In this talk, I will discuss the stability conditions for a free boundary problem of compressible Euler equations coupled with a nonlinear Poisson equation of electric potential. Under those stability conditions, a priori estimates of Sobolev norms and the bounds for geometric quantities of the free surface are given. I will compare the isentropic and non-isentropic cases for the different considerations. The talk is based on the recent joint work with K. Trivisa and H. H. Zeng.