# Accession Number:

## ADA265805

# Title:

## Force-Free Magnetic Fields, Curl Eigenfunctions, and the Sphere in Transform Space, With Applications to Fluid Dynamics and Electromagnetic Theory

# Descriptive Note:

## Interim rept.,

# Corporate Author:

## PHILLIPS LAB HANSCOM AFB MA

# Personal Author(s):

# Report Date:

## 1993-01-08

# Pagination or Media Count:

## 33.0

# Abstract:

The mathematical foundation of a new description of force free magnetic fields FFMFs is given using Moses curl eigenfunctions, in preparation for an investigation of solar magnetic clouds and their interaction with the Earths magnetosphere and perturbation of the radiation belts. Constant-alpha FFMFs are defined completely on the unit hemisphere in Fourier transform space, reducing the three-dimensional physical space problem to a two dimensional 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 2-dimensional transform sphere sets are exhibited. Four applications illustrate the technique 1 the constant-alpha 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 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 FFMFs are mentioned. Future directions for development are indicated, and extensive connections to related work are documented.

# Descriptors:

# Subject Categories:

- Electricity and Magnetism