Unified Theory of Ghost and Quadratic-Flux-Minimizing Surfaces
Unified Theory of Ghost and Quadratic-Flux-Minimizing Surfaces
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鬼影和二次通量最小化曲面的统一理论
DOI：
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发表时间：
2010
期刊：
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通讯作者：
A. M. Gibson
中科院分区：
文献类型：
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作者：
R. Dewar;S. Hudson;A. M. Gibson
给出了鬼面（由作用梯度流定义的曲面）的广义Hamilton定义，并将其专用于通常的拉格朗日定义。数值计算表明，对于作用角坐标系中弱扰动的混沌磁场，未校正的二次通量极小化（QFMin）和拉格朗日鬼面给出了非常相似的结果，描述为$L = L_0 + L_1$，其中$L_0（dot{ heta}）$（with $dot{ heta}$表示$d heta/dzeta$）是可积的场线拉格朗日量，并且$zeta $是微扰参数。这是解释使用的辅助极向角$θ $，纠正QFMin表面，使他们也是鬼面的扰动建设。校正后的表面和未校正的表面之间的差异为O（ε ^2），这解释了观测到的差异很小。鬼面的另一种定义也被引入，基于动作梯度流在$Theta$，这似乎有上级属性时，统一与QFMin表面。
A generalized Hamiltonian definition of ghost surfaces (surfaces defined by an action-gradient flow) is given and specialized to the usual Lagrangian definition. Numerical calculations show uncorrected quadratic-flux-minimizing (QFMin) and Lagrangian ghost surfaces give very similar results for a chaotic magnetic field weakly perturbed from an integrable case in action-angle coordinates, described by $L = L_0 + epsilon L_1$, where $L_0(dot{ heta})$ (with $dot{ heta}$ denoting $d heta/dzeta$) is an integrable field-line Lagrangian and $epsilon$ is a perturbation parameter. This is explained using a perturbative construction of the auxiliary poloidal angle $Theta$ that corrects QFMin surfaces so they are also ghost surfaces. The difference between the corrected and uncorrected surfaces is $O(epsilon^2)$, explaining the observed smallness of this difference. An alternative definition of ghost surfaces is also introduced, based on an action-gradient flow in $Theta$, which appears to have superior properties when unified with QFMin surfaces.