Action Principles for Extended MHD Models

Understand

The general, non-dissipative, two-fluid model in plasma physics is Hamiltonian, but this property is sometimes lost or obscured in the process of deriving simplified (or reduced) two-fluid or one-fluid models from the two-fluid equations of motion.

• To ensure that the reduced models are Hamiltonian, we start with the general two-fluid action functional, and make all the approximations, changes of variables, and expansions directly within the action context.
• The resulting equations are then mapped to the Eulerian fluid 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, and electron MHD from a unified framework.