  We have investigated the phase transition of the gas-liquid type, with an
upper critical point, in a variant of the One Component Plasma model (OCP) that
has a uniform but compressible compensating background. We have calculated the
parameters of the critical and triple points, spinodals, and two-phase
coexistence curves (binodals). We have analyzed the connection of this simplest
plasma phase transition with anomalies in the spatial charge profiles of
equilibrium non-uniform plasma in the local-density approximations of
Thomas-Fermi or Poisson-Boltzmann-type.
