螺线管透镜的三级李映射

Third Order Lie Map for the Solenoidal Lenses

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 。

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.