根据拉格朗日方程对电子在平滑会切磁场中的径向波动与速度零散的关系进行讨论。运用Matlab, Magic软件相互结合的方法设计电子枪结构和磁场。用Matlab程序模拟单电子在给定电场、磁场中的运动, 分析了单电子径向速度对零散的影响, 并优化磁场分布。设计的磁场可以有效地减小单电子束径向速度, 降低电子束速度零散。用Magic软件对电流为1 A、能量为30 keV的电子束在优化磁场中的运动进行仿真, 得到的电子束速度比约为2, 速度零散小于2.5%, 轴向速度零散小于8.5%。

The Lagrangian formula is used to analyze the velocity spread and beam ripple of electrons in smooth cusp magnetic field. The characteristics of the cusp electron gun including cusp magnets are calculated by co-simulation employing softwares Matlab and Magic. A Matlab code is written to simulate the motion of single electron in a given electric field, and a given magnetic field, which shows the relationship between the electron’s radial velocity and velocity spread. The cusp magnetic field optimized accordingly can reduce the radial velocity at the anode region, which is the key to achieve small beam velocity spread. When the cusp electron gun is designed to generate a 1 A, 30 keV beam, an optimized velocity spread less than 2.5% can be obtained with an axial velocity spread less than 8.5% and a velocity ratio about 2.