  We develop an approach for the description of the dynamics of large
populations of phase oscillators based on "circular cumulants" instead of the
Kuramoto-Daido order parameters. In the thermodynamic limit, these variables
yield a simple representation of the Ott-Antonsen invariant solution [E. Ott
and T. M. Antonsen, CHAOS 18, 037113 (2008)] and appear appropriate for
constructing the perturbation theory on top of the Ott-Antonsen ansatz. We
employ this approach to study the impact of small intrinsic noise on the
dynamics. As a result, a closed system of equations for the two leading
cumulants, describing the dynamics of noisy ensembles, is derived. We exemplify
the general theory by presenting the effect of noise on the Kuramoto system and
on a chimera state in two symmetrically coupled populations.
