Linear Force-free Magnetic Fields and Coronal Models

Abstract

The mathematical properties of linear force-free fields generated by the Helmholtz equation are reviewed, and the solutions in terms of spherical, cartesian and cylindrical coordinate systems are discussed. When only the normal component of the field on a single (photospheric) surface is available as a boundary condition, the solutions are not niquely determined. If further conditions are imposed, solutions may be unique or multiple or may not exist. The