Ionic Bose polarons are quantum entities emerging from the interaction between an ion and a Bose-Einstein condensate, featuring long-ranged interactions that can compete with the gas healing length, resulting in strong interparticle correlations and enhancement of the gas density around the ion. Full numerical treatment of such systems is computationally very expensive and does not easily allow one to study the system dynamics. For this purpose, we study a mean-field-based description of such systems in the co-moving frame. We find that it captures a sizable change in the gas density and qualitatively reproduces the available results based on Monte Carlo simulations. We consider a couple of scenarios which consist of a single ion and two pinned ions, where it is possible to extract their effective interaction induced by the bath. This approach seems to be promising for studying transport and nonequilibrium dynamics of charged (bi)polarons in condensed media.
