Energy stability analysis for a hybrid fluid-kinetic plasma model

TL;DR

This paper analyzes the energy stability of a Hamiltonian hybrid fluid-kinetic plasma model, deriving explicit conditions for stability using the energy-Casimir method, which imply both linear and nonlinear stability.

Contribution

It provides the first Hamiltonian structure and explicit stability criteria for a hybrid fluid-kinetic plasma model in two dimensions.

Findings

Derived explicit stability conditions using the energy-Casimir method.

Established the Hamiltonian structure and Casimir invariants for the model.

Suggested nonlinear stability based on spectral analysis.

Abstract

In plasma physics, a hybrid fluid-kinetic model is composed of a magnetohydrodynamics (MHD) part that describes a bulk fluid component and a Vlasov kinetic theory part that describes an energetic plasma component. While most hybrid models in the plasma literature are non-Hamiltonian, this paper investigates a recent Hamiltonian variant in its two-dimensional configuration. The corresponding Hamiltonian structure is described along with its Casimir invariants. Then, the energy-Casimir method is used to derive explicit sufficient stability conditions, which imply a stable spectrum and suggest nonlinear stability.