  The Euler Poisson equations describe important physical phenomena in many
applications such as semiconductor modeling and plasma physics. This paper is
to advance our understanding of critical threshold phenomena in such systems in
the presence of different forces. We identify critical thresholds in two damped
Euler Poisson systems, with and without alignment, both with attractive
potential and spatially varying background state. For both systems, we give
respective bounds for subcritical and supercritical regions in the space of
initial configuration, thereby proving the existence of a critical threshold
for each scenario. Key tools include comparison with auxiliary systems, phase
space analysis of the transformed system.
