  We employ the circular cumulant approach to construct a low dimensional
description of the macroscopic dynamics of populations of phase oscillators
(elements) subject to non-Gaussian white noise. Two-cumulant reduction
equations for alpha-stable noises are derived. The implementation of the
approach is demonstrated for the case of the Kuramoto ensemble with
non-Gaussian noise. The results of direct numerical simulation of the ensemble
of N=1500 oscillators and the "exact" numeric solution for the fractional
Fokker-Planck equation in the Fourier space are found to be in good agreement
with the analytical solutions for two feasible circular cumulant model
reductions. We also illustrate that the two-cumulant model reduction is useful
for studying the bifurcations of chimera states in hierarchical populations of
coupled noisy phase oscillators.
