High-power accelerators are being studied for several projects including accelerator driven neutron or neutrino sources. The low energy part of these facilities has to be carefully optimized to match the beam requirements of the higher energy parts. In this low energy part, the space charge self force, induced by a high intensity beam, has to be carefully controlled. This nonlinear force can generate a large and irreversible emittance growth of the beam. To reduce the space charge (SC), neutralization of the beam charge can be done by capturing some particles of the ionised residual gas in the vacuum chamber. This space charge compensation (SCC) regime complicates the beam dynamics study. This contribution aims to modelize the beam behavior in such a regime and to give order of magnitude to the linac designer for the neutralization rise time and the induced emittance growth.