The development of negative ion (NI) sources for ITER is strongly accompanied by modelling activities. The ONIX code addresses the physics of formation and extraction of negative hydrogen ions at caesiated sources as well as the amount of co-extracted electrons. In order to be closer to the experimental conditions the code has been improved. It includes now the bias potential applied to first grid (plasma grid) of the extraction system, and the presence of Cs+ ions in the plasma. The simulation results show that such aspects play an important role for the formation of an ion–ion plasma in the boundary region by reducing the depth of the negative potential well in vicinity to the plasma grid that limits the extraction of the NIs produced at the Cs covered plasma grid surface. The influence of the initial temperature of the surface produced NI and its emission rate on the NI density in the bulk plasma that in turn affects the beam formation region was analysed. The formation of the plasma meniscus, the boundary between the plasma and the beam, was investigated for the extraction potentials of 5 and 10 kV. At the smaller extraction potential the meniscus moves closer to the plasma grid but as in the case of 10 kV the deepest meniscus bend point is still outside of the aperture. Finally, a plasma containing the same amount of NI and electrons , representing good source conditioning, was simulated. It is shown that at such conditions the extracted NI current can reach values of ∼32 mA cm−2 using ITER-relevant extraction potential of 10 kV and ∼19 mA cm−2 at 5 kV. These results are in good agreement with experimental measurements performed at the small scale ITER prototype source at the test facility BATMAN.