电磁多极场的分析和计算

多极系统是由几个对称地放置在方位角方向上、并具有一定电(磁)位的电(磁)极所组成的系统。它们所产生的非旋转对称场称为多极场。多极场是一种广泛类型的电磁场。例如包括了各种偏转场,四极、六极、八极透镜场等。它们在电子束器件、电子光学仪器和高能加速器中得到广泛应用。本文采用傅里叶展开法将求解空间(三维)的电磁多极场问题化为求解一系列的二维谐波电(磁)位的问题。这些谐波电(磁)位满足一定的二阶偏微分方程,在一定的边界条件下,可以采用逐次张弛方法进行求解。然后将谐波电(磁)位迭加,便得到所要求的多极场的电(磁)位分布。编制了计算电磁多极场的通用程序。对于几种典型的多极场模型(单个和二单元的四极透镜,以及圆柱环形偏转线圈等)进行了计算与检验。计算实践表明,这种傅里叶展开法适用于计算电子束器件和各种电子光学仪器中的多极场,并可算出其边缘效应(弥散场),因此具有一定的意义。 关键词：

ON THE ANALYSIS AND CALCULATION OF STATIC ELECTRO-MAGNETIC MULTIPOLE FIELDS

The multipole fields are widely used in electron-optical devices and instruments. The multipole fields are generated by several azimuthaly-arranged electrodes or pole-pieces and, are thereby not rotational symmetric. They generally possess some planes of symmetry or anti-symmetry.The Fourier-transform method is used to decompose the three dimensional potential distribution into a series of independent two dimensional potentials, which can be calculated easily by the relaxation method. For this purpose, the three dimensional boundary values must be expressed in Fourier-series with respect to the azimuth θ in eylindrical coordinates. After these treatments, the corresponding two dimensional potentials can be calculated and superimposed.A computer program has been worked out for calculation of the properties of the multipole fields and its fringe fields. Some examples of importance such as quadrupole lens or doublet, and a toroidal deflection coil have been treated in detail. The numerieal results show that the Fourier-transform method for multipole field is a useful means for analysis and design of electron-optical devices.