The plasma‐assisted slow wave oscillator (Pasotron) employs a plasma lens for initial focusing of the driving electron beam, enabling operation without a magnetic field. In this study, the XOOPIC particle‐in‐cell code is used to model the beam interaction with an expanding background neutral gas. The 40 kV beam electrons impact‐ionize the background gas, displacing the less energetic plasma electrons, and focusing the nominally 50 A beam in the neutralizing space charge of the remaining plasma ions. A particle‐in‐cell (PIC) Monte Carlo collision (MCC) model is described. The model treats charged particles (beam electrons, plasma electrons and ions) as particles. Collisions between charged particles (electrons and ions) and neutrals are included using a Monte Carlo collision model with a spatially‐dependent helium gas background. Time‐dependent space charge and self‐magnetic forces are included. The model is used to study beam focusing, as well as oscillations and instabilities at higher currents. © 2003 American Institute of Physics