|icc_2006_helicityupdate.pdf||2006-03-09 15:11:03||Michael Schaffer|
Physically Motivated and Mathematically Consistent Formulation of Magnetic Helicity and Its Evolution - 3
Author: Michael J Schaffer
Submitted: 2005-12-26 16:00:05
3550 General Atomics Court
San Diego, CA 92121-1
Magnetic helicity is a quantitative measure of the global topological linkage of a complete magnetic field B. Helicity conservation, injection, flow and/or transport are invoked in several MFE concepts, but poor formulations can be physically misleading. Many systems of interest have a time-dependent volume V(t) bounded by a translating and deforming closed surface S(t) that contains only part of the field. This work develops a physically interpretable and mathematically consistent formulation of magnetic helicity and its evolution that is valid in both simply and toroidally connected deforming volumes arbitrarily linked by external magnetic flux and penetrated by B. This is a continuation of work presented previously at the ICC (Madison, WI, 2004) and APS/DPP (Savannah, GA, 2004) meetings.
The physical content of this theory is the topological linkage and relative helicity enunciated by Berger & Field, but generalized from stationary simply connected volumes to deforming toroidally connected ones. Field continuity and jump conditions across the moving and deforming boundary are derived and applied to preserve gauge independence and physical content. Further physics insight into relative helicity and its evolution is gained by decomposing B into closed (does not penetrate S) and open (penetrates S) field components. New work includes careful attention to boundary conditions, completeness and solution uniqueness, especially in the field decomposition. The choice of a reference field for relative helicity, having considerable freedom, is used to simplify to a few physically interpretable terms. Helicity flow is calculated across a moving, deforming, penetrated, toroidally or simply connected surface. Helicity injection and transport are then discussed.
This work was supported by the U.S. Department of Energy under DE-FG03-99ER54522, DE-FG02-00ER54604, and by General Atomics.
 Berger & Field, J. Fluid Mech. 147, 133 (1984).
Areas of Interest: E1, E3