带电粒子束偏转系统像差分析的自动微分方法

AUTOMATIC DIFFERENTIATION METHOD FOR ABERRATION ANALYSIS OF DEFLECTION SYSTEMS OF CHARGED PARTICLE BEAM

根据AD技术的基本原理，研究了对带电粒子光学系统进行像差分析的AD方法，给出了偏转系统高斯光学性质及三阶几何像差系数的AD表述。利用面向对象的编程技术，在Visual C++中编制了一个软件包，实现了基本AD功能及带电粒子光学计算功能。用此软件计算了鞍型线圈磁偏转器的高斯光学性质及三阶像差，其结果具有非常高的精度，高斯光学性质的计算相对误差仅为10－１３量级甚至更低。证明AD方法对带电粒子光学系统的像差分析是极其有效的。

Based on Automatic Differentiation (AD), a new technique in computer numerical analy sis, a new method for aberration analysis of charged particle optical systems was studied. The AD representations for Gaussian proper ties and thirdorder geometric aberrations of deflection system are obtained. A package with AD technique inside and including functions for numerical calculation of charged particle optics was developed in Visual C++ language with the adva ntage of Object Oriented Programming technique. The Gaussian properties and third order aberrations of saddlecoil magnetic deflector were calculated. The results are of extrahigh accuracy while relative errors of the Gaussian properties are on the scale of 10－１３ or smaller. It is concluded that AD method is a rather effective tool for the aberration analysis of charged particle optica l systems.