用电荷密度法计算静电场的程序和误差分析
CHARGE-DENSITY METHOD FOR SOLVING ELECTROSTATIC FIELD: PROGRAM AND ERROR ANALYSIS
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摘要: 正 电荷密度法是一种数值求解积分方程的方法,用于设计静电透镜系统有很多优点。它避开了真空边界的赋值问题,从而有可能用较少内存、较短机时达到较高精度。如图1所示,Ⅰ、Ⅱ、Ⅲ分别表示三个旋转对称的电极,阴影区表示待求场区。有限差分法要求事先给出虚线所示真空边界点的电位,作为重复迭代的不变出发值,这是误差的一个重要来源。为了减少这种误差,可把虚线边界扩大到足够远,从而按电位为零处理,但网格点数大大增加,往往达到不能接受的程度。电荷密度法则不需要处理真空边界,也不需要划分
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Abstract: The charge-density method is investigated mainly on the errors which arise from the finite segments and their distribution. It is proved that the higher accuracy will reach if more segments are chosen. at where the charge density is high and at the region nearby the area where the field is to be ealculated. A program is set up. The differencc between the ealeulated data. and the published ones given by E. Harting and F. H. Eead (1976) is less than 1%. -
J. W. Ward and R. L.Seliger, T. Vac. Sci. Ioclwtol.,19(1981),1082.[2]A. Renau, F. H. Read and J, N. H. Brunt,J. Phys. E: Sci. Instrum., 15(1982), 347.[3]E, Harting and F. H. read, Electrostatic Lenses, Amsterdam: Elsevier (1976)[4] S. Natali, D. Di Chio and C. E. Kuyatt, Rev. Sci, Instrum., 43(1972), 80.[4]A. B. El-Kareh and J. C. J. EL-Kareh, Electron Beams, Lenses and Optics, Academic Press, New York, London, 1970.[5]屠聿善,电子学通讯,4(1982), 372. -
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