静电分析器非线性轨迹的Lie代数分析

介绍了Lie代数的方法，用Lie代数方法分析了静电分析器对束流传输过程的非线性影响，其计算结果分析到三级近似. 首先给出了静电分析器的哈密顿函数，然后将哈密顿函数展开为齐次多项式的和，再求Lie映射，最后得到粒子轨迹各级近似解.

Nonlinear Analysis for the Electrostatic Analyzers with Lie Algebraic Methods

With the Lie algebraic methods,the charged particle trajectories in electrostatic analyzers are analyzed and the third order solutions obtained. In this paper,we briefly describe the Lie algebraic methods and the procedures of calculating the nonlinear orbits. The procedures are:first,set up the Hamiltonian; then expand the Hamiltonian into a sum of homogeneous polynomials of different degrees; next,calculate the Lie map associating to the Hamiltonian; finally,apply the Lie map on the particle initial coordinates in the phase space,and obtain the particle nonlinear trajectories of the first order,the second order,and the third order approximations respectively. Higher orders solutions could be obtained if needed.