[en] This paper deals with the space charge effects suffered by an ionic beam of homogeneous density, composed with ions of various charges and submitted to crossed electric and magnetic fields. We consider the physical and geometric conditions in the region between an ion source and the extraction electrode. We propose two different methods that allow to reach a numerical solution of the problem. The first one is founded on the idea that the large number of particles of the beam can be replaced in the calculations by a reduced number of highly charged particles. The second one consists in considering the widening of the beam through the evolution of the beam envelope. We apply these two methods to physical situations found in published experimental data. (Author)