鬼面是二次通量最小化的吗？
Are ghost surfaces quadratic-flux-minimizing?
摘要：
通过磁岛的“几乎不变”环形表面的两个候选者，即二次通量最小化（QFMin）表面和鬼面，使用周期性伪轨道族（即作用不完全极值的路径）。与坐标相关的QFMin伪轨道是从修改的磁场获得的场线，并且鬼面伪轨道是通过在磁作用的最陡下降方向$\oint \vec{A}\cdot\mathbf{dl}$上移位闭合场线获得的。给出了鬼曲面的广义Hamilton定义，并将其特殊化为通常的Lagrange定义。引入了一个修正的Hamilton原理，它允许使用拉格朗日积分来计算QFMin伪轨道。数值计算表明，QFMin和拉格朗日鬼面给出了非常相似的结果，从一个可积的情况下扰动的混沌磁场，这是解释使用微扰建设的辅助极向角的QFMin和拉格朗日鬼面是相同的二阶。虽然在三维磁场线系统的背景下，这些概念是适用于定义几乎不变的环面在其他$1{1/2}$度的自由不可积拉格朗日/哈密顿系统。
英文摘要：
Two candidates for "almost-invariant" toroidal surfaces passing through magnetic islands, namely quadratic-flux-minimizing (QFMin) surfaces and ghost surfaces, use families of periodic pseudo-orbits (i.e. paths for which the action is not exactly extremal). QFMin pseudo-orbits, which are coordinate-dependent, are field lines obtained from a modified magnetic field, and ghost-surface pseudo-orbits are obtained by displacing closed field lines in the direction of steepest descent of magnetic action, $\oint \vec{A}\cdot\mathbf{dl}$. A generalized Hamiltonian definition of ghost surfaces is given and specialized to the usual Lagrangian definition. A modified Hamilton's Principle is introduced that allows the use of Lagrangian integration for calculation of the QFMin pseudo-orbits. Numerical calculations show QFMin and Lagrangian ghost surfaces give very similar results for a chaotic magnetic field perturbed from an integrable case, and this is explained using a perturbative construction of an auxiliary poloidal angle for which QFMin and Lagrangian ghost surfaces are the same up to second order. While presented in the context of 3-dimensional magnetic field line systems, the concepts are applicable to defining almost-invariant tori in other $1{1/2}$ degree-of-freedom nonintegrable Lagrangian/Hamiltonian systems.
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