Modeling of Space Charge Effects in Intense Electron Beams: Kinetic Equation Method Versus PIC Method

In this paper, we present the simulation results for the most important 1-D problems of current flow in planar vacuum diodes. For the first time, classical problems of vacuum electronics have been solved using the basic principles of nonequilibrium physical kinetics. This approach is based on the accurate numerical solution of the Vlasov-Poisson equation system to find the electron distribution function. We have obtained time-dependent numerical solutions that satisfactorily agree with theoretical approximations and with particle-in-cell simulations as well.