gyrokinetic湍流中相空间结构的von Neumann熵
von Neumann entropy of phase space structures in gyrokinetic plasma turbulence
AI总结：
本文提出基于SVD的von Neumann熵方法，用于量化gyrokinetic湍流中相空间复杂性，并揭示了波数依赖性的相混合机制。
摘要：
我们引入一种数据驱动的诊断方法，将奇异值分解（SVD）与信息论熵相结合，以量化gyrokinetic湍流中扰动分布函数的相空间复杂性。将此框架应用于非线性通量管模拟，该模拟解决了由实空间中的傅里叶模式表示的离子分布函数的时间演化，我们定义了von Neumann熵（vNE）以分析速度空间结构。在波数空间中的全局调查揭示了速度空间结构中vNE随波数的依赖性变化：在低波数处vNE保持较低，但随着$ k_\perpρ_{t\mathrm{i}}\sim 1 $增加而上升。Hermite/Laguerre分解显示，在垂直方向（磁矩方向）的有限朗姆半径（FLR）相混合是活跃的。同时，对于$ k_\perpρ_{t\mathrm{i}} $的系统性增加与Hermite谱的展宽相关，表明增强的平行相混合（Landau共振）是观察到的波数依赖性的主要机制。这些结果表明，基于SVD的vNE提供了一种无需预定义基函数的紧凑的动能复杂性度量，能够实现gyrokinetic湍流中相混合过程波数依赖性的全局映射。
英文摘要：
We introduce a data-driven diagnostic that combines the singular value decomposition (SVD) with an information-theoretic entropy to quantify the phase-space complexity of perturbed distribution functions in gyrokinetic turbulence. Applying this framework to nonlinear flux-tube simulations that solve the time evolution of the ion distribution function represented by Fourier modes with the wavenumber for real space, we define the von Neumann entropy (vNE) to analyze the velocity-space structure. A global survey in the wavenumber space reveals a wavenumber-dependent variation of the vNE in velocity-space structure: the vNE remains low at low wavenumber but increases across $k_\perpρ_{t\mathrm{i}}\sim 1$. Hermite/Laguerre decompositions revealed that the finite Larmor radius (FLR) phase mixing in the perpendicular (magnetic-moment) direction is active. Simultaneously, the systematic increase in vNE for $k_\perpρ_{t\mathrm{i}}$ correlates with the broadening of the Hermite spectrum, suggesting enhanced parallel phase mixing (Landau resonance) as the primary mechanism for the observed wave number dependence. These results demonstrate that the SVD-based vNE provides a compact measure of kinetic complexity without assuming a predefined basis and enables a global mapping of its wavenumber dependence of phase-mixing processes in gyrokinetic turbulence.
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