  The one dimensional Coulomb lattice fluid in a capacitor configuration is
studied. The model is formally exactly soluble via a transfer operator method
within a field theoretic representation of the model. The only interactions
present in the model are the one dimensional Coulomb interaction between
cations and anions and the steric interaction imposed by restricting the
maximal occupancy at any lattice site to one particle. Despite the simplicity
of the model, a wide range of intriguing physical phenomena arise, some of
which are strongly reminiscent of those seen in experiments and numerical
simulations of three dimensional ionic liquid based capacitors. Notably we find
regimes where over-screening and density oscillations are seen near the
capacitor plates. The capacitance is also shown to exhibit strong oscillations
as a function of applied voltage. It is also shown that the corresponding mean
field theory misses most of these effects. The analytical results are confirmed
by extensive numerical simulations.
