Forcefree magnetic fields, curl eigenfunctions, and the sphere in transform space, with applications to fluid dynamics and electromagnetic theory
Abstract
The mathematical foundation of a new description of force free magnetic fields (FFMF's) is given, using Moses' curl eigenfunctions, in preparation for an investigation of solar magnetic clouds and their interaction with the Earth's magnetosphere and perturbation of the radiation belts. Constantalpha FFMF's are defined completely on the unit hemisphere in Fourier transform space. This reduces the threedimensional physical space problem to a twodimensional transform space problem. A scheme for classifying these fields by the dimensionality, symmetry, and complexity of their supporting sets in transform space is sketched. The fields corresponding to the simplest 0, 1, and 2dimensional transform sphere sets are exhibited. Four applications illustrate the technique: (1) the constantalpha FFMF vector potential is shown to be unimodal; (2) alpha is identified with a normalized magnetic helicity; (3) the helicity hierarchy for Trkalian fluids is shown to depend only on alpha and the mean kinetic energy; and (4) the Maxwell equations are reduced to an FFMF problem, providing a new point of view for electromagnetic theory. Speculative applications to turbulence and the laboratory modeling of astrophysical FFMF's are mentioned. Future directions for development are indicated, and extensive connections to related work are documented.
 Publication:

Interim Report Phillips Lab
 Pub Date:
 January 1993
 Bibcode:
 1993phil.reptQ....M
 Keywords:

 Astrophysics;
 Earth Magnetosphere;
 Eigenvectors;
 Field Theory (Physics);
 ForceFree Magnetic Fields;
 Fourier Transformation;
 Radiation Belts;
 Spheres;
 Turbulence Models;
 Boundary Value Problems;
 Cosmic Rays;
 Magnetic Clouds;
 Magnetic Fields;
 Maxwell Equation;
 Perturbation;
 Solar Wind;
 Astrophysics