  The Casimir force for a planar gauge model is studied considering perfect
conducting and perfect magnetically permeable boundaries. By using an effective
model describing planar vortex excitations, we determine the effect these can
have on the Casimir force between parallel lines. Two different mappings
between models are considered for the system under study, where generic
boundary conditions can be more easily applied and the Casimir force be derived
in a more straightforward way. It is shown that vortex excitations can be an
efficient suppressor of vacuum fluctuations. In particular, for the model
studied here, a planar Chern-Simons type of model that allows for the presence
of vortex matter, the Casimir force is found to be independent of the choice of
boundary conditions, at least for the more common types, like Neumann, perfect
conducting and magnetically permeable boundary conditions. We give an
interpretation for these results and some possible applications for them are
also discussed.
