  This paper is concerned with the linear stability analysis for the Couette
flow of the Euler-Poisson system for both ionic fluid and electronic fluid in
the domain $\bb{T}\times\bb{R}$. We establish the upper and lower bounds of the
linearized solutions of the Euler-Poisson system near Couette flow. In
particular, the inviscid damping for the solenoidal component of the velocity
is obtained.
