The spherical curl transform of a linear force-free magnetic field Available to Purchase

The description of linear force-free magnetic fields in terms of the Moses eigenfunctions of the curl operator begun previously is here completed by the derivation of a general expression for the field’s spherical curl transform. This enables the transform space representation of a given field to be determined and compared with that of other fields, assisting the analysis and classification of this type of magnetic field as well as providing a basis for generalization. The result obtained gives the spherical curl transform as a weighted projection of the vector Radon transform of the field on the appropriate curl eigenvector. The process is exemplified by the determination of the transforms of three fields: the simplest force-free magnetic field, and the Lundquist and classical spheromak fields. The latter two are both of interest as models of the magnetic fields of solar magnetic clouds, while the classical spheromak field is relevant to the design of nuclear fusion reactors as well. The use of the transform in generalizing the Lundquist field is briefly discussed. As before, all results apply equally well to the description of the Trkalian subset of Beltrami fields in fluid dynamics.