论文标题
哈密顿的扰动无耗散等离子体方程的配方
Hamiltonian formulations for perturbed dissipationless plasma equations
论文作者
论文摘要
扰动的Vlasov-Maxwell方程和受扰动的理想磁性水力动力学（MHD）方程的Hamiltonian配方以扰动派生$ \ partial $ \ partial {\ cal f}/\ cal f}/\partialε\ equiv [ vlasov-maxwell字段的f} [\vbψ] $ （无量纲）扰动参数$ε$。在这里，$ [\;，\;] $表示每组等离子方程的功能泊松支架，并且呈扰动{\ it Action}函数$ {\ cal s} $表示会生成血浆场的动态可访问的可动扰动。新的哈密顿扰动配方为等离子体物理学中的功能扰动方法引入了一个框架，并突出了Vlasov-Maxwell和Ideal MHD MHD扰动理论中极化和磁化所发挥的关键作用。本文考虑的一种应用是血浆稳定性的一种表述，可确保动态可访问性并导致对高阶扰动理论的自然概括。
The Hamiltonian formulations for the perturbed Vlasov-Maxwell equations and the perturbed ideal magnetohydrodynamics (MHD) equations are expressed in terms of the perturbation derivative $\partial{\cal F}/\partialε\equiv [{\cal F}, {\cal S}]$ 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 $ε$. 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.
