  We study a two-dimensional Coulomb gas consisting of a mixture of particles
carrying various positive multiple integer charges, confined on a unit circle.
We consider the system in the canonical and grand canonical ensembles, and
attempt to calculate the partition functions analytically, using Toeplitz and
confluent Vandermonde determinants. Just like in the simple one-component
system (Dyson gas), the partition functions simplify at special temperature
$\beta=2$, allowing us to find compact expressions for them.
