The rapidly charging event (RCE) is a new category of spacecraft charging, which was first observed at an international space station in 2006. It occurred in the presence of the eclipse, with the floating potential increasing abruptly to tens of volts, well beyond the safety level of –40 V, within a few seconds. The RCE has not yet been understood thoroughly until now. Based on Ferguson and Craven’s theory, we developed a physical model for the rapidly charging events recently and gave satisfactory predictions compared with the observations. In this paper, we investigate the physical process and mechanism in detail, and explain the statistical characteristics and the underlying physics through the model calculations. It is shown that the rapidly charging event is a non-equilibrium charging process and driven by the high voltage solar arrays. The rapid charging is mainly due to the fact that the cover glass blocking effect cannot follow the rapid increasing of the solar voltage when it is abruptly turned on at the exit of eclipse. As the RCE reaches equilibrium it acts as a normal charging event. The rapidly charging amplitudes depend on many factors, such as the switch-on time of the solar arrays, the pattern of switch-on, etc., which play key roles, and so that the floating potential data exhibit a spread to a certain extent. The maximum potential decreases with electron density increasing, which is in good agreement with observations.