  We study the onset of the reheating epoch at the end of axion-driven
inflation where the axion is coupled to an Abelian, $U(1)$, gauge field via a
Chern-Simons interaction term. We focus primarily on $m^2\phi^2$ inflation and
explore the possibility that preheating can occur for a range of coupling
values consistent with recent observations and bounds on the overproduction of
primordial black holes. We find that for a wide range of parameters preheating
is efficient. In certain cases the inflaton is seen to transfer all its energy
to the gauge fields within a few oscillations. In most cases, we find that the
gauge fields on sub-horizon scales end preheating in an unpolarized state due
to the existence of strong rescattering between the inflaton and gauge-field
modes. We also present a preliminary study of an axion monodromy model coupled
to $U(1)$ gauge fields, seeing a similarly efficient preheating behavior as
well as indications that the coupling strength has an effect on the creation of
oscillons.
