Energy-Casimir stability of hybrid Vlasov-MHD models

TL;DR

This paper analyzes the stability of hybrid Vlasov-MHD models for plasma, using Hamiltonian structures and energy-Casimir methods to derive stability conditions and equilibrium equations, including a generalized Grad-Shafranov equation.

Contribution

It compares two planar Vlasov-MHD models' stability properties using Hamiltonian structures and develops a generalized Grad-Shafranov equation for one model.

Findings

Stability conditions are derived for hybrid Vlasov-MHD models.

Kinetic particle effects influence classical MHD stability.

Equilibrium equations are obtained from a variational principle.

Abstract

Different variants of hybrid kinetic-fluid models are considered for describing the interaction of a bulk fluid plasma obeying MHD and an energetic component obeying a kinetic theory. Upon using the Vlasov kinetic theory for energetic particles, two planar Vlasov-MHD models are compared in terms of their stability properties. This is made possible by the Hamiltonian structures underlying the considered hybrid systems, whose infinite number of invariants makes the energy-Casimir method effective for determining stability. Equilibrium equations for the models are obtained from a variational principle and in particular a generalized hybrid Grad-Shafranov equation follows for one of the considered models. The stability conditions are then derived and discussed with particular emphasis on kinetic particle effects on classical MHD stability.