Lagrangian structure of hydrodynamic plasma models and conservation laws

The Lagrangian structure of hydrodynamic plasma models (the multifluid plasma model, the Hall MHD model, and the electron MHD model) is studied. The conservation laws for these models are derived in a general form with the help of Noether's theorem. Each of these models is shown to admit symmetry transformations under which the energy, momentum, and angular momentum are invariant. These models also admit the relabeling symmetry, which ensures the conservation of the averaged components of the generalized momentum. For the electron MHD equations, the symmetry group obtained is proved to be exhaustive in the class of the first-order Lie-Bauecklund symmetries. It is shown that an infinite set of kinematic invariants of motion (Casimirs) can be readily singled out by the transition to the Lagrangian basis