基于表面电荷法的像管静电场计算

与传统的有限差分法和有限元法相比,表面电荷法可降低单元剖分难度并能处理开放边界,更适于计算静电透镜的静电场。针对轴对称及非轴对称两类结构,采用样条函数及奇异形状函数改进电极表面的电荷密度估计,讨论了二维及三维表面电荷法的实现。与具有解析解的单位圆盘进行比较,分析了表面电荷法的电位计算精度,并用于轴对称及非轴对称像管计算。结果表明：对轴对称系统,在文中给定步长下,二维及三维表面电荷法与有限差分法计算相对误差不超过10^-3,且二维方法精度整体高于三维方法,二维、三维表面电荷法对3种像面位置的计算结果与有限差分法结果相比,最大误差不超过0.6mm;对非轴对称系统,3种方案下轴外电子运行轨迹的差异明显,非对称因素所产生的干涉场影响是不可忽略的。

Calculation of Electrostatic Field of Image Tube Based on Surface Charge Method

Compared with the traditional FDM（Finite Differential Method）and FEM（Finite Elements Method）,SCM（Surface Charge Method）is fitter for calculating electrostatic lens＇ potential,since the method can mesh more easily and dispose open boundary.Through spline and singular shape function approximating charge density,two-dimensional and three-dimensional SCM for axis-symmetric and asymmetric systems are discussed.Compared with calculation on unit disc with analytic solution,SCM＇s precision is discussed,and the method is applied to the calculation on image tube.The results indicate that under a given step of mesh in the article,the relative error of two-dimensional and three-dimensional SCM is less than 10^-3,and compared with the one of FDM,and the precision of two-dimensional SCM is higher than the one of three-dimensional SCM in overall;compared with results of FDM,maximum relative error of two-dimensional and three-dimensional SCM for three kind of image plane position is less than 0.6 mm.As for three dimensional asymmetric system,off-axis electron trajectory＇s differences are significant with three kind of methods and interference field can not be ignored which comes from asymmetric factors.