高能物理与核物理
高能物理與覈物理
고능물리여핵물리
HIGH ENERGY PHYSICS AND NUCLEAR PHYSICS
2005年
7期
695-699
,共5页
Lie代数%非线性%静电分析器%束流光学
Lie代數%非線性%靜電分析器%束流光學
Lie대수%비선성%정전분석기%속류광학
Lie algebraic methods%nonlinear orbit%electrostatic analyzer%beam optics
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.
介紹瞭Lie代數的方法,用Lie代數方法分析瞭靜電分析器對束流傳輸過程的非線性影響,其計算結果分析到三級近似.首先給齣瞭靜電分析器的哈密頓函數,然後將哈密頓函數展開為齊次多項式的和,再求Lie映射,最後得到粒子軌跡各級近似解.
개소료Lie대수적방법,용Lie대수방법분석료정전분석기대속류전수과정적비선성영향,기계산결과분석도삼급근사.수선급출료정전분석기적합밀돈함수,연후장합밀돈함수전개위제차다항식적화,재구Lie영사,최후득도입자궤적각급근사해.
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.
