Joint inverse cascade of magnetic energy and magnetic helicity in MHD
  turbulence
  We show that oppositely directed fluxes of energy and magnetic helicity
coexist in the inertial range in fully developed magnetohydrodynamic (MHD)
turbulence with small-scale sources of magnetic helicity. Using a helical shell
model of MHD turbulence, we study the high Reynolds number magnetohydrodynamic
turbulence for helicity injection at a scale that is much smaller than the
scale of energy injection. In a short range of scales larger than the forcing
scale of magnetic helicity, a bottleneck-like effect appears, which results in
a local reduction of the spectral slope. The slope changes in a domain with a
high level of relative magnetic helicity, which determines that part of the
magnetic energy related to the helical modes at a given scale. If the relative
helicity approaches unity, the spectral slope tends to $-3/2$. We show that
this energy pileup is caused by an inverse cascade of magnetic energy
associated with the magnetic helicity. This negative energy flux is the
contribution of the pure magnetic-to-magnetic energy transfer, which vanishes
in the non-helical limit. In the context of astrophysical dynamos, our results
indicate that a large-scale dynamo can be affected by the magnetic helicity
generated at small scales. The kinetic helicity, in particular, is not involved
in the process at all. An interesting finding is that an inverse cascade of
magnetic energy can be provided by a small-scale source of magnetic helicity
fluctuations without a mean injection of magnetic helicity.
