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

TL;DR

This paper introduces two advanced hybrid kinetic-Hall MHD models that incorporate energetic particles and analyze their effects on plasma equilibrium and stability, extending existing models with new coupling schemes and Hamiltonian structures.

Contribution

The paper develops two generalized hybrid kinetic-Hall MHD models with current and pressure coupling schemes, including Hamiltonian structures and a generalized equilibrium system.

Findings

Models recover standard Hall MHD and hybrid models in specific limits.

Hamiltonian structures enable stability analysis via energy-Casimir methods.

Derived a generalized equilibrium system accounting for energetic particles and anisotropic pressure.

Abstract

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