带电粒子运动的逐次逼近
Successive approximations for charged particle motion
摘要：
电子显微镜、离子或电子光刻仪器、粒子加速器和粒子光谱仪中的单粒子动力学是用弱非线性常微分方程描述的。因此，通常求解运动方程的线性部分，然后用迭代法依次求解非线性效应。当使用合适的计算方法时，这些方程的哈密顿性质可以导致通过光学设备的粒子输运的简化计算。H. Rose和他的小组由于程函方法的结构简单。在加速器物理学领域，程函法从未流行过。因此，在这里我将推广程函方法，并从加速器物理界非常熟悉的哈密顿量推导出它。随着高能极化电子束的出现和高能质子束的计划，自旋运动中的非线性效应在高能加速器中变得越来越重要。我将介绍一个逐次逼近的非线性效应耦合的自旋和轨道运动的带电粒子，类似于一些简化的纯轨道运动的程函方法。
英文摘要：
Single particle dynamics in electron microscopes, ion or electron lithographic instruments, particle accelerators, and particle spectrographs is described by weakly nonlinear ordinary differential equations. Therefore, the linear part of the equation of motion is usually solved and the nonlinear effects are then found in successive order by iteration methods. A Hamiltonian nature of these equations can lead to simplified computations of particle transport through an optical device when a suitable computational method is used. Many ingenious microscopic and lithographic devices were found by H. Rose and his group due to the simple structure of the eikonal method. In the area of accelerator physics the eikonal method has never become popular. Here I will therefore generalize the eikonal method and derive it from a Hamiltonian quite familiar to the accelerator physics community. With the event of high energy polarized electron beams and plans for high energy proton beams, nonlinear effects in spin motion have become important in high energy accelerators. I will introduce a successive approximation for the nonlinear effects in the coupled spin and orbit motion of charged particles which resembles some of the simplifications resulting from the eikonal method for the pure orbit motion.
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