  Nuclear rings at the centers of barred galaxies are known to be strongly
magnetized. To explore the effects of magnetic fields on star formation in
these rings and nuclear gas flows, we run magnetohydrodynamic simulations in
which there is a temporally-constant magnetized inflow to the ring,
representing a bar-driven inflow. The mass inflow rate is
$1\,M_\odot\,\mathrm{yr}^{-1}$, and we explore models with a range of field
strength in the inflow. We adopt the TIGRESS framework developed by Kim &
Ostriker to handle radiative heating and cooling, star formation, and resulting
supernova (SN) feedback. We find that magnetic fields are efficiently amplified
in the ring due to rotational shear and SN feedback. Within a few
$100\,\mathrm{Myr}$, the turbulent component $B_\mathrm{trb}$ in the ring
saturates at $\sim 35\,\mu\mathrm{G}$ (in rough equipartition with the
turbulent kinetic energy density), while the regular component $B_\mathrm{reg}$
exceeds $50\,\mu\mathrm{G}$. Expanding superbubbles created by clustered SN
explosions vertically drag predominantly-toroidal fields from near the midplane
to produce poloidal fields in high-altitude regions. The growth of magnetic
fields greatly suppresses star formation at late times. Simultaneously, strong
magnetic tension in the ring drives radially inward accretion flows from the
ring to form a circumnuclear disk in the central region; this feature is absent
in the unmagnetized model.
