Dust dynamics in RAMSES -- I. Methods and turbulent acceleration
  Supernova ejecta and stellar winds are believed to produce interstellar dust
grains with relatively large sizes. One way to produce smaller grains is via
the shattering of large grains that have been stochastically accelerated to
high velocities. To understand this stochastic acceleration, we have
implemented novel magnetohydrodynamic(MHD)-particle-in-cell(PIC) methods into
the astrophysical fluid code RAMSES. We treat dust grains as a set of massive
"superparticles" that experience aerodynamic drag and Lorentz force. We subject
our code to a range of numerical tests designed to validate our method in
different physical conditions, as well as to illustrate possible mechanisms by
which grains can be accelerated. As a final test as well as a foundation for
future work, we present the results of decaying dusty MHD turbulence
simulations with grain parameters chosen to resemble 1-2 $\mu$m grains in
typical cold neutral medium conditions. We find that in these conditions, these
grains can be effectively accelerated to well beyond their shattering
velocities. This is true for both electrically charged and neutral grains.
While the peak of the gas-grain relative drift velocity distribution is higher
for neutral grains, the drift velocity distribution of charged grains exhibits
an extended exponential tail out to much greater velocities. Even so, the
shapes of the distributions are such that the extra gas-grain coupling provided
by the Lorentz force offers grains relative protection from shattering.
