Common Hamiltonian and topological properties of extended MHD models

Extended MHD, a 1-fluid model endowed with 2-fluid effects (electron inertia and Hall drift) possesses a Hamiltonian structure [1-4]. This formulation is described, as it unifies different classes of extended MHD models (including those that have mutually exclusive effects) [2]. The unification is further highlighted by showing that these models possess common topological invariants that are the generalizations of the fluid/magnetic helicity [3]. They can be expressed naturally in a knot-theoretic framework via the Jones polynomial by exploiting techniques from Chern-Simons theory. It is also shown that extended MHD exhibits other commonalities such as: generalized Kelvin circulation theorems, and the existence of two Lie-dragged 2-forms closely connected with generalizations of the fluid vorticity. \\ \noindent [1] H. M. Abdelhamid, Y. Kawazura & Z. Yoshida, J. Phys. A, 48, 235502 (2015) \\ \noindent [2] M. Lingam, P. J. Morison & G. Miloshevich, Phys. Plasmas, 22, 072111 (2015) \\ \noindent [3] M. Lingam, G. Miloshevich & P. J. Morrison, Phys. Lett. A, 380, 2400 (2016) \\ \noindent[4] E. C. D'Avignon, P. J. Morrison & M. Lingam, Phys. Plasmas, 23, 062101 (2016) \\