[en] The ion beam-plasma interaction is a relevant topic in several fields of plasma physics, from fusion devices to modern ion sources. This paper discusses the numerical modelling of the whole beam-plus-plasma-target system in case of 1+  ions entering an ECR-based charge breeder (ECR-CB). The model is able to reproduce the ion capture and the creation of the first charge states in the selected physics case, i.e. the interaction of a ⁸⁵Rb¹⁺ ions with the plasma of the 14.5 GHz PHOENIX ECR-CB installed at the Laboratoire de Physique Subatomique et de Cosmologie (LPSC) of Grenoble. The results show that a very narrow window of physical parameters for both the beam (energy and energy spread especially) and plasma (ion temperature, density, density structural distribution, self-generated ambipolar fields) exists which is able to reproduce very well the experimental results, providing an exhaustive picture of the involved phenomena. Possible non-linear interactions and the role played by the eventual onset of instabilities are also discussed. (paper)