电子光学中四极场分布的半解析法计算

 采用一种新的半解析法，对电子光学中3种不同形状电极产生的四极场进行分析计算。半解析法中极点的确定方法简单有效，可以结合电极的形状填充等效源，并且极点位置确定极为精确。在四极场的计算中，该方法具有表达式简单，求解变量少，而且计算精度和效率高的优点。对凸圆柱电极、内凹圆柱电极以及平板电极产生的四极场进行了求解，并将计算结果进行了比较，应用半解析法在计算凸圆柱电极产生的四极场具有更为明显的优势,精度可达0.001%。由于半解析法可得出标量电位函数的解析级数表达式，因此，场强的计算更加简便，同时也更容易保证场强的计算精度，这也有利于四极场的设计和优化。

Semi-analytical method of analyzing quadrupole field in eletron optics

Semi-analytical method , a new solution to calculate electromagnetic field, is applied to analyze three kinds of quadrupole field of shape-varied electrodes in electron optics. Positions of polar points can be determined precisely, simply and efficiently by equivalent source filling according to the different shape of electrodes. Since the general solution of this method is analytic series of scalar potential, electric field intensity could be obtained by first derivation. Calculation relative errors are almost 10-3 for quadrupole fields of curved cylindrical electrodes and plat plate electrodes, while 0.001% for field of prominence cylindrical electrodes.