  In this paper, both smooth subsonic and transonic flows to steady
Euler-Poisson system in a concentric cylinder are studied. We first establish
the existence of cylindrically symmetric smooth subsonic and transonic flows to
steady Euler-Poisson system in a concentric cylinder. On one hand, we
investigate the structural stability of smooth cylindrically symmetric subsonic
flows under three-dimensional perturbations on the inner and outer cylinders.
On the other hand, the structural stability of smooth transonic flows under the
axi-symmetric perturbations are examined. There is no any restrictions on the
background subsonic and transonic solutions. A deformation-curl-Poisson
decomposition to the steady Euler-Poisson system is utilized in our work to
deal with the hyperbolic-elliptic mixed structure in subsonic region. It should
be emphasized that there is a special structure of the steady Euler-Poisson
system which yields a priori estimates and uniqueness of a second order
elliptic system for the velocity potential and the electrostatic potential.
