  The small-scale magnetic field is ubiquitous at the solar surface---even at
high latitudes. From observations we know that this field is uncorrelated (or
perhaps even weakly anticorrelated) with the global sunspot cycle. Our aim is
to explore the origin, and particularly the cycle dependence of such a
phenomenon using three-dimensional dynamo simulations. We adopt a simple model
of a turbulent dynamo in a shearing box driven by helically forced turbulence.
Depending on the dynamo parameters, large-scale (global) and small-scale
(local) dynamos can be excited independently in this model. Based on
simulations in different parameter regimes, we find that, when only the
large-scale dynamo is operating in the system, the small-scale magnetic field
generated through shredding and tangling of the large-scale magnetic field is
positively correlated with the global magnetic cycle. However, when both
dynamos are operating, the small-scale field is produced from both the
small-scale dynamo and the tangling of the large-scale field. In this
situation, when the large-scale field is weaker than the equipartition value of
the turbulence, the small-scale field is almost uncorrelated with the
large-scale magnetic cycle. On the other hand, when the large-scale field is
stronger than the equipartition value, we observe an anticorrelation between
the small-scale field and the large-scale magnetic cycle. This anticorrelation
can be interpreted as a suppression of the small-scale dynamo. Based on our
studies we conclude that the observed small-scale magnetic field in the Sun is
generated by the combined mechanisms of small-scale dynamo and tangling of the
large-scale field.
