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 $\vb{\psi} = (f,{\bf E},{\bf B})$ 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 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.

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扰动无耗散等离子体方程的哈密顿公式

微扰 Vlasov-Maxwell 方程和微扰理想磁流体动力学 (MHD) 方程的哈密顿公式表示为微扰导数 $\partial{\cal F}/\partial\epsilon \equiv [{\cal F}, { \cal S}]$ 的 Vlasov-Maxwell 域的任意泛函 ${\cal F}[\vb{\psi}]$ $\vb{\psi} = (f,{\bf E},{\ bf B})$ 或理想的 MHD 场 $\vb{\psi} = (\rho,{\bf u},s,{\bf B})$，假设它们连续依赖于（无量纲）扰动参数 $\epsilon$。这里，$[\;,\;]$ 表示每组等离子体方程的泛函泊松括号，并且扰动 {\it action} 泛函 ${\cal S}$ 被称为产生等离子体场的动态可访问扰动。