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Previous axisymmetric investigations in two dimensions (2D) have shown thatrings and gaps develop naturally in non-ideal magnetohydrodynamic (MHD)disk-wind systems, especially in the presence of ambipolar diffusion (AD). Herewe extend these 2D simulations to three dimensions (3D) and find that rings andgaps are still formed in the presence of a moderately strong ambipolardiffusion. The rings and gaps form from the same basic mechanism that wasidentified in the 2D simulations, namely, the redistribution of the poloidalmagnetic flux relative to the disk material as a result of the reconnection ofa sharply pinched poloidal magnetic field lines. Thus, the less dense gaps aremore strongly magnetized with a large poloidal magnetic field compared to theless magnetized (dense) rings. The rings and gaps start out rather smoothly in3D simulations that have axisymmetric initial conditions. Non-axisymmetricvariations arise spontaneously at later times, but they do not grow to such anextent as to disrupt the rings and gaps. These disk substructures persist tothe end of the simulations, lasting up to 3000 orbital periods at the inneredge of the simulated disk. The longevity of the perturbed yet still coherentrings make them attractive sites for trapping large grains that would otherwisebe lost to rapid radial migration due to gas drag. As the ambipolar diffusivitydecreases, both the disk and the wind become increasingly turbulent, driven bythe magnetorotational instability, with tightly-wound spiral arms becoming moreprominent in the disk.

The formation of rings and gaps in wind-launching non-ideal MHD disks: three-dimensional simulations