标题： 带电粒子运动的逐次逼近方法 显示英文标题

标题： Successive approximations for charged particle motion

摘要： 单粒子在电子显微镜、离子或电子光刻仪器、粒子加速器和粒子光谱仪中的动力学由弱非线性常微分方程描述。 因此，通常先求解运动方程的线性部分，然后通过迭代方法依次找到非线性效应。 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器件的粒子传输计算的简化。 由于射影法的简单结构，H. Rose和他的小组发现了许多巧妙的显微和光刻装置。 在加速器物理领域，射影法从未流行过。 因此，我将推广射影法，并从加速器物理界非常熟悉的哈密顿量出发推导它。 随着高能极化电子束的出现和高能质子束计划的提出，自旋运动中的非线性效应在高能加速器中变得重要。 我将引入一种对带电粒子耦合自旋和轨道运动中的非线性效应的逐次逼近方法，这种方法类似于射影法在纯轨道运动中产生的某些简化。 显示英文摘要

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.