  Rider, Sinclair and Xu (2013) introduced a solvable two charge ensemble of
interacting charged particles on the real line in the presence of the harmonic
oscillator potential. It can be seen as a special form of a grand canonical
ensemble with the total charge being fixed and unit charge particles being
random. Moreover, it serves as an interpolation between the Gaussian orthogonal
and the Gaussian symplectic ensembles and maintains the Pfaffian structure of
the eigenvalues. A similar solvable ensemble of charged particles on the unit
circle was studied by Shum and Sinclair (2014) and Forrester (2010). In this
paper we explore the sharp asymptotic behavior of the number of unit charge
particles on the line and on the circle, as the total charge goes to infinity.
We establish extended central limit theorems, Berry-Esseen estimates and
precise moderate deviations using the machinery of the mod-Gaussian
convergence. Also a large deviation principle is derived using the
G\"artner-Ellis theorem.
