  The scale separation approximation, which is in the base of the solar mean
field dynamo models, can be hardly justified both by observations and
theoretical applications to astrophysical dynamos.{ The general expression for
the mean turbulent electromotive force can be written in integral form with
convolution of the turbulent effects and mean magnetic field variations over
scales of the turbulent flows and global scales of the mean field dynamo.
Following results of DNS, which had been reported earlier, we take the
Lorentzian form of the integral convolution kernels as an experimental fact.
}It allows us to approximate the governing equation for the mean electromotive
force by the reaction--diffusion type equation. Solution of the eigenvalue
problem reveals a few curious properties of the dynamo model with the nonlocal
mean electromotive force. We find a decrease of the critical dynamo instability
threshold, and an increase the dynamo periods of the unstable modes, as
reported in earlier studies. Simultaneously, the nonlocal model shows
substantially lower growth rate of the unstable dynamo modes in proximity of
the critical threshold than the model which employ the scale separation
approximation. We verify these findings using the nonlinear solar dynamo model.
For the supercritical regime, when the $\alpha$ effect magnitude is about twice
of the instability threshold, the model shows the Parker's dynamo wave
solutions with the wave propagating from the mid latitude at the bottom of the
convection zone toward the solar equator at the surface. In the weakly
nonlinear regime, when the $\alpha$ effect magnitude is near the instability
threshold, the interference of the dynamo modes of different spatial
localization shows the Grand activity cycles of a period about 300 years.
