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on the other hand, come and go quite rapidly and put the plasma constituents
in motion perpendicular to
B
. Electric fields thus play a dominant role in the
dynamics of the ionosphere. In the next sections we briefly discuss the genera-
tion and mapping of electric fields. Specific electric field sources are discussed as
they arise in subsequent chapters.
2.3 Generation of Electric Fields
Although we have allowed for the possibility of an electric field in the earth's
upper atmosphere, we have yet to show that such fields exist. The other forces
in (2.28) are, for our present purposes, given quantities—that is, the forces due
to the plasma pressure gradients to the magnetic and gravitational fields, and to
the atmospheric winds. Electric fields arise as a result of these forces when the
ions and electrons respond differently to them. This is expressed quantitatively
via the current divergence equation
∇·
J
=−
∂ρ
c
/∂
t
(2.42)
Any charge density,
ρ
c
, of course, must create electric fields through Poisson's
equation
∇·
E
=
ρ
c
/ε
0
(2.43)
Given the complexity of the forces in (2.28), it is not surprising that the electric
current associated with the difference between the ion and electron velocities has
a finite divergence. However, this divergence creates a charge density via (2.42)
that, via (2.43), creates an electric field that forces the divergence to zero. In
other words, if the complex forces acting on the ion and electron fluids create a
divergence in
J
, an electric field builds up quickly to modify the fluid velocities
so that once again
0.
For example, consider an electric field of 10mV
∇·
J
=
/
m, which is large by equatorial
and midlatitude standards. Assuming a scale length of 1 km in (2.43), we find
ρ
m
3
, which amounts to an excess of ions or electrons of a few
thousand per cubic meter compared to a total of at least 10
9
m
−
3
. The time scale
for buildup of such a charge density can be estimated from (2.42) and (2.43).
From (2.42)
10
−
17
C
=
8
.
85
×
/
c
τ
∼
ρ
c
/
∇·
J
=
ε
0
∇·
E
/
∇·
J
Assuming for the moment that
σ
is uniform and isotropic, then
J
=
σ
E
and
τ
=
ε
0
/σ
(2.44)
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