The Numerical Advanced Model of Electron Cyclotron Resonance Ion Source (NAM-ECRIS) is applied for studies of processes in the source. Solutions of separately operating electron and ion modules of NAM-ECRIS are matched in iterative way such as to obtain the spatial distributions of the plasma density and of the plasma potential. Results reveal complicated profiles with the maximized plasma density close to the ECR surface and on the source axis. The ion-trapping potentials are calculated to be on the level of ~0.01 V. The biased electrode effect is shown to be connected to formation of “electron string” along the source axis by the reflection of electrons by electric fields close to the biased electrode and to the extraction aperture. Parameters of the extracted argon ion beams are obtained for different levels of the injected microwave electric field amplitudes and gas flow.