Energy-Casimir stability of hybrid Vlasov-MHD models

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.

arXiv comment15 pages; no figures

References in corpus (9)

• Hybrid Vlasov-MHD models: Hamiltonian vs. non-Hamiltonian
• Hamiltonian magnetohydrodynamics: symmetric formulation, Casimir invariants, and equilibrium variational principles
• Hamiltonian approach to hybrid plasma models
• Hamiltonian Magnetohydrodynamics: Lagrangian, Eulerian, and Dynamically Accessible Stability - Theory
• Euler-Poincaré formulation of hybrid plasma models
• Ideal magnetohydrodynamic equilibria with helical symmetry and incompressible flows
• Singular Casimir Elements of the Euler Equation and Equilibrium Points
• Stability of compressible reduced magnetohydrodynamic equilibria - analogy with magnetorotational instability
• Energy stability analysis for a hybrid fluid-kinetic plasma model

Cited by in corpus (10)

• A Hamiltonian Five-Field Gyrofluid Model
• Hamiltonian kinetic-Hall Magnetohydrodynamics with fluid and kinetic ions in the current and pressure coupling schemes
• Existence of Global Weak Solutions to a Hybrid Vlasov-MHD Model for Magnetized Plasmas
• Linear stability of magnetic vortex chains in a plasma in the presence of equilibrium electron temperature anisotropy
• Complex fluid models of mixed quantum-classical dynamics
• Hamiltonian Structure and Nonlinear Stability of Steady Solutions of the Generalized Hasegawa-Mima Equation for Drift Wave Turbulence in Curved Magnetic Fields
• Axisymmetric hybrid Vlasov equilibria with applications to tokamak plasmas
• Guiding Center Derivation of the Generalized Hasegawa-Mima Equation for Drift Wave Turbulence in Curved Magnetic Fields
• Global well-posedness and decay rates of strong solutions to the incompressible Vlasov-MHD system
• A Reduced Ideal MHD System for Nonlinear Magnetic Field Turbulence in Plasmas with Approximate Flux Surfaces