  Using direct numerical simulations we demonstrate that magnetic helicity
exhibits a bidirectional turbulent cascade at high but finite magnetic Reynolds
numbers. Despite the injection of positive magnetic helicity in the flow, we
observe that magnetic helicity of opposite signs is generated between large and
small scales. We explain these observations by carrying out an analysis of the
magnetohydrodynamic equations reduced to triad interactions using the Fourier
helical decomposition. Within this framework, the direct cascade of positive
magnetic helicity arises through triad interactions that are associated with
small scale dynamo action, while the occurrence of negative magnetic helicity
at large scales is explained through triad interactions that are related to
stretch-twist-fold dynamics and small scale dynamo action, which compete with
the inverse cascade of positive magnetic helicity. Our analytical and numerical
results suggest that the direct cascade of magnetic helicity is a finite
magnetic Reynolds number $Rm$ effect that will vanish in the limit $Rm \to
\infty$.
