Summary form only given. The electron beam neutralization effect takes place in long pulse and CW gyrotrons as has been observed experimentally. A number of the remaining air molecules (since the vacuum in the gyrotron is not perfect) are ionized when they collide with the beam electrons. The accumulation of positive ions leads to a partial or total neutralization of the beam space charge. The simulation of this effect may shed new light to the beam neutralization mechanism. For this purpose the two-dimensional, electrostatic and parallel code Ariande++ has been upgraded to an hybrid code. For each time step, the state of the beam is calculated self-consistently, while for the calculation of the ions' current state the PIC techique is used. The effect of beam neutralization is different in case of operation with or without depressed collector. In case of operation with depressed collector the electrons generated by the ionization are able to escape toward the walls only by radial diffusion across the magnetic field lines. In this preliminary study this will be considered using a simplified model. The study of the neutralization effect has been done on the electron beam of the EU 170 GHz, 2 MW, coaxial cavity gyrotron for ITER.