Hamiltonian formulations for perturbed dissipationless plasma equations

Abstract

The Hamiltonian formulations for the perturbed Vlasov-Maxwell equations and the perturbed ideal magnetohydrodynamics (MHD) equations are expressed in terms of the perturbation derivative $\partial \mathcal{F}/\partial \epsilon \equiv [\mathcal{F},\mathcal{S}]$ of an arbitrary functional ${\cal F}[\vbψ]$ of the Vlasov-Maxwell fields $\vbψ = ({\sf f},{\bf E},{\bf B})$ or the ideal MHD fields $\vbψ = (ρ,{\bf u},s,{\bf B})$, which are assumed to depend continuously on the (dimensionless) perturbation parameter $\epsilon$. Here, $[,]$ denotes the functional Poisson bracket for each set of plasma equations and the perturbation {\it action} functional $\mathcal{S}$ is said to generate dynamically accessible perturbations of the plasma fields. The new Hamiltonian perturbation formulation introduces a framework for functional perturbation methods in plasma physics and highlights the crucial roles played by polarization and magnetization in Vlasov-Maxwell and ideal MHD perturbation theories. One application considered in this paper is a formulation of plasma stability that guarantees dynamical accessibility and leads to a natural generalization to higher-order perturbation theory.

15 pages

References in corpus (2)

• A general theory for gauge-free lifting
• Variational mean-fluctuation splitting and drift-fluid models

Cited by in corpus (3)

• Hamiltonian reduction of Vlasov-Maxwell to a dark slow manifold
• Hamiltonian structure of the guiding-center Vlasov-Maxwell equations
• A Tale of Two Polarization Paradoxes I: the Diamagnetic Polarization Paradox