  Under ideal MHD conditions the magnetic field strength should be correlated
with density in the interstellar medium (ISM). However, observations indicate
that this correlation is weak. Ambipolar diffusion can decrease the
flux-to-mass ratio in weakly ionized media; however, it is generally thought to
be too slow to play a significant role in the ISM except in the densest
molecular clouds. Turbulence is often invoked in astrophysical problems to
increase transport rates above the (very slow) laminar values predicted by
kinetic theory. We describe a series of numerical experiments addressing the
problem of turbulent transport of magnetic fields in weakly ionized gases. We
show, subject to various geometrical and physical restrictions, that turbulence
in a weakly ionized medium rapidly diffuses the magnetic flux to mass ratio
through the buildup of appreciable ion-neutral drifts on small scales. These
results are applicable to the fieldstrength - density correlation in the ISM,
as well as the merging of flux systems such as protostar and accretion disk
fields or protostellar jets with ambient matter, and the vertical transport of
galactic magnetic fields.
