Helical turbulence is thought to provide the key to the generation of
large-scale magnetic fields. Turbulence also generically leads to rapidly
growing small-scale magnetic fields correlated on the turbulence scales. These
two processes are usually studied separately. We give here a unified treatment
of both processes, in the case of random fields, incorporating also a simple
model non-linear drift. In the process we uncover an interesting plausible
saturated state of the small-scale dynamo and a novel analogy between quantum
mechanical (QM) tunneling and the generation of large scale fields. The steady
state problem of the combined small/large scale dynamo, is mapped to a
zero-energy, QM potential problem; but a potential which, for non-zero mean
helicity, allows tunneling of bound states. A field generated by the
small-scale dynamo, can 'tunnel' to produce large-scale correlations, which in
steady state, correspond to a force-free 'mean' field.Comment: 4 pages, 1 figure, Physical Review Letters, in pres
