基于ArcPIC代码采用PIC-MCC方法, 模拟研究了轴对称真空二极管放电时电子密度和阴极表面场强分布情况, 同时给出了二维空间电荷限制流的一阶和二阶拟合公式。研究发现, 真空二极管放电时阴极表面电场会随阴极注入电流密度的增加而增加, 而后出现振荡并趋于一个稳定状态; 二维空间电荷限制流密度值随阴极发射半径的增大而减小, 且阴极发射半径越大越接近一维空间电荷限制流值。

Based on the ArcPIC code, this paper analyzes the distribution of electron density and the field on the cathode surface using the PIC-MCC method. At the same time, it gives the fitting formula of two-dimensional space charge limited current. This provides a theoretical reference for the design and application of vacuum diodes. It is found that the electric field of cathode surface increases with the increase of cathode current density, then oscillates and tends to a stable state. The two-dimensional space charge limited current density decreases with the increase of cathode emission radius, and the larger the cathode emission radius, the closer the current to the one-dimensional space charge limited current.