and

Let us now use the smallness of the mass ratio to further simplify these equations. In particular, we would like to write the electron and ion fluid velocities in terms of the centre-of-mass velocity,

and the plasma current

where . According to the ordering scheme adopted in the previous section, in the cold-plasma limit. We shall continue to regard the mean-free-path parameter as .

It follows from Eqs. (370) and (371) that

Equations (366), (368), (372), and (373) yield the
*continuity equation*:

(374) |

Equations (367) and (369) can be summed to give the
*equation of motion*:

(375) |

Finally, Eqs. (367), (372), and (373) can be combined and to give
a modified *Ohm's law*:

(376) | |||

The first term on the right-hand side of the above equation corresponds to