Forcefree Magnetic Fields: The Magnetofrictional Method
Abstract
The 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 magnetofrictional 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 forcefree 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.
 Publication:

The Astrophysical Journal
 Pub Date:
 October 1986
 DOI:
 10.1086/164610
 Bibcode:
 1986ApJ...309..383Y
 Keywords:

 Boundary Value Problems;
 ForceFree Magnetic Fields;
 Lorentz Force;
 Magnetic Field Configurations;
 Aerospace Environments;
 Boundary Conditions;
 Friction;
 Iteration;
 Velocity;
 Astrophysics;
 HYDROMAGNETICS