Journal
PHYSICS LETTERS A
Volume 380, Issue 31-32, Pages 2400-2406Publisher
ELSEVIER
DOI: 10.1016/j.physleta.2016.05.024
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Funding
- NSF [AGS-1338944]
- DOE [DE-AC02-09CH-11466]
- DOE Office of Fusion Energy Sciences [DE-FG02-04ER-54742]
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The paper describes the unique geometric properties of ideal magnetohydrodynamics (MHD), and demonstrates how such features are inherited by extended MHD, viz. models that incorporate two-fluid effects (the Hall term and electron inertia). The generalized helicities, and other geometric expressions for these models are presented in a topological context, emphasizing their universal facets. Some of the results presented include: the generalized Kelvin circulation theorems; the existence of two Lie dragged 2-forms; and two concomitant helicities that can be studied via the Jones polynomial, which is widely utilized in Chern-Simons theory. The ensuing commonality is traced to the existence of an underlying Hamiltonian structure for all the extended MHD models, exemplified by the presence of a unique noncanonical Poisson bracket, and its associated energy. (C) 2016 Elsevier B.V. All rights reserved.
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