  We use a pin-grid electrode to introduce a corrugated electrical potential
into a planar dielectric-barrier discharge (DBD) system, so that the amplitude
of the applied electric field has the profile of a two-dimensional square
lattice. The lattice potential provides a template for the spatial distribution
of plasma filaments in the system and has pronounced effects on the patterns
that can form. The positions at which filaments become localized within the
lattice unit cell vary with the width of the discharge gap. The patterns that
appear when filaments either overfill or under-fill the lattice are reminiscent
of those observed in other physical systems involving 2d lattices. We suggest
that the connection between lattice-driven DBDs and other areas of physics may
benefit from the further development of models that treat plasma filaments as
interacting particles.
