Large-scale magnetic fields play a vital role in determining the angular momentum transport and generating jets/outflows in accreting systems, yet their origins remain poorly understood. We focus on radiatively inefficient accretion flows (RIAFs) around black holes (BHs), and conduct 3D general-relativistic magnetohydrodynamic simulations using the Athena++ code. We first reconfirm that the magnetorotational instability driven dynamo in the RIAF alone does not spontaneously form a magnetically arrested disk (MAD), conducive for strong-jet formation. We next investigate the other possibility, where the large-scale magnetic fields are advected inward from external sources (e.g., the companion star in X-ray binaries and the magnetized ambient medium in active galactic nuclei). Although the actual configurations of the external fields could be complex and uncertain, they are likely to be closed. As a first study, we treat them as closed field loops of different sizes, shapes, and field strengths. Unlike earlier studies of flux transport, where the magnetic flux is injected into the initial laminar flow, we inject the magnetic field loops into the quasi-stationary turbulent RIAF in inflow equilibrium, then follow their evolution. We find that a substantial fraction (~15%-40%) of the flux injected at large radii reaches the BH, with a weak dependence on the loop parameters, except when the loops are injected at high latitudes, away from the midplane. The relatively high efficiency of the flux transport observed in our study hints that a MAD might easily be formed relatively close to the BH, provided that a source of the large-scale field exists at larger radii.
