  We report on a global, three-dimensional GRMHD simulation of an accretion
torus embedded in a large scale vertical magnetic field orbiting a
Schwarzschild black hole. This simulation investigates how a large scale
vertical field evolves within a turbulent accretion disk and whether global
magnetic field configurations suitable for launching jets and winds can
develop. We find that a "coronal mechanism" of magnetic flux motion, which
operates largely outside the disk body, dominates global flux evolution. In
this mechanism, magnetic stresses driven by orbital shear create large-scale
half-loops of magnetic field that stretch radially inward and then reconnect,
leading to discontinuous jumps in the location of magnetic flux. In contrast,
little or no flux is brought in directly by accretion within the disk itself.
The coronal mechanism establishes a dipole magnetic field in the evacuated
funnel around the orbital axis with a field intensity regulated by a
combination of the magnetic and gas pressures in the inner disk. These results
prompt a reevaluation of previous descriptions of magnetic flux motion
associated with accretion. Local pictures are undercut by the intrinsically
global character of magnetic flux. Formulations in terms of an "effective
viscosity" competing with an "effective resistivity" are undermined by the
nonlinearity of of the magnetic dynamics and the fact that the same turbulence
driving mass motion (traditionally identified as "viscosity") can alter
magnetic topology.
