Context . Magnetohydrodynamic (MHD) turbulence plays a crucial role in the dust dynamics of protoplanetary discs. It affects planet formation, vertical settling, and is one possible origin of the large scale axisymmetric structures, such as rings, recently imaged by ALMA and SPHERE. Among the variety of MHD processes in discs, the magnetorotational instability (MRI) has raised particular interest since it provides a source of turbulence and potentially organizes the flow into large scale structures. However, the weak ionization of discs prevents the MRI from being excited beyond 1 AU. Moreover, the low velocity dispersion observed in CO and strong sedimentation of millimetre dust measured in T-Tauri discs are in contradiction with predictions based on ideal MRI turbulence. Aims . In this paper, we study the effects of non-ideal MHD and magnetized winds on the dynamics and sedimentation of dust grains. We consider a weakly ionized plasma subject to ambipolar diffusion characterizing the disc outer regions (?1 AU). Methods . To compute the dust and gas motions, we performed numerical MHD simulations in the stratified shearing box, using a modified version of the PLUTO code. We explored different grain sizes from micrometre to few centimetres and different disc vertical magnetizations with plasma beta ranging from 10~(3)to 10~(5). Results . Our simulations show that the mm-cm dust is contained vertically in a very thin layer, with typical heightscale ?0.4 AU at R = 30 AU, compatible with recent ALMA observations. Horizontally, the grains are trapped within the pressure maxima (or zonal flows) induced by ambipolar diffusion, leading to the formation of dust rings. For micrometre grains and strong magnetization, we find that the dust layer has a size comparable to the disc heightscale H . In this regime, dust settling cannot be explained by a simple 1D diffusion theory but results from a large scale 2D circulation induced by both MHD winds and zonal flows. Conclusions . Our results suggest that non-ideal MHD effects and MHD winds associated with zonal flows play a major role in shaping the radial and vertical distribution of dust in protoplanetary discs. Leading to effective accretion efficiency α ? 10~(?3)–10~(?1), non-ideal MHD models are also a promising avenue to reconcile the low turbulent activity measured in discs with their relatively high accretion rates.
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