静电分析器非线性轨迹的Lie代数分析(英文)  

Nonlinear Analysis for the Electrostatic Analyzers with Lie Algebraic Methods

作　　者：李金海[1] 吕建钦[1] 

机构地区：[1]北京大学重离子物理研究所,北京100871

出　　处：《高能物理与核物理》2005年第7期695-699,共5页High Energy Physics and Nuclear Physics

摘　　要：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.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.

关 键 词：静电分析器 代数分析 Lie代数方法 非线性影响 哈密顿函数 齐次多项式 Lie映射 传输过程 三级近似 计算结果 函数展开 粒子轨迹 近似解 

分 类 号：O572[理学—粒子物理与原子核物理]