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Most numerical investigations on the role of magnetic fields in turbulentmolecular clouds (MCs) are based on ideal magneto-hydrodynamics (MHD). However,MCs are weakly ionized, so that the time scale required for the magnetic fieldto diffuse through the neutral component of the plasma by ambipolar diffusion(AD) can be comparable to the dynamical time scale. We have performed a seriesof 256^3 and 512^3 simulations on supersonic but sub-Alfvenic turbulent systemswith AD using the Heavy-Ion Approximation developed in Li, McKee, & Klein(2006). Our calculations are based on the assumption that the number of ions isconserved, but we show that these results approximately apply to the case oftime-dependent ionization in molecular clouds as well. Convergence studiesallow us to determine the optimal value of the ionization mass fraction whenusing the heavy-ion approximation for low Mach number, sub-Alfvenic turbulentsystems. We find that ambipolar diffusion steepens the velocity and magneticpower spectra compared to the ideal MHD case. Changes in the density PDF, totalmagnetic energy, and ionization fraction are determined as a function of the ADReynolds number. The power spectra for the neutral gas properties of a stronglymagnetized medium with a low AD Reynolds number are similar to those for aweakly magnetized medium; in particular, the power spectrum of the neutralvelocity is close to that for Burgers turbulence.

Sub-Alfvenic Non-Ideal MHD Turbulence Simulations with Ambipolar Diffusion: I. Turbulence Statistics