具有各向异性温度的流体模型的入门指南第2部分--动力学理论、Padé近似和Landau流体封闭
An introductory guide to fluid models with anisotropic temperatures Part 2 -- Kinetic theory, Padé approximants and Landau fluid closures
摘要：
在无碰撞流体模型指南的第2部分中，我们集中讨论朗道流体闭包。这些封闭是由哈米特和帕金斯开创的，并允许将无碰撞的朗道阻尼严格纳入流体框架。朗道阻尼是传统流体模型和无碰撞动力学理论的鲜明区别，也是通常流体模型不能收敛到动力学描述的主要原因，即使在长波低频极限下也是如此。我们首先简要介绍动力学理论，在那里我们详细讨论了等离子体色散函数$Z(ζ)$，和相关的等离子体响应函数$R(ζ)=1+ζZ(ζ)=-Z'(ζ)/2$。然后，我们考虑一个1D（静电）的几何形状，并作出重大努力，映射所有可能的朗道流体封闭，可以在四阶矩水平。这些封闭的平行时刻具有普遍的有效性，从最大的天体物理尺度下降到德拜长度，我们验证了它们的有效性，考虑的例子（质子和电子）朗道阻尼的离子声学模式，和电子朗道阻尼的朗缪尔模式。我们继续考虑高阶矩比四阶矩更高阶的一维闭包，正如第1部分所得出的结论，如果没有朗道流体闭包，这是不可能的。我们表明，它是可以重现线性朗道阻尼流体框架中的任何所需的精度，从而显示收敛的流体和无碰撞动力学的描述。然后，我们考虑一个3D（电磁）的几何结构中的gyrotropic（长波长低频率）的限制和地图的所有封闭，可在四阶矩水平。在附录A中，我们提供了$R(ζ)$直到8阶极点的Padé逼近的综合表，其中许多以解析形式给出。
英文摘要：
In Part 2 of our guide to collisionless fluid models, we concentrate on Landau fluid closures. These closures were pioneered by Hammett and Perkins and allow for the rigorous incorporation of collisionless Landau damping into a fluid framework. It is Landau damping that sharply separates traditional fluid models and collisionless kinetic theory, and is the main reason why the usual fluid models do not converge to the kinetic description, even in the long-wavelength low-frequency limit. We start with a brief introduction to kinetic theory, where we discuss in detail the plasma dispersion function $Z(ζ)$, and the associated plasma response function $R(ζ)=1+ζZ(ζ)=-Z'(ζ)/2$. We then consider a 1D (electrostatic) geometry and make a significant effort to map all possible Landau fluid closures that can be constructed at the 4th-order moment level. These closures for parallel moments have general validity from the largest astrophysical scales down to the Debye length, and we verify their validity by considering examples of the (proton and electron) Landau damping of the ion-acoustic mode, and the electron Landau damping of the Langmuir mode. We proceed by considering 1D closures at higher-order moments than the 4th-order, and as was concluded in Part 1, this is not possible without Landau fluid closures. We show that it is possible to reproduce linear Landau damping in the fluid framework to any desired precision, thus showing the convergence of the fluid and collisionless kinetic descriptions. We then consider a 3D (electromagnetic) geometry in the gyrotropic (long-wavelength low-frequency) limit and map all closures that are available at the 4th-order moment level. In the Appendix A, we provide comprehensive tables with Padé approximants of $R(ζ)$ up to the 8th-pole order, with many given in an analytic form.
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