解冻Casimir不变量：引起禁戒不稳定性的奇异扰动
Unfreezing Casimir invariants: singular perturbations giving rise to forbidden instabilities
摘要：
流体和等离子体的无限维力学可以表述为欧拉变量相空间上的“非正则”哈密顿系统。奇异的泊松括号运营商产生奇异的卡西米尔元素，叶状相空间，施加拓扑约束的动力学。在这里，我们提供了一个物理解释的Casimir元素为\emph{adiabatic invariants} --在粗粒化微观角度变量，我们得到了一个宏观层次上的分离的作用变量成为绝热不变量。在反射时，卡西米尔元素可以通过恢复相应的角度变量而成为\emph{unfrozen};这样的自由度的增加被公式化为\emph{singular perturbation}。作为一个例子，我们提出了一个规范化的泊松括号运营商的线性化磁流体力学方程的共振奇异性，通过该理想的障碍（共振Casimir元素）约束的动态是解冻，引起撕裂模式不稳定性。
英文摘要：
The infinite-dimensional mechanics of fluids and plasmas can be formulated as "noncanonical" Hamiltonian systems on a phase space of Eulerian variables. Singularities of the Poisson bracket operator produce singular Casimir elements that foliate the phase space, imposing topological constraints on the dynamics. Here we proffer a physical interpretation of Casimir elements as \emph{adiabatic invariants} ---upon coarse graining microscopic angle variables, we obtain a macroscopic hierarchy on which the separated action variables become adiabatic invariants. On reflection, a Casimir element may be \emph{unfrozen} by recovering a corresponding angle variable; such an increase in the number of degrees of freedom is, then, formulated as a \emph{singular perturbation}. As an example, we propose a canonization of the resonant-singularity of the Poisson bracket operator of the linearized magnetohydrodynamics equations, by which the ideal obstacle (resonant Casimir element) constraining the dynamics is unfrozen, giving rise to a tearing-mode instability.
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