A Simple Space Charge Limited Emission Algorithm for 1-D Particle-in-Cell Simulations

Abstract

Most vacuum electronic devices (VEDs) have cathode emission operating in a space-charge limited regime, indicating that the self-field of space charges limits the current density that can be drawn. In particle-in-cell (PIC) simulations, implementing space charge-limited emission can be nontrivial and may generate over-emission or nonphysical effects. In this work, we present a simple algorithm applying the Child-Langmuir law at the first grid instead of attempting to zero the field at the surface, making the algorithm particularly well suited to the PIC simulations. To demonstrate this, a space charge limited (SCL) diode, where the steady-state limiting current should follow the Child-Langmuir law, is simulated using the 1-D bounded electrostatic PIC code, XPDP1, developed by the Plasma Theory and Simulation Group (PTSG), formerly at UC Berkeley, now at Michigan State University. After implementing the simple SCL algorithm in the XPDP1 code, the surface electric field is computed accurately by applying the Gauss law to the surface grid, and the turn-on of the SCL emission in the planar diode is studied carefully. The simple algorithm can be further implemented in 2-D or 3-D PIC simulations for modeling VEDs with SCL emission. The detailed implementation and simulation results will be presented and discussed.