The basic approach is to use coupled fluid equations for the electrons and the
multiple participating neutral and ion species, with appropriate loss terms.
Number conservation, momentum conservation and energy conservation equations are used.
Below these equations are written in terms of number densities 
rather
than mass densities 
.
and
etc. The last two sets of terms in the momentum equations relate to ion-electron interactions and neutral-electron and neutral-ion interactions. These equations should then be solved simultaneously with appropriate boundary conditions. Figure 16.3 used this type of calculation.
Rather than address details here, let us focus on the important qualitative points. The first and most
major point is that the electric field 
in (16.14 - 15) cannot, in general, be ignored when gravity is
retained ( 
). Instead, ionospheres
tend to have significant polarization electric fields. Physically the reason is as follows: due to their
much smaller masses, electrons will be able to reach much greater altitudes than ions with the same
temperature, thereby causing a steady-state charge separation. This charge-separation sets up an
``ambipolar'' electric field which pulls ions up to higher altitudes and resists the motion of
electrons to higher altitudes, setting up a situation in which approximate charge-neutrality exists.
This electric field has a number of consequences that are
described below.