  An understanding of the post-impact dynamics of ejecta clouds are crucial to
the planning of a kinetic impact mission to an asteroid, and also has great
implications for the history of planetary formation. The purpose of this
article to track the evolution of ejecta produced by AIDA mission, which
targets for kinetic impact the secondary of near-Earth binary asteroid 65803
Didymos on 2022, and to feedback essential informations to AIDA's ongoing
phase-A study. We present a detailed dynamic model for the simulation of an
ejecta cloud from a binary asteroid that synthesizes all relevant forces based
on a previous analysis of the mechanical environment. We apply our method to
gain insight into the expected response of Didymos to the AIDA impact,
including the subsequent evolution of debris and dust. The crater scaling
relations from laboratory experiments are employed to approximate the
distributions of ejecta mass and launching speed. The size composition of
fragments is modeled with a power law fitted from observations of real asteroid
surface. A full-scale demonstration is simulated using parameters specified by
the mission. We report the results of the simulation, which include the
computed spread of the ejecta cloud and the recorded history of ejecta
accretion and escape. The violent period of the ejecta evolution is found to be
short, and is followed by a stage where the remaining ejecta is gradually
cleared. Solar radiation pressure proves to be efficient in cleaning dust-size
ejecta, and the simulation results after two weeks shows that large debris on
polar orbits (perpendicular to the binary orbital plane) has a survival
advantage over smaller ejecta and ejecta that keep to low latitudes.
