Two-Fluid Ambipolar Diffusion in Molecular Cloud Cores at Low Ionization Fractions

Molecular clouds are the sites of star formation. The densities within these clouds are large enough that the interiors are shielded from external sources of ionization, leading to the bulk of the gas partially decoupling from the magnetic field. It is therefore desirable to have numerical methods that can accurately and efficiently treat ambipolar diffusion at low ionization fractions. We present such a method here using a two-fluid (neutral and ionized) formulation, and demonstrate that it can reproduce the relevant dispersion relations and track the structure of C-shocks. We proceed to examine the collapse of a partially-ionized rotating molecular cloud core.