Electric field and plasma flow: What drives what?

The MHD approximation connects the plasma bulk how velocity and the electric field, but it does not say whether one of them can be considered as causing or producing the other, and if so, which one. This question is often viewed as one having no unambiguous answer and possibly no physical meaning. However, a definite answer can be obtained by solving the basic equations with appropriate initial values, with the result that, for the commonly considered case where the Alfven speed is small compared to the speed of light, (1) a given plasma bulk flow produces an electric field, (2) a given electric field does not produce a plasma bulk flow. The general result can also be derived as a simple consequence of conserving the total (plasma plus electromagnetic field) linear momentum.