  The existence of a dynamo effect in a simplified magnetohydrodynamic model of
turbulence is considered when the magnetic Prandtl number approaches zero or
infinity. The magnetic field is interacting with an incompressible
Kraichnan-Kasantzev model velocity field augmented with a viscous scale cutoff.
An approximate system of equations in the different scaling ranges can be
formulated and solved, so that the solution tends to the exact one when the
viscous and magnetic-diffusive cutoffs approach zero. In this approximation we
are able to determine analytically the conditions for the existence of a dynamo
effect and give an estimate of the dynamo growth rate. Among other things we
show that in the large Prandtl number case the dynamo effect is always present.
Our analytical estimates are in good agreement with previous numerical studies
of the Kraichnan-Kasantzev dynamo by D. Vincenzi.
