Turbulent Diffusion of Magnetic Fields in Weakly Ionized Gas

The diffusion of uni-directional magnetic fields by two dimensional turbulent flows in a weakly ionized gas is studied. The fields here are orthogonal to the plane of fluid motion. This simple model arises in the context of the decay of the mean magnetic flux to mass ratio in the interstellar medium. When ions are strongly coupled to neutrals, the transport of a large--scale magnetic field is driven by both turbulent mixing and nonlinear, ambipolar drift. Using a standard homogeneous and Gaussian statistical model for turbulence, we show rigorously that a large-scale magnetic field can decay on at most turbulent mixing time scales when the field and neutral flow are strongly coupled. There is no enhancement of the decay rate by ambipolar diffusion. These results extend the Zeldovich theorem to encompass the regime of two dimensional flows and orthogonal magnetic fields, recently considered by Zweibel (2002). The limitation of the strong coupling approximation and its implications are discussed.