  In our conventional understanding, large-scale magnetic fields are thought to
originate from an inverse cascade in the presence of magnetic helicity,
differential rotation, or a magneto-rotational instability. However, as recent
simulations have given strong indications that an inverse cascade (transfer)
may occur even in the absence of magnetic helicity, the physical origin of this
inverse cascade is still not fully understood. We here present two simulations
of freely decaying helical \& non-helical magnetohydrodynamic (MHD) turbulence.
We verified the inverse transfer of helical and non-helical magnetic fields in
both cases, but we found the underlying physical principles to be fundamentally
different. In the former case, the helical magnetic component leads to an
inverse cascade of magnetic energy. We derived a semi analytic formula for the
evolution of large scale magnetic field using $\alpha$ coefficient and compared
it with the simulation data. But in the latter case, the $\alpha$ effect,
including other conventional dynamo theories, are not suitable to describe the
inverse transfer of non-helical magnetic. To obtain a better understanding of
the physics at work here, we introduced a `field structure model' based on the
magnetic induction equation in the presence of inhomogeneities. This model
illustrates how the curl of the electromotiveforce (EMF) leads to the build up
of a large-scale magnetic field without the requirement of magnetic helicity.
And we applied a Quasi Normal approximation to the inverse transfer of magnetic
energy.
