Force-Free Magnetic Fields: The Magneto-Frictional Method,
STANFORD UNIV CA CENTER FOR SPACE SCIENCE AND ASTROPHYSICS
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The problem under discussion is that of calculating magnetic field configurations in which the Lorentz force jxB 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 alphs 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. 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 toward the force free state. Apply the method first to a simple problem in two rectangular dimensions and then to a problem of cylindrical symmetry. In one important respect, the new results differ from the earlier results. It is concluded that the earlier article was in error. Keywords Hydromagnetics Reprints.
- Electricity and Magnetism