Ionospheric Response to Electric Fields - The Earth's Ionosphere: Plasma Physics and Electrodynamics - page 436

V t .
This point is commonly called the supersonic transition in fluid theory. In a
multiple ion species plasma the plasma sound speed is not given by V js but for
convenience here, we to refer to V js >

This first-order differential equation for V js has a singularity where V js =

V t as representing the supersonic flow
of the j th species. Figure 9.2 shows the family of solutions for (9.9), using the
hydrogen Mach number M j = V t plotted as a function of altitude. The physi-

cally meaningful solutions are those with M j >

V js /

1 at all altitudes and one solution
(marked as curve A) passing through the transitional point at M j =

1 for which
the flow is subsonic at low altitudes and supersonic at higher altitudes. A simi-
lar analysis has been done for the solar wind in the pioneering work by Parker
(1958).
The solutions of these hydrodynamic equations are now sophisticated enough
that the details of heat transfer and energy balance may be considered in addition
to the momentum and density distribution of various ion species. In such models
the acceleration of minor ion species with mass less than the mean ion mass can
occur in which ion-ion collisions are sufficient to produce frictional heating and
anisotropic ion temperatures. In the high-latitude ionosphere, both H + and He +
can be accelerated through the O + gas and be subjected to this heating process.
The existence of different temperatures and temperature distributions in the ion
species can induce motion in these species that (depending on the ion mass) either
resists or assists their outward flow.

3.0

2.5

2.0 A

H
IN O , O, H, O 2 , N 2
T e T i 3000 K

1.5

T n

1000K

1.0

A

0.5

0.0
0.2 1.0 2.0 3.0 4.0 5.0

Altitude (10 3 km)

6.0 7.0 8.0 9.0 10.0

Figure 9.2 Solutions of the hydrodynamic equations for the hydrogen ion Mach number
as a function of altitude in a gas containing O + ions as well as the neutral species O, H,
O 2 , and N 2 . Curve A provides a transition from subsonic to supersonic flow. In this figure,
u is the hydrogen ion bulk velocity and c is the hydrogen velocity given by (9.10). [After
Banks and Holzer (1969). Reproduced with permission of the American Geophysical
Union.]