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Force-free magnetic fields - The magneto-frictional methodThe problem under discussion is that of calculating magnetic field configurations in which the Lorentz force j x B is everywhere zero, subject to specified boundary conditions. We choose to represent the magnetic field in terms of Clebsch variables in the form B = grad alpha x grad beta. These variables are constant on any field line so that each field line is labeled by the corresponding values of alpha and beta. When the field is described in this way, the most appropriate choice of boundary conditions is to specify the values of alpha and beta on the bounding surface. We show that such field configurations may be calculated by a magneto-frictional method. We imagine that the field lines move through a stationary medium, and that each element of magnetic field is subject to a frictional force parallel to and opposing the velocity of the field line. This concept leads to an iteration procedure for modifying the variables alpha and beta, that tends asymptotically towards the force-free state. We apply the method first to a simple problem in two rectangular dimensions, and then to a problem of cylindrical symmetry that was previously discussed by Barnes and Sturrock (1972). In one important respect, our new results differ from the earlier results of Barnes and Sturrock, and we conclude that the earlier article was in error.
Document ID
19870033191
Document Type
Reprint (Version printed in journal)
External Source(s)
Authors
Yang, W. H. (Stanford Univ. CA, United States)
Sturrock, P. A. (Stanford Univ. CA, United States)
Antiochos, S. K. (Stanford University CA, United States)
Date Acquired
August 13, 2013
Publication Date
October 1, 1986
Publication Information
Publication: Astrophysical Journal, Part 1
Volume: 309
ISSN: 0004-637X
Subject Category
ASTROPHYSICS
Report/Patent Number
AD-A179083
Funding Number(s)
CONTRACT_GRANT: NGL-05-020-272
CONTRACT_GRANT: N00014-85-K-0111
CONTRACT_GRANT: NAGW-92
CONTRACT_GRANT: NSF ATM-84-14380
Distribution Limits
Public
Copyright
Other