Design and simulation of low-velocity-spread cusp electron gun

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 electrons 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.