  We consider a natural generalization of the Kazantsev-Kraichnan model for
small-scale turbulent dynamo. This generalization takes account of statistical
time asymmetry of a turbulent flow, and, thus, allows to describe velocity
fields with energy cascade. For three-dimensional velocity field, generalized
Kazantsev equation is derived, and evolution of the second order magnetic field
correlator is investigated for large but finite magnetic Prandtl numbers. It is
shown that as $Pr_m \to \infty$, the growth increment tends to the limit known
from the T-exponential (Lagrangian deformation) method. Magnetic field
generation is shown to be weaker than that in the Gaussian velocity field for
any direction of the energy cascade, and depends essentially on the Prandtl
number.
