ner_tags: O O O O O O O O O O O O O O O O O O O O O O O O O O B-Model O B-Model I-Model O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation O O O O O O O O O O O O O O O O B-Citation I-Citation O O O O O O O O B-Citation I-Citation I-Citation I-Citation O O O O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation O O B-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O
tokens: The saturation of the MRI and the outcome of a disc subject to these non-ideal effects is still the subject of intense debate. Stratified models including Ohmic and ambipolar diffusion only have shown that the disc could become essentially laminar (i.e. not turbulent) in the midplane, with a strong magnetically driven jet at the disc surface ( Bai Stone 2013 ; Simon et al. 2013 ; Gressel et al. 2015 ). For radii 1 between 1 and 10 au (where Hall effect dominates diffusive processes) a large-scale midplane stress is found by adding the Hall effect, with a strong field polarity dependence and no turbulence ( Lesur et al. 2014 ; Bai 2014 ), whereas the outer disc is found to be essentially insensitive to the Hall effect ( Bai 2015 ), though some polarity dependence could persist ( Simon et al. 2015 ). The results of Lesur et al. (2014) and Bai (2014) and, in particular, the presence of a large-scale “laminar” stress are both important and potentially problematic results. In effect, these simulations were done in the stratified shearing box framework ( Hawley et al. 1995 ) with a very limited radial extension (typically a few scale heights), so the Lesur et al. (2014) and Bai (2014) results indicate that the MRI is indeed active in these simulations, but it tends to produce structures that are larger than the simulation box. As a matter of fact, unstratified shearing box models have already indicated that the Hall-dominated MRI is prone to produce large-scale structures, such as zonal fields and flows ( Kunz Lesur 2013 , hereafter KL13) in wide enough boxes. All of these elements tend to point toward the fact that the Hall effect could be an efficient mechanism for triggering self-organisation in protoplanetary discs. In this paper, we explore this hypothesis using full 3D cylindrical models of accretion discs dominated by the Hall effect. Our aim is not to reproduce the exact structure of a disc with its detailed ionisation equilibrium but to test the hypothesis of self-organisation in a global model, free of the artefacts found in local, i.e. shearing-box simulations. We start by describing the physical framework in detail and giving and some remarkable facts concerning Hall dynamics. We then depict our numerical model and present the tests performed to validate it along with a reproduction and discussion of the multifluid models of O’Keeffe Downes (2014) . Next, we move to the core of the paper with the presentation and characterisation of several Hall-dominated models, putting emphasis on the physical mechanisms driving self-organisation. We then explore some potential treats to these mechanisms such as diffusive effects and more complex field configurations. We conclude by discussing the link between these results and recent observations along with extensions of this work to more realistic numerical setups. 2. Framework 2.1. Physical model We want to model a thin disc of partially ionised gas orbiting a central mass and threaded by a