The aim of this paper is to investigate, through particle-in-cell with Monte Carlo collisions (PIC-MCC) simulations, the effects of collisions on the expansion of an ion–ion beam formed by the alternate extraction of oppositely charged ions. This beam is extracted from an ion–ion plasma, formed in the downstream of a radiofrequency magnetically filtered iodine electronegative plasma, by the mean of two extraction grids. In this grid system, the screen grid is biased with a square voltage waveform, in the low MHz range, while the acceleration grid is grounded. The collisionless interaction between the extracted ion packets involves and enhances electrostatic waves propagating at beam velocity. Our results show that in addition to these electrostatic waves, the presence of significant fraction of low energy ions, produced by charge exchange, beside extracted fast ions gives rise to two-stream instability. Furthermore, space and time dependent electric field might accelerate the slow ions, produced by charge exchange collision. This acceleration, involving Landau damping and its inverse mechanism, is mainly due to the interaction between ions and potential patterns inherent to two-stream instability.