The unshielded nature of gravity means that stellar systems are inherently inhomogeneous. As a result, stars do not move in straight lines. This obvious fact severely complicates the kinetic theory of stellar systems because position and velocity turn out to be poor coordinates with which to describe stellar orbits - instead, one must use angle-action variables. Moreover, the slow relaxation of star clusters and galaxies can be enhanced or suppressed by collective interactions ('polarisation' effects) involving many stars simultaneously. These collective effects are also present in plasmas; in that case, they are accounted for by the Balescu-Lenard (BL) equation, which is a kinetic equation in velocity space. Recently several authors have shown how to account for both inhomogeneity and collective effects in the kinetic theory of stellar systems by deriving an angle-action generalisation of the BL equation. Unfortunately their derivations are long and complicated, involving multiple coordinate transforms, contour integrals in the complex plane, and so on. On the other hand, Rostoker's superposition principle allows one to pretend that a long-range interacting $N$-body system, such as a plasma or star cluster, consists merely of uncorrelated particles that are 'dressed' by polarisation clouds. In this paper we use Rostoker's principle to provide a simple, intuitive derivation of the BL equation for stellar systems which is much shorter than others in the literature. It also allows us to straightforwardly connect the BL picture of self-gravitating kinetics to the classical 'two-body relaxation' theory of uncorrelated flybys pioneered by Chandrasekhar.

中文翻译：

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恒星系统的 Balescu-Lenard 动力学方程的简单启发式推导

引力的非屏蔽性质意味着恒星系统本质上是不均匀的。因此，恒星不会沿直线运动。这一显而易见的事实使恒星系统的动力学理论严重复杂化，因为位置和速度被证明是描述恒星轨道的不良坐标——相反，人们必须使用角作用变量。此外，星团和星系的缓慢弛豫可以通过同时涉及许多恒星的集体相互作用（“极化”效应）来增强或抑制。这些集体效应也存在于等离子体中。在这种情况下，它们由 Balescu-Lenard (BL) 方程解释，该方程是速度空间中的动力学方程。最近，几位作者展示了如何通过推导出 BL 方程的角作用推广来解释恒星系统动力学理论中的不均匀性和集体效应。不幸的是，它们的推导又长又复杂，涉及多个坐标变换、复平面中的轮廓积分等。另一方面，Rostoker 的叠加原理允许人们假装远程相互作用的 $N$ 体系统，例如等离子体或星团，仅由被偏振云“修饰”的不相关粒子组成。在本文中，我们使用 Rostoker 原理为恒星系统提供了一个简单、直观的 BL 方程推导，该方程比文献中的其他方程短得多。