Abstract The DART spacecraft will impact Dimorphos (the secondary body of the Didymos binary asteroid) to test the kinetic impactor deflection method against possibly hazardous near-Earth asteroids. The DART impact ejecta plume, and possibly the impact crater, will be imaged by the LICIACube spacecraft, hosted as a piggyback and released by DART just before the impact, and then, several years later, by the Hera probe. To exploit the wealth of data obtained and understand the physics of the whole impact experiment, it is of paramount importance to properly model the dynamics of the binary system pre- and postimpact and the dynamics of the particles ejected from the impact crater. A model was developed to simulate the evolution of the ejecta particles created during the impact in order to first interpret the LICIACube images and then test the survival of particles on long intervals of time that might be detected by the Hera mission either as individual bodies or as parts of rings. The dynamical evolution of the particles is simulated over different timescales to highlight the most important perturbations and their relative importance. The ejecta dynamics turns out to be highly chaotic due to repeated close encounters with the two asteroids. However, we find that some ejecta survive in the binary orbital environment for timescales comparable to the Hera arrival time. The effects of the particles reimpacting against either one of the components is also analyzed to estimate the amount of momentum transfer to the target bodies.