Common Hamiltonian structure and concomitant topological invariants for extended magnetohydrodynamics models

Extended magnetohydrodynamics (XMHD) includes 2-fluid effects such as electron inertia and the Hall drift absent in ideal MHD. Hamiltonian structure of the XMHD models (Hall MHD, inertial MHD [3] and full XMHD) is presented [1]. Existence of elegant variable transformations that map every XMHD model to a common noncanonical Poisson bracket is highlighted [2]. The bracket is used to derive the existence of two unique helicities (Casimir invariants) for these models, each of which exhibits close similarities with the magnetic and fluid helicities [1,2] - this is highly significant as the latter are important topological invariants. The Lagrangian origins of the helicities and variable transforms, and avenues for future work are outlined.\\[4pt] [1] H.M.~Abdelhamid, Y. Kawazura \& Z. Yoshida, J.~Phys.~A {\bf48}, 235502 (2015) \\[0pt] [2] M.~Lingam, P.J.~Morrison \& G.~Miloshevich, Phys.~Plasmas {\bf22}, 072111 (2015) \\[0pt] [3] M.~Lingam, P.J.~Morrison \& E.~Tassi, Phys.~Lett.~A {\bf379}, 570 (2015)