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We present two generalized hybrid kinetic-Hall magnetohydrodynamics (MHD)models describing the interaction of a two-fluid bulk plasma, which consists ofthermal ions and electrons, with energetic, suprathermal ion populationsdescribed by Vlasov dynamics. The dynamics of the thermal components aregoverned by standard fluid equations in the Hall MHD limit with the electronmomentum equation providing an Ohm's law with Hall and electron pressure termsinvolving a gyrotropic electron pressure tensor. The coupling of the bulk,low-energy plasma with the energetic particle dynamics is accomplished throughthe current density (current coupling scheme; CCS) and the ion pressure tensorappearing in the momentum equation (pressure coupling scheme; PCS) in the firstand the second model, respectively. The CCS is a generalization of twowell-known models, because in the limit of vanishing energetic and thermal iondensities we recover the standard Hall MHD and the hybridkinetic-ions/fluid-electron model, respectively. This provides us with thecapability to study in a continuous manner the global impact of the energeticparticles in a regime extending from vanishing to dominant energetic particledensities. The noncanonical Hamiltonian structures of the CCS and PCS, whichcan be exploited to study equilibrium and stability properties through theenergy-Casimir variational principle, are identified. As a first applicationhere, we derive a generalized Hall MHD Grad--Shafranov--Bernoulli system fortranslationally symmetric equilibria with anisotropic electron pressure andkinetic effects owing to the presence of energetic particles using the PCS.

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