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Lie algebraic methods are used in the analysis of particle trajectories in the quadrupole magnets. The solutions of particle trajectories of third order approximation are obtained. Higher order aberrations could be extended if desired. 用Lie代数方法分析了带电粒子在四极透镜中的运动 ,得到六维相空间中粒子轨迹的三级近似解 ,并包含了运动的相对论效应。当需要时 ,还可以扩展到更高级像差。 Solenoidal lenses are usually used to focus charged particle beams moving in inductive accelerators,electron linear accelerators,proton linear accelerators,low energy beam transport systems as well as some cathode ray tubes. To understand the nonlinear optical properties of solenoidal lenses,Lie algebraic methods are used in the analysis of particle trajectories in this kind of lenses,and the results of third order approximation are obtained. Because of the existence of fringing fields,one should divide the... Solenoidal lenses are usually used to focus charged particle beams moving in inductive accelerators,electron linear accelerators,proton linear accelerators,low energy beam transport systems as well as some cathode ray tubes. To understand the nonlinear optical properties of solenoidal lenses,Lie algebraic methods are used in the analysis of particle trajectories in this kind of lenses,and the results of third order approximation are obtained. Because of the existence of fringing fields,one should divide the fringing field into several small segments,and apply the Lie map to each of the segments. 用李代数方法分析了带电粒子在螺线管透镜中的运动 ,得到六维相空间中粒子轨迹的三级近似解 ,并包含了运动的相对论效应 .当需要时 ,还可以扩展到更高级像差 Under the condition of holding variable power, with the movement of compensating lens group and multifocal lens group, considering the influence of highgrade aberration on optimum position of image, adjusting the space length between all lens groups, making the space suitable for displacement of optimum position of image plane of every focal length, the Gauss image plane would be finally in accordance with every focal length. 通过移动变倍组和补偿组,在保证所要求的变焦倍率的同时,考虑高级像差对最佳像面的影响,调整各组之间的间隔,使之尽量符合各焦距最佳像面的位移变化,最终达到在各种焦距位置时对高斯像面的严格一致。
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