  Protoplanetary disks form through angular momentum conservation in collapsing
dense cores. In this work, we perform the first simulations with a maximal
resolution down to the astronomical unit (au) of protoplanetary disk formation,
through the collapse of 1000 solar mass clumps, treating self-consistently both
non-ideal magnetohydrodynamics with ambipolar diffusion as well as radiative
transfer in the flux-limited diffusion approximation including stellar
feedback. Using the adaptive mesh-refinement code RAMSES, we investigate the
influence of the magnetic field on the disks properties with three models. We
show that, without magnetic fields, a population dominated by large disks is
formed, which is not consistent with Class 0 disk properties as estimated from
observations. The inclusion of magnetic field leads, through magnetic braking,
to a very different evolution. When it is included, small < 50 au disks
represent about half the population. In addition, about ~ 70% of the stars have
no disk in this case which suggests that our resolution is still insufficient
to preserve the smaller disks. With ambipolar diffusion, the proportion of
small disks is also prominent and we report a flat mass distribution around
0.01-0.1 solar mass and a typical disk-to-star mass ratios of ~0.01-0.1. This
work shows that the magnetic field and its evolution plays a prominent role in
setting the initial properties of disk populations.
