The generation of high-power THz using BWO requires an electron beam with high current density and high energy. PS discharge-driven electron beam source is a gas discharge-based electron beam source capable of producing high-current density, high-energy pulsed electron beam within a short duration of time. Also, the gas discharge-based e-beam source can be used conveniently with a plasma-assisted beam-wave interaction structure to develop a plasma-assisted THz BWO. A 3D simulation study of the electron beam source can assist in providing a better understanding of the effect of various parameters on the electron beam generation to produce the desirable beam. In this work, the simulation study of a Pseudospark electron beam source is carried out using the Particle-in-cell (PIC) method. For this study, a 3D simulation model is developed using the software VSim Multiphysics. The electrostatic field penetration inside the hollow cathode (HC) cavity, the particle-field dynamics, and the current profile of the generated e-beam at the anode are studied for the gap voltage 20 and 30 kV, and the HC gas pressure 1, 10, and 20 Pa.