论文标题
恒星系统的Baescu-Lenard动力学方程的简单，启发式衍生
A simple, heuristic derivation of the Balescu-Lenard kinetic equation for stellar systems
论文作者
论文摘要
重力的不屏蔽性意味着恒星系统本质上是不均匀的。结果，恒星不会直线移动。这个明显的事实严重使恒星系统的动力学理论复杂化，因为位置和速度被证明是可描述恒星轨道的坐标差 - 相反，必须使用角度变量。此外，通过同时涉及许多恒星的集体相互作用（“极化”效应）可以增强或抑制星形簇和星系的缓慢松弛。这些集体效应也存在于等离子中。在这种情况下，它们是由Balescu-Lenard（BL）方程来解释的，这是速度空间中的动力学方程。最近，几位作者通过得出BL方程的角度概括来说明如何在恒星系统动力学理论中考虑不均匀性和集体效应。不幸的是，它们的派生是漫长而复杂的，涉及多个坐标变换，复杂平面中的轮廓积分等等。另一方面，Rostoker的叠加原理使人们可以假装一个远距离相互作用的$ N $体系统（例如等离子体或星形群）仅由无关的粒子组成，这些粒子是通过极化云“打扮”的。在本文中，我们使用Rostoker的原理为恒星系统的BL方程式提供了简单，直观的推导，该恒星系统比文献中的其他系统短得多。它还使我们能够直接将自我磨损动力学的BL图片与Chandrasekhar开创的不相关的Flybys的经典“两体松弛”理论联系起来。
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.
