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.