2016/02/29 by Manasvi Lingam, George Miloshevich, P. Morrison +1
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Classical mechanics #Combinatorics #Hamiltonian (control theory) #Lie algebra #Magnetic field #Magnetohydrodynamics #Mathematics #Nonlinear Waves and Solitons #Physics #Poisson bracket #Quantum mechanics #Solar and Space Plasma Dynamics #Theoretical physics #Topology (electrical circuits) #astro-ph.IM #math-ph #math.MP #physics.flu-dyn #physics.plasm-ph
paper · pdf · doi:10.1016/j.physleta.2016.05.024
9 pages, 0 figures; accepted for publication in Phys. Lett. A
arxiv created 2016/05/18 · openalex publication_date 2016/05/18 · arxiv updated 2016/06/03 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/06
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.