[en] A hydrodynamic model is used to help isolate possible three dimensional space charge instabilities in beam plasmas of concern in designing heavy ion accelerators for inertial confinement fusion energy applications. The model provides an economic means for searching the large parameter space relevant to problems in which coupling of longitudinal and transverse motions is allowed. It is shown that the equilibrium axial hydrodynamic pressure of the beam plasma has a significant effect on the stability boundaries of a two-rotating-stream instability. When considering the resistive wall effect, this model shows a kink instability. The growth rate of some modes could be enhanced by increasing the equilibrium axial pressure