Geoscience Reference
In-Depth Information
Perkins' breakthrough idea was to note that the entire layer could equally well
be considered a single particle if the content was integrated over altitude. This
is the field line-integrated ionospheric model, also known as the Ping-Pong ball
model, which is illustrated in Fig. 5.10. In (6.18a),
v
in
is the plasma density-
weighted collision frequency
v
in
=
∫
(
=
∫
(
)
n
(
z
)
v
in
(
z
)
dz
n
z
v
in
(
z
)
dz
∫
n
(
z
)
dz
N
Ne
2
2
The field line-integrated Pedersen conductivity is thus
i
.
Equivalently, an eastward electric field can support the layer in the vertical
direction. In this case the condition becomes
P
=
v
in
/
M
E
e
B
cos
I
sin
2
I
=
(
g
/
ν
in
)
(6.18b)
If
u
s
and
E
e
are given, 6.18a and b can be combined and solved for
v
in
, which
can be expressed as
g
sin
2
I
u
s
cos
I
sin
I
v
in
(
h
)
=
(6.19)
+
(
E
e
/
)
B
cos
I
v
in
(
)
is a monotonically decreasing function of height, this equation
determines the height of the F layer. In the electric field case there is a net pole-
ward horizontal motion as the ionosphere moves up perpendicular to
B
and falls
down parallel to
B
. For a pure southward wind there is no net equatorward
displacement of the layer. For a Chapman alpha-layer it can be shown that
Since
h
. Perkins used the height-integrated Pedersen conductivity as
one of his variables
v
in
=
v
in
(
h
max
)
e
2
M
i
e
2
N
M
i
P
=
n
(
z
)ν
in
(
z
)
dz
=
i
ν
in
(6.20)
2
i
2
Thus,
P
is also a surrogate for height. Since the electric field does not vary along
B
, the potential is also a “layer” variable. Perkins derived two time derivatives
of importance:
∂
N
∂
=
0
(6.21a)
t
eg
sin
2
I
∂
P
∂
−
P
E
e
cos
I
BH
=
BH
N
(6.21b)
t
where
H
is the neutral scale height. The first equation is simply a statement
that the TEC does not change in this model. Perkins thus studied an ionosphere
high enough that recombination could be ignored. The second equation can be
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