We consider the classical Euler-Poisson system for electrons and ions, interacting through an electrostatic field. The mass ratio of an electron and an ion is small and we establish an asymptotic expansion of solutions, where the main term is obtained from a solution to a self-consistent equation involving only the ion variables. Moreover, the validity of such an expansion is established even with "ill-prepared" Cauchy data, by including an additional initial layer correction. This talk is based on a joint work with Professors E. Grenier (ENS de Lyon), Y. Guo (Brown Univ.), and B. Pausader (Brown Univ.).