: 1981, Astrophysical J. 246, 331CrossRefADSGoogle Scholar
  36. Taylor J B: 1974, Physical Review Letters 33, 1139CrossRefADSGoogle Scholar
  37. Taylor J B: 1986, Rev. Modern Physics 58, 741CrossRefADSGoogle Scholar
  38. Vekstein G E: 1987, Astronomy and Astrophysics 182, 324MATHADSGoogle Scholar
  39. Woltjer L: 1958, Proceedings National Academy of Science USA 44, 489MathSciNetMATHCrossRefADSGoogle Scholar
  40. Wright A N: 1987, Planet. Space Sci. 35, 813CrossRefADSGoogle Scholar
  41. Wright A N and Berger M A: 1989, J. Geophysical Research 94, 1295CrossRefADSGoogle Scholar
  42. Zayer I, Solanki S K, and Stenflo J O: 1989, Astronomy and Astrophysics 211, 463ADSGoogle Scholar
  43. Zweibel E G and Li H S: 1987, Astrophysical J. 312, 423CrossRefADSGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1991

Authors and Affiliations

  • Mitchell A. Berger
    • 1
  1. 1.Mathematics DepartmentUniversity College LondonLondonEngland

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