  Context: Chondrules originate from the reprocessing of dust grains. They are
key building blocks of telluric planets, yet their formation, which must happen
in strongly localized regions of high temperature, remains poorly understood.
Aims: We examine the dust spatial distribution near regions of strong local
heating produced by current sheets, as a step toward exploring a potential path
for chondrule formation. We further aim to investigate current sheet formation
under various conditions in protoplanetary disks in the presence of ambipolar
diffusion and Ohmic resistivity and the effect of current sheet morphology on
dust dynamics in their vicinity. Methods: We use the RAMSES code including
modules for non-ideal magnetohydrodynamics and solution of the dynamics of
multiple sizes of dust grains to compute unstratified shearing box simulations
of current sheet formation. We investigate, through seven models the effect of
the ambipolar diffusion and Ohmic resistivity strength, the initial density,
and magnetic field, as well as the resolution and box size. Results: We find
that current sheets form in all our models, with typical widths of 0.001-0.01
AU and that strong dust fraction variations occur for millimeter-sized grains.
These variations are typically of an order of magnitude and up to two orders of
magnitude for the most favorable cases. We also show that the box size and
resolution has a strong impact on the current sheet distribution and intensity.
Conclusions: The formation of current sheets that can intensely heat their
surroundings near strong dynamical dust fraction variations could have
important implications for chondrule formation, as it appears likely to happen
in regions of large dust fraction.
