Modelling ambipolar diffusion with two-fluid smoothed particle hydrodynamics

We describe a fully three-dimensional, Lagrangian magnetohydrodynamics code that is able to treat self-gravitating gas dynamics and to take account of ambipolar diffusion. The ion density is given as a function of the local neutral density, using an expression derived from models of ionization balance in molecular clouds. In turn, the ion density determines the strength of the coupling between the ionized and neutral fluids. The code is tested by modelling the evolution of a dense core, which is initially thermally supercritical but magnetically subcritical. The core steadily loses its magnetic support through ambipolar diffusion, and eventually becomes unstable against collapse. Our results agree well with those obtained by Fiedler and Mouschovias, who modelled the same system using a two-dimensional finite-difference code. In a second paper, we apply this code to the collapse and fragmentation of a rotating prestellar core.