Traces of large-scale dynamo action in the kinematic stage
  Using direct numerical simulations (DNS) we verify that in the kinematic
regime, a turbulent helical dynamo grows in such a way that the magnetic energy
spectrum remains to high precision shape-invariant, i.e., at each wavenumber
$k$ the spectrum grows with the same growth rate. Signatures of large-scale
dynamo action can be identified through the excess of magnetic energy at small
$k$, of one of the two oppositely polarized constituents. Also a suitably
defined planar average of the magnetic field can be chosen such that its rms
value isolates the strength of the mean field. However, these different means
of analysis suggest that the strength of the large-scale field diminishes with
increasing magnetic Reynolds number ${\rm Re}_{\rm M}$ like ${\rm Re}_{\rm
M}^{-1/2}$ for intermediate values and like ${\rm Re}_{\rm M}^{-3/4}$ for
larger ones. Both an analysis from the Kazantsev model including helicity and
the DNS show that this arises due to the magnetic energy spectrum still peaking
at resistive scales, even when helicity is present. As expected, the amplitude
of the large-scale field increases with increasing fractional helicity,
enabling us to determine the onset of large scale dynamo action and
distinguishing it from that of the small-scale dynamo. Our DNS show that,
contrary to earlier results for smaller scale separation (only 1.5 instead of
now 4), the small-scale dynamo can still be excited at magnetic Prandtl numbers
of 0.1 and only moderate values of the magnetic Reynolds numbers ($\sim 160$).
