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 ∂F/∂ǫ ≡ [F, S] of an arbitrary functional F[ψ] of the Vlasov-Maxwell fields ψ = (f, E, B) or the ideal MHD fields ψ = (ρ, u, s, B), which are assumed to depend continuously on the (dimensionless) perturbation parameter ǫ. Here, [ , ] denotes the functional Poisson bracket for each set of plasma equations and the perturbation action functional S is said to generate dynamically accessible perturbations of the plasma fields. The new Hamiltonian perturbation formulation introduces the framework for the application of functional Lie-transform perturbation methods in plasma physics and highlights the crucial roles played by polarization and magnetization in Vlasov-Maxwell and ideal MHD perturbation theories.