Concomitant Hamiltonian and topological structures of extended magnetohydrodynamics [Cross-Listing]

The paper describes the unique geometric properties of ideal magnetohydrodynamics (MHD), and demonstrates how such features are inherited by extended MHD models, which incorporate two-fluid effects. The helicities and other geometric expressions for these models are presented in a topological context, emphasizing their universal features. Some of the results presented include: the generalized Kelvin circulation theorems, the existence of two Lie-dragged 2-forms, and two concomitant helicities (which can be studied via the Jones polynomial from 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.