  The model under consideration is an asymmetric two-dimensional Coulomb gas of
positively (q_1=+1) and negatively (q_2=-1/2) charged pointlike particles,
interacting via a logarithmic potential. This continuous system is stable
against collapse of positive-negative pairs of charges for the dimensionless
coupling constant (inverse temperature) \beta<4. The mapping of the Coulomb gas
is made onto the complex Bullough-Dodd model, and recent results about that
integrable 2D field theory are used. The mapping provides the full
thermodynamics (the free energy, the internal energy, the specific heat) and
the large-distance asymptotics of the particle correlation functions, in the
whole stability regime of the plasma. The results are checked by a small-\beta
expansion and close to the collapse \beta=4 point. The comparison is made with
the exactly solvable symmetric version of the model (q_1=+1, q_2=-1), and some
fundamental changes in statistics caused by the charge asymmetry are pointed
out.
