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

Action Principles for Extended MHD Models