A Tutorial on One-Dimensional Numerical Simulation of Virtual Cathode Oscillation

This review article is the continuation of a previous publication, by the same author, on one dimensional theory of space charge effect and virtual cathode. The virtual cathode is known to be unstable. However, the process of virtual cathode oscillation is very complicated both physically and mathematically. No satisfactory theoretical model exists that can fully describe the oscillatory behavior of the virtual cathode. On the other hand, computer simulations allow us to numerically observe this phenomenon and establish certain relations between the electron beam parameters and the virtual cathode characteristics. This article explains the detailed procedure of numerical modeling by dealing with the one-dimensional case as an example. A sample code written in the C language is attached at the end following the main text. This article is expected to serve as a reference for young researchers and students who are interested in computer simulations of intense particle beams and high-power microwave generation.