  Accretion disks are likely threaded by external vertical magnetic flux, which
enhances the level of turbulence via the magnetorotational instability (MRI).
Using shearing-box simulations, we find that such external magnetic flux also
strongly enhances the amplitude of banded radial density variations known as
zonal flows. Moreover, we report that vertical magnetic flux is strongly
concentrated toward low-density regions of the zonal flow. Mean vertical
magnetic field can be more than doubled in low-density regions, and reduced to
nearly zero in high density regions in some cases. In ideal MHD, the scale on
which magnetic flux concentrates can reach a few disk scale heights. In the
non-ideal MHD regime with strong ambipolar diffusion, magnetic flux is
concentrated into thin axisymmetric shells at some enhanced level, whose size
is typically less than half a scale height. We show that magnetic flux
concentration is closely related to the fact that the magnetic diffusivity of
the MRI turbulence is anisotropic. In addition to a conventional Ohmic-like
turbulent resistivity, we find that there is a correlation between the vertical
velocity and horizontal magnetic field fluctuations that produces a mean
electric field that acts to anti-diffuse the vertical magnetic flux. The
anisotropic turbulent diffusivity has analogies to the Hall effect, and may
have important implications for magnetic flux transport in accretion disks. The
physical origin of magnetic flux concentration may be related to the
development of channel flows followed by magnetic reconnection, which acts to
decrease the mass-to-flux ratio in localized regions. The association of
enhanced zonal flows with magnetic flux concentration may lead to global
pressure bumps in protoplanetary disks that helps trap dust particles and
facilitates planet formation.
