Hamiltonian dynamics and stability analysis of neutral electro-magnetic fluids with induction, Phys

The Lie-Poisson Hamiltonian structure of the special-relativistic electromagnetic fluid equations i derived. This Hamilto-nian structure provides ynthesis and insight leading to new conservation laws and stability conditions for the equilibrium solutions. A corollary of the stability results generalizes Rayleigh's inflectional instability criterion for ideal incompressible fluids to the present case. Another alternative, Hamiltonian formulation of relativistic electromagnetic fluid dynamics is constructed systematically via Lie-algebraic considerations of the Poisson bracket. (In particular, elativistic magnetohydrody-namics emerges naturally from these considerations.) The nonrelativistic limits of these two formulations are also determined and are shown to be regular and to preserve the corresponding Lie-Poisson structures. 1