equation, can be further simplified by using the properties of the magnetic and velocity correlation functions. In order to obtain equations for $M_L$ and $H$, we multiply Eq. (\[meq\]) by $(r^ir^j )/ r^2$ and $\epsilon_{ijf}r^f$ and use the identities $$M_L(r)= M_{ij}(r^ir^j / r^2), \  
H(r) =M_{ij} \epsilon_{ijf}r^f/ (2 r^2) .$$ We have given some steps in simplifying the first two terms in appendix A. The 3rd and 4th terms add to give a contribution $4C(0)\epsilon_{jqm}(\partial M_{im}/\partial r^q) + 2T_{LL}(0) 
\nabla^2 M_{ij}$ to the RHS of Eq. (\[meq\]) , hence justifying their being called “turbulent transport” of $M_{ij}$.

The last two nonlinear terms give the effects of the back reaction due to ambipolar drift on the magnetic fluctuations. In evaluating this term, we will neglect the effects of the subdominant mean field compared to the back reaction effects of the fluctuating field. In this case the nonlinear terms add to give a contribution $-8aH(0,t)\epsilon_{jqm}(\partial M_{im}/\partial r^q) + 4aM_L(0,t) 
\nabla^2 M_{ij}$ to the RHS of Eq. (\[meq\]) . The Gaussian assumption of the magnetic correlations results in the nonlinearity of this term appearing as a nonlinearity in the coefficient, rather than the correlation function itself. Gathering together all the terms, we get 