A NEW DESCRIPTION OF FORCE-FREE MAGNETIC-FIELDS

The Moses curl eigenfunctions are used to describe linear force-free magnetic fields, enabling a proof that such fields are defined entirely by the value of their curl transform on the unit hemisphere in transform space. This change of viewpoint suggests an orderly approach to the exploration and classification of the properties of such fields, which is briefly sketched. The simplest force-free fields defined on zero-, one-, and two-dimensional sets on the transform sphere are exhibited, and the possibility of fields with fractal support sets suggested. Connections with other mathematical descriptions are pointed out, as well as several promising directions for further exploration. All results apply equally well to the description of the Trkalian subset of Beltrami fields in fluid dynamics. © 1995 American Institute of Physics.