The problem of the dynamo effect for a Kraichnan incompressible helicity-free
velocity field is considered. Exploiting a quantum formalism first introduced
by Kazantsev (A.P. Kazantsev, Sov. Phys. JETP 26, 1031-1034 (1968)), we show
that a critical magnetic Reynolds number exists for the presence of dynamo. The
value of the Prandtl number influences the spatial distribution of the magnetic
field and its growth in time. The magnetic field correlation length is always
the largest between the diffusive scale and the viscous scale of the flow. In
the same way the field growth is characterized by a time scale that corresponds
to the largest between the diffusive and the viscous characteristic time.Comment: 16 pages, 6 figure
