Simulation research of thermionic emission process and impact of voltage parameters in the three-pole electron gun

• Height of potential barrier on the cathode is tens of micros and non-uniform. • Non-uniform potential of the barrier leads to non-uniform emission. • The change of bias voltage significantly affects both emission area and density. • Child-Langmuir law does not suitable for the three-pole electron gun. • Modified formula reflects the effect of both bias voltage and accelerating voltage. The three-pole electron gun is composed of cathode, anode and grid electrode, which can effectively control the emission beam current and is widely used in welding and additive manufacturing equipment. However, the characteristics of the emission beam and the process of beam control have yet to be fully and accurately elucidated. Considering that the characteristics of the electron beam at the emission stage have a significant effect on the beam quality, the electric field distribution and electron beam trajectory at the emission stage are studied based on the simulation method of bidirectionally coupled particle tracing. The results show that a spatial potential barrier several tens of microns high is formed on the cathode surface. The different relative potential across the barrier at different positions leads to the non-uniform effective emission beam density of the cathode. With the increase of bias voltage, the effective emission area and emission beam density decrease simultaneously. The average emission beam density varies with the accelerating voltage, which does not follow the Child-Langmuir law, but exhibits a more significant trend of variation. The present work proposes a modified formula suitable for the three-pole electron gun for calculating the average emission beam density, obtaining good fitting results.