The Kraichnan–Kazantsev Dynamo

We investigate the dynamo effect generated by an incompressible, helicity-free flow drawn from the Kraichnan statistical ensemble. The quantum formalism introduced by Kazantsev [A. P. Kazantsev, Sov. Phys. JETP26, 1031–1034 (1968)] is shown to yield the growth rate and the spatial structure of the magnetic field. Their dependences on the magnetic Reynolds number and the Prandtl number are analyzed. The growth rate is found to be controlled by the largest between the diffusive and the viscous characteristic times. The same holds for the magnetic field correlation length and the corresponding spatial scales.