force on the ions is balanced by their friction with the neutrals. Under this approximation the Euler equation for the ions reduces to : $$\rho_i \nu_{in} ({\bf v}_i -{\bf v}_n ) \equiv \rho_i \nu_{in} {\bf v}_D 
= [({\bf \nabla } \times {\bf B}) \times {\bf B}]/ (4\pi),$$ where $\rho_i$ is the mass density of ions, $\nu_{in}$ the ion-neutral collision frequency and ${\bf v}_n $ the velocity of the neutral particles. We have also defined here ${\bf v}_D$, the ambipolar drift velocity.

Using the Euler equation for the ions and substituting for ${\bf v}_i$, the induction equation becomes the nonlinear equation $${\partial {\bf B}\over \partial t} =
{\bf \nabla } \times \left[ {\bf v}_n \times {\bf B}+ 
a[(({\bf \nabla } \times {\bf B}) \times {\bf B}) \times {\bf B} ]
 -\eta {\bf \nabla } \times {\bf B} \right], 
\label{basic}$$ where we have defined $$a = {1 \over 4 \pi \rho_i \nu_{in} }
\label{adef}$$

We have derived the above equation as one which describes the effect of ambipolar drift. However, one can also view Eq. (\[basic\]) as describing a model nonlinear problem, where the nonlinear effects of the Lorentz force are taken into account as simple modification of the velocity field. Such 