  Previous treatments of ambipolar diffusion in star-forming molecular clouds
do not consider the effects of fluctuations in the fluid fields about their
mean values. This paper generalizes the ambipolar diffusion problem in
molecular cloud layers to include such fluctuations. Because magnetic diffusion
is a nonlinear process, fluctuations can lead to an enhancement of the
ambipolar diffusion rate. In addition, the stochastic nature of the process
makes the ambipolar diffusion time take on a distribution of different values.
In this paper, we focus on the case of long wavelength fluctuations and find
that the rate of ambipolar diffusion increases by a significant factor $\Lambda
\sim 1 - 10$. The corresponding decrease in the magnetic diffusion time helps
make ambipolar diffusion more consistent with observations.
