Instabilities and Structure in the High-Latitude Ionosphere - The Earth's Ionosphere: Plasma Physics and Electrodynamics - page 505

The importance of electric field mapping in the ionosphere lies in the fact that
electric fields created locally in a region of poor horizontal conductivity can map
to an altitude where the horizontal conductivity is much larger. The presence of
an electric field in a conducting region will drive a horizontal current that will
tend to short the applied electric field. The electric field can then be maintained
at the generator only if it can supply the current required in the conducting
region. Let us consider the forces acting on a plasma concentration structure in
an ionosphere with a vertical magnetic field. First, a pressure gradient force will
exist on both the ions and the electron gases. But, as shown previously, owing to
the different masses of these particles and their correspondingly different collision
frequencies and gyrofrequencies, these two species will move at different rates.
Any tendency for separation of the ions and electrons in this manner will produce
an electric force.
The horizontal motion of the electrons and ions subject to these forces can
be determined by manipulation of the steady-state equations of motion for each
species. Rather complex expressions result if all the terms in these equations are
retained. This is the usual practice in computer models, but in order to illustrate
the dominant physics we consider only the horizontal ion motion and assume
that electron-ion collisions have a negligible effect. At high latitudes we may
assume g 0, in which case the horizontal motions are not affected by

gravity. Then from (2.36b)

× B =

) ∇ x n (10.15)
Here x again denotes the direction of the gradient, and we have set n i =

V ix = (σ Pi / en ) E − ( D i ⊥ / n

n e = n

due to the quasi-neutrality condition. The ion Pedersen conductivity, or σ Pi , and

the ion perpendicular diffusion coefficient, D i ⊥ , are given in general form by

e 2 n

ν in M i

in

2
i

2

σ Pi = + ν

D i ⊥ = k B T i ν in M i

in

2
i

2

+ ν

Similarly, the horizontal electron velocity can be expressed as

V ex =− (σ ei / en ) E − ( D e ⊥ / n ) ∇ x n + RV ix (10.16)

where the factor R is given by

e

=

ν ie /ν in + ν ei /ν e

R

e
and arises because ion-electron collisions are not always negligible for the elec-
trons. Finally, Eqs. (10.15) and (10.16) can be combined to yield an expression
for the local horizontal Pedersen current,

e

+ ν

J P =[ ( 1 − R )σ Pi + σ Pe ] E − e [ ( 1 − R ) D i ⊥ − D e ⊥ ]∇ x n (10.17)