一种自动微分技术:微分代数及其在带电粒子光学中的应用  

AN AUTOMATIC DIFFERENTIATION TECHNIQUE: DIFFERENTIAL ALGEBRA AND ITS APPLICATION IN CHARGED PARTICLE OPTICS

作　　者：王莉萍[1] 唐天同[1] 

机构地区：[1]西安交通大学光电子与物理电子工程系

出　　处：《计算物理》1999年第3期225-234,共10页Chinese Journal of Computational Physics

摘　　要：微分代数是带电粒子光学中新近出现的一个很有前途的数学工具。作为一种自动微分技术，它结合了非标准分析、简正级数理论等的思想。微分代数提供了一种可达到机器精度的研究非线性系统任意阶性质的极为简便的方法，故应用领域非常广泛，对带电粒子光学中的轨迹追踪、高阶像差分析与校正、灵敏度分析与结构优化设计等都是一个很有效的工具。综述了微分代数的基本原理和独特性，分析了它在带电粒子光学中的应用，以及在不同计算机语言中的软件实现，提出了今后的一些发展方向。Differential algebra is a new mathematical method and a promising tool in charged particle optics. As a kind of automatic differentiation techniques, it is based on the nonstandard analysis and normal power series theory. It presents a straightforward method for the study of arbitrary order property of nonlinear systems, with accuracy limited only by the computer. The differential algebraic method is widely applicable, and it is an effective and elegant tool for the tracking, analysis and correction of high_order aberrations, sensitivity analysis and optimization of structure design, etc., of the charged particle optical systems. The principle and virtues of differential algebra are summarized. The application of differential algebra method in charged particle optics and its implementation in various computer languages are analysed. Some new research subjects in this field are discussed.

关 键 词：微分代数 自动微分 粒子光学 非标准分析 

分 类 号：O463.1[机械工程—光学工程] TP391.75[理学—电子物理学]