[en] The neutralization of positive space charge is studied in a case where heavy positive ions are added to a limited region of length L in a collisionfree magnetized plasma. It is found that electrons which become accelerated towards the positive space charge can only achieve a partial neutralization: they overshoot, and the positive region becomes surrounded by negative space charges which screen the electric field from the surroundings. The process is studied both analytically and by computer simulations with consistent results: large positive potentials (U>>kT_e/e) can be built up with respect to the surrounding plasma. In the process of growth, the potential maximum traps electrons in transit so that quasineutrality is maintained. The potential U is proportional to the ambient electron temperature and the square of the plasma density increase, but independent of both the ion injection rate and the length L. The process explains several features of the Porcupinge xenon beam injection experiment. It could also have importance for the electrodynamic coupling between plasmas of different densities, e.g. the injection of neutral clouds in the ionosphere of species that becomes rapidly photoionized, or penetration of dense plasma clouds from the solar wind into the magnetosphere. (31 refs.) (authors)