Self-consistent Mean Field Theory in Weakly Ionized Gas

We present a self-consistent mean field theory of the dynamo in 3D and turbulent diffusion in 2D in weakly ionized gas. We find that in 3D, the backreaction does not alter the beta effect while it suppresses the alpha effect when the strength of a mean magnetic field exceeds the critical value Bc ∼ √ νinτn〈v2〉/Rm. Here, νin, τn, and Rm are ion-neutral collision frequency, correlation time of neutrals, and magnetic Reynolds number, respectively. These results suggest that a mean field dynamo operates much more efficiently in weakly ionized gas where νinτn ≫ 1, compared to the fully ionized gas. Furthermore, we show that in 2D, the turbulent diffusion is suppressed by back reaction when a mean magnetic field reaches the same critical strength Bc, with the upper bound on turbulent diffusion given by its kinematic value. Astrophysical implications are discussed. Subject headings: ISM:magnetic fields—MHD—turbulence