  We prove the unique existence of supersonic solutions of the Euler- Poisson
system for potential flow in a three-dimensional rectangular cylinder when
prescribing the velocity and the strength of electric field at the entrance.
Overall, the main framework is similar to [1], but there are several technical
differences to be taken care of vary carefully. And, it is our main goal to
treat all the technical differences occurring when one considers a three
dimensional supersonic solution of the steady Euler-Poisson system.
