稳定自引力系统碰撞演化的Balescu-Lenard型动力学方程
A Balescu-Lenard type kinetic equation fot the collisional evolution of stable self-gravitating systems
摘要：
建立了稳定束缚自引力慢弛豫体系碰撞演化的动力学方程，该方程在组分数很大时成立。它解释了详细的动力学和自洽敷料碰撞粒子的集体引力相互作用，系统的不均匀性和不同组分的质量。在作用角空间中描述了单体分布函数的演化。碰撞算子用现有分布函数在任何给定时间所允许的集体响应函数来表示，并涉及共振运动中的粒子。一组方程描述的分布函数和潜在的耦合演化的球形系统。在均质极限下，虽然牺牲了对系统空间结构演化的描述，但保留了集体引力修整的影响，动力学方程简化为类似于等离子体物理的Balescu-Lenard方程的形式。
英文摘要：
A kinetic equation for the collisional evolution of stable, bound, self gravitating and slowly relaxing systems is established, which is valid when the number of constituents is very large. It accounts for the detailed dynamics and self consistent dressing by collective gravitational interaction of the colliding particles, for the system's inhomogeneity and for different constituent's masses. The evolution of the one-body distribution function is described in action angle space. The collision operators are expressed in terms of the collective response function allowed by the existing distribution functions at any given time and involve particles in resonant motions. The set of equations which describe the coupled evolution of the distribution functions and of the potential is derived for spherical systems. In the homogeneous limit, which sacrifices the description of the evolution of the spatial structure of the system, but retains the effects of collective gravitational dressing, the kinetic equation reduces to a form similar to the Balescu-Lenard equation of plasma physics.
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