静电偏转器高阶像差的三维微分代数计算

Differential Algebraic Calculation of High Order Aberrations of 3-Dimensional Electrostatic Deflection

本文研究了静电偏转器高阶像差在三维空间的微分代数计算。利用有限元方法计算了静电偏转器电场的三维分布,通过三维数据拟合方法构造电磁场分布的三维局部解析式,将电场量转化为微分代数扩展数,利用微分代数方法分析计算偏转系统直至五阶的像差。验证了数据拟合方法的精度和可靠性,结果表明该方法具有非常高的精度,完全可以满足工程设计分析的需要。编写了相关的计算软件,具体分析计算了一个八瓣电极偏转器直至五阶的几何像差。

A novel 3-dimensional simulation algorithm for the electromagnetic deflection was developed. First, the 3D electric/magnetic field distributions weremathematically modeled and numerically simulated in finite element method. Then, the corresponding analytical expressions of the local field were formulated by fitting the simulated 3D data. And last, the high-order aberrations of the deflection were calculated in differential algebraic method. An example was given to prove the accuracy and validity of the data fitting scheme. The simulated results show thatthe newly-developed 3D simula- tion algorithm does a good job for the engineering purposes. In addition, the aberrations up to fifth-order of anoctupole electrostatic deflection were calculated with the self-developed software.