  The Hamiltonian formulations for the perturbed Vlasov-Maxwell equations and
the perturbed ideal magnetohydrodynamics (MHD) equations are expressed in terms
of the perturbation derivative $\partial{\cal F}/\partial\epsilon \equiv [{\cal
F}, {\cal S}]$ of an arbitrary functional ${\cal F}[\vb{\psi}]$ of the
Vlasov-Maxwell fields $\vb{\psi} = ({\sf f},{\bf E},{\bf B})$ or the ideal MHD
fields $\vb{\psi} = (\rho,{\bf u},s,{\bf B})$, 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 ${\cal S}$ 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.
