field ${\bf v}_0$ and the mean magnetic field ${\bf B}_0$ and most importantly a non-liner term incorporating the effects of ambipolar drift. We get $$\begin{aligned}
{\partial M_{ij} \over \partial t}
&=& <\int \ ^yR_{jpq}\left[v_T^p({\bf y},t) \ ^xR_{ilm}(v_T^l({\bf x},s) 
[M_{mq}+ B_0^m({\bf x}) B_0^q({\bf y}))\right ] ds > \nonumber\\
&+&
 <\int \ ^xR_{ipq}\left[v_T^p({\bf x},t) \ ^yR_{jlm}(v_T^l({\bf y},s) 
[M_{qm} +  B_0^q({\bf x}) B_0^m({\bf y}))\right ] ds >  
\nonumber\\ &+&
<\int \ ^yR_{jpq}\left(v_T^p({\bf y},t) \ ^yR_{qlm}(v_T^l({\bf y},s) 
M_{im})\right ) ds >  \nonumber\\ &+&
<\int \ ^xR_{ipq}\left(v_T^p({\bf x},t) \ ^xR_{qlm}(v_T^l({\bf x},s) 
M_{mj})\right ) ds > \nonumber\\ 
&+& \eta [ \nabla_y^2M_{ij} + \nabla_x^2 M_{ij}] + 
^yR_{jpq}\left(v_0^p({\bf y}) M_{iq} \right) +
^xR_{ipq}\left(v_0^p({\bf x}) M_{qj} \right)
\nonumber\\ 
&+& 
^yR_{jpq}\left(<v_D^p({\bf y}) \delta B_i({\bf x})B_q({\bf y})> \right) +
^xR_{ipq}\left(<v_D^p({\bf x}) B_q({\bf x})\delta B_j({\bf y})> \right) 
\label{meq}\end{aligned}$$ where we have defined the operators $$^xR_{ipq}= \epsilon_{ilm}\epsilon_{mpq}
(\partial /\partial x^l) \ {\rm and} \ ^yR_{ipq}= \epsilon_{ilm}\epsilon_{mpq}
(\partial /\partial y^l) .$$

The first two terms on the RHS of Eq. (\[meq\]) represent the effect of velocity correlations on the magnetic fluctuations ($M_{ij}$) and the mean field ($B_0^i$). The next two terms the “turbulent transport” of the magnetic fluctuations by the turbulent velocity, the 5th and 6th terms the “microscopic diffusion”. The 7th and 8th 