静电聚焦同心球系统的成像电子光学A章:电子轨迹方程

Imaging Electron Optics of Electrostatic Focusing Concentric Spherical System Part A:Electron Trajectory Equations

在成像电子光学中,静电聚焦同心球系统具有一系列宝贵的性质,其电位分布与电子轨迹能以解析形式表示,可以定量地研究系统的电子光学成像特性与横向像差。尽管前人已有不少研究,但都限于零级近似成像的认识,且其中存在着不少谬误。本系列文章将全面研究静电聚焦两电极与多电极同心球系统中电子的运动轨迹、电子光学成像特性与横向像差,探讨电子束在成像段形成的图像弥散,得出一些新的结论和认识,纠正文献中存在的一些谬误,建立自己的理论体系。本系列文章的第一篇主要探讨电子在两电极同心球系统中在静电场作用下的运动轨迹,导出了两电极静电聚焦同心球系统中自阴极面逸出的电子轨迹在极坐标系下的表示式ρ=f(φ)与圆柱坐标系下新的轨迹方程的表示式r=r(z),给出了自光阴极逸出的电子在成像段的行进轨迹的交轴位置及其斜率的近似和精确表示式。本文为全面研究静电聚焦同心球系统的电子光学性质及其像差奠定基础。

In imaging electron optics,the electrostatic focusing concentric spherical system has a series of valuable properties,its potential distribution and electron trajectory can be represented by analytical form,and the electron optical imaging characteristics and its lateral aberrations can be quantitatively studied.Although there are many literatures on electron optical imaging,they are limited to the understanding of zero-order approximation imaging,and a lot of fallacies exist in it.This series of articles fully study the electron motion trajectory,electron optical imaging characteristics,and lateral aberrations in the electrostatic focusing concentric spherical system composed of two electrodes or multiple electrodes,investigate the image dispersion formed by the electron beam in the imaging segment,put forward some new idea and recognition,correct some fallacies in literatures,and establish my own theoretical system.The first article of this series mainly explores the electron moving trajectory under the electrostatic field in the concentric spherical electrostatic focusing system composed of two electrodes,deduces the new representations for the trajectory of electrons emitted from the photocathodes of the concentric spherical system with electrostatic focus of two electrodes in the polar coordinate systemρ=f(φ)and in the cylindrical coordinate system r=r(z),and explores the exact and approximate formulae of axial intersection position and its angle of inclination at the image section for the electrons emitted from the photocathode.This paper lays a foundation in studying the electron optical properties and lateral aberrations of the electrostatic focusing concentric spherical system.