Hamiltonian kinetic-Hall magnetohydrodynamics with fluid and kinetic ions in the current and pressure coupling schemes

We present two generalized hybrid kinetic-Hall magnetohydrodynamics (MHD) models describing the interaction of a two-fluid bulk plasma, which consists thermal ions and electrons, with energetic, suprathermal ion populations described by Vlasov dynamics. The dynamics components are governed standard fluid equations in Hall MHD limit electron momentum equation providing an Ohm's law pressure terms involving gyrotropic tensor. coupling bulk, low-energy plasma energetic particle is accomplished through current density (current scheme; CCS) tensor appearing (pressure PCS) first second model, respectively. CCS generalization well-known models, because vanishing densities we recover kinetic-ions/fluid-electron This provides us capability to study continuous manner global impact particles regime extending from dominant densities. noncanonical Hamiltonian structures PCS, can be exploited equilibrium stability properties energy-Casimir variational principle, identified. As application here, derive Grad--Shafranov--Bernoulli system for translationally symmetric equilibria anisotropic kinetic effects owing presence using PCS.