KA, Vainshtein and Kichatinov 1986).

An important facet of MHD equations is the conservation of magnetic helicity, in the absense of microscopic diffusion. Magnetic helicity is defined as $$I_M = \int {\bf A}.{\bf B} \ d^3{\bf x}$$ where ${\bf A}$ is the vector potential. One can show, (cf. Moffat 1978) $I_M$ is conserved in the ideal limit. In case we have no mean fields, we also have $I_M = \cal V <{\bf A}.{\bf B}>$ and $${1 \over \cal V} {dI_M \over dt} = -2\eta < {\bf B}.({\bf \nabla} \times 
{\bf B}) >.
\label{imcon}$$ (Note that we are assuming that integration over a large volume $\cal V$ is same as the ensemble average). It is interesting to display this conservation explicitely from our equations. This will also act as check on some part of the algebra.

For this let us go over to the vector potential representation of the fluctuating field and write $\delta {\bf B} = {\bf \nabla} \times \delta {\bf A}$. We also define the equal time correlation fuction of the fluctuating component of the vector potential as $P^{ij} = <\delta A^i \delta A^j >$. Since we have taken the fluctuting magnetic field as a homogeneous, isotropic, Gaussian random 