  Topological photonic crystals, which offer topologically protected and
back-scattering-immune transport channels, have recently gained significant
attention for both scientific and practical reasons. Although most current
studies focus on dielectric materials with weak dispersions, this study focuses
on topological phases in dispersive materials and presents a numerical study of
Chern insulators in gaseous-phase plasma cylinder cells. We develop a numerical
framework to address the complex material dispersion arising from the plasma
medium and external magnetic fields and identify Chern insulator phases that
are experimentally achievable. Using this numerical tool, we also explain the
flat bands commonly observed in periodic plasmonic structures, via local
resonances, and how edge states change as the edge termination is periodically
modified. This work opens up opportunities for exploring band topology in new
materials with non-trivial dispersions and has potential RF applications,
ranging from plasma-based lighting to plasma propulsion engines.
