To optimize the multicusp ion source, understanding of transport properties of electrons is indispensable. Since the transport of electrons in the multicusp ion source is a three-dimensional problem, we use the 3D computer code Geant4, to model the particle trajectories. The goal is to study the effect of electron injection into a cylindrical gas chamber and the electron trajectories. The role of the magnetic filter in contemporary negative ion sources is analyzed. The conditions in the magnetic filter adjacent to the plasma electrode optimum for the generation, formation, and extraction of an H⁻ ion beam are found. The simulation results are in good agreement with the experimental data.