Formal Mathematical Solutions of the Force-Free Equations, Spontaneous Discontinuities, and Dissipation in Large-Scale Magnetic Fields

  1. C. T. Russell,
  2. E. R. Priest and
  3. L. C. Lee
  1. E. N. Parker

Published Online: 21 MAR 2013

DOI: 10.1029/GM058p0195

Physics of Magnetic Flux Ropes

Physics of Magnetic Flux Ropes

How to Cite

Parker, E. N. (1990) Formal Mathematical Solutions of the Force-Free Equations, Spontaneous Discontinuities, and Dissipation in Large-Scale Magnetic Fields, in Physics of Magnetic Flux Ropes (eds C. T. Russell, E. R. Priest and L. C. Lee), American Geophysical Union, Washington, D. C.. doi: 10.1029/GM058p0195

Author Information

  1. Enrico Fermi Institute, Department of Physics and of Chicago, 933 E. 56th St., Chicago, Illinois 60637

Publication History

  1. Published Online: 21 MAR 2013
  2. Published Print: 1 JAN 1990

ISBN Information

Print ISBN: 9780875900261

Online ISBN: 9781118663868

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Keywords:

  • Solar photosphere;
  • Magnetic flux;
  • Astrophysics

Summary

Direct integration of the force-free field equation ∇ × B = αB, in the simple case of the local deformation of a laminar field, produces field configurations containing tangential discontinuities (current sheets). Whereas continuous solutions allow only restricted field topologies, the discontinuities provide the necessary release from those restrictions in more general topologies. Magnetic fields in nature are strongly deformed by convection, so as to contain significant internal discontinuities. The bipolar magnetic fields containing the active x-ray corona of the sun are a case in point. It appears that the dissipation caused by the discontinuities may be the primary heat source producing the x-ray corona.