Action principles for extended magnetohydrodynamic models

The general, non-dissipative, two-fluid model in plasma physics is, but this property is sometimes lost or obscured in the process of simplified (or reduced) two-fluid or one-fluid models from the-fluid equations of motion. To ensure that the reduced models are, we start with the general two-fluid action functional, and make the approximations, changes of variables, and expansions directly within action context. The resulting equations are then mapped to the Eulerian variables using a novel nonlocal Lagrange-Euler map. Using this method, recover L\\"{u}st's general two-fluid model, extended MHD, Hall MHD, and MHD from a unified framework. The variational formulation allows us to Noether's theorem to derive conserved quantities for each symmetry of the.