Conditions for justifying single-fluid approximation for charged and
  neutral dust fluids and a smoothed particle magnetohydrodynamics method for
  dust-gas mixture
  We describe a numerical scheme for magnetohydrodynamics simulations of
dust-gas mixture by extending smoothed particle magnetohydrodynamics. We employ
the single-species particle approach to describe dust-gas mixture with several
modifications from the previous studies. We assume that the charged and neutral
dusts can be treated as single-fluid and the electro-magnetic force acts on the
gas and that on the charged dust is negligible. The validity of these
assumption in the context of protostar formation is not obvious and is
extensively evaluated. By investigating the electromagnetic force and electric
current with terminal velocity approximation, it is found that as the dust size
increases, the contribution of dust to them becomes smaller and negligible. We
conclude that our assumptions of the electro-magnetic force on the dusts is
negligible are valid for the dust size with a d & 10{\mu}m. On the other hand,
they do not produce the numerical artifact for the dust a d . 10{\mu}m in
envelope and disk where the perfect coupling between gas and dusts realizes.
However, we also found that our assumptions may break down in outflow (or under
environment with very strong magnetic field and low density) for the dust a d .
10{\mu}m. We conclude that our assumptions are valid in almost all cases where
macroscopic dust dynamics is important in the context of protostar formation.
We conduct numerical tests of dusty wave, dusty magnetohydrodynamics shock, and
gravitational collapse of magnetized cloud core with our simulation code. The
results show that our numerical scheme well reproduces the dust dynamics in the
magnetized medium.
