  The eigenvalue probability density functions of the classical random matrix
ensembles have a well known analogy with the one component log-gas at the
special couplings \beta = 1,2 and 4. It has been known for some time that there
is an exactly solvable two-component log-potential plasma which interpolates
between the \beta =1 and 4 circular ensemble, and an exactly solvable
two-component generalized plasma which interpolates between \beta = 2 and 4
circular ensemble. We extend known exact results relating to the latter --- for
the free energy and one and two-point correlations --- by giving the general
(k_1+k_2)-point correlation function in a Pfaffian form. Crucial to our working
is an identity which expresses the Vandermonde determinant in terms of a
Pfaffian. The exact evaluation of the general correlation is used to exhibit a
perfect screening sum rule.
