Hybrid fluid-kinetic Hall Magnetohydrodynamics: Hamiltonian structure and equilibrium equations*

We present two hybrid kinetic-Hall MHD models describing the interaction of a two-fluid plasma consisting of thermal ions and massless electrons with energetic ion populations described by Vlasov dynamics. The coupling of the bulk plasma with the energetic particle component is accomplished through the current density (Current Coupling Scheme-CCS) and the ion pressure tensor appearing in the momentum equation (Pressure Coupling Scheme-PCS) in the first and the second model, respectively. The noncanonical Hamiltonian structures of the aforementioned models,  which can be employed  to study equilibrium and stability properties via the energy-Casimir variational principle, are identified. As a first application here, we derive a generalized Hall MHD Grad-Shafranov-Bernoulli system that governs translationally symmetric equilibria with anisotropic electron pressure and energetic particle contributions in the PCS.