We present a self-consistent mean field theory of the dynamo in three dimensions and turbulent diffusion in two dimensions in weakly ionized gases. We find that in three dimensions, the back-reaction does not alter the β-effect while it suppresses the α-effect when the strength of a mean magnetic field exceeds the critical value Bc ∼ (v inτ v2/Rm)1/2. Here, v in is the ion-neutral collision frequency, τ the correlation time of ions, and Rm the magnetic Reynolds number. These results suggest that a mean field dynamo operates much more efficiently in a weakly ionized gas where vinτ ≫ 1 than in a fully ionized gas. Furthermore, we show that in two dimensions, the turbulent diffusion is suppressed by the back-reaction when a mean magnetic field reaches the same critical strength Bc, with the upper bound on the turbulent diffusion given by its kinematic value. Astrophysical implications are discussed.
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- ISM: magnetic fields
ASJC Scopus subject areas
- Astronomy and Astrophysics
- Space and Planetary Science