Two-dimensional geometry effect on space-charge-limited current in axially symmetrical planar diode

Two-dimensional (2-D) geometry effect on space-charge-limited (SCL) current of an axially symmetrical planar diode was studied with 2.5 D particle-in-cell(PIC) simulation. A volume-weighting cloud-in-cell model was used to improve the accuracy of the PIC method in z-r coordinates system. The simulations with various emitter radii were carried out on the same diode with the applied voltages being 100 kV and 1 MV respectively. The simulation results show that the 2 D geometry effect on SCL current monotonically diminishes with the dimensionless ratio of emitter radius to gap separation, whether in relativistic or non-relativistic regime. When the ratio is more than 0.5, the first-order analytical theory well predicts the limiting current. But when the ratio is no more than 0.5, the second-order correction must be considered.