Geoscience Reference
In-Depth Information
the Chapman function under the following simplifying assumptions as e.g. described
by Todorova (
2008
):
•
only the solar radiation is taken into account, i.e. the impact of the cosmic rays,
which are the second main (but less strong) cause of ionization, is neglected;
•
the atmosphere consists of a one-component isothermal gas distributed in hori-
zontally stratified shells with constant scale height;
•
the solar radiation is monochromatic and absorbed proportionally to the concen-
tration of gas particles.
To describe the vertical structure of electron density in the ionosphere, a Chapman
profile function can be derived. Taking the hydrostatic equilibrium assumption of the
height
H
as a linear function of ion altitude.
Now we introduce the ion production rate under simplifying assumptions men-
Chapman function
−
h
h
0
q
0
e
(
1
−
z
−
sec
χ
e
−
z
)
(
,χ)
=
=
,
q
h
and
z
(44)
H
where
(
,χ)
q
h
ion production rate,
z
scaled altitude,
q
0
maximum ion production rate at
0,
h
0
reference height of maximum ion production at
χ
=
χ
= 0, i.e. the Sun at zenith,
H
scale height, and
χ
Sun zenith angle.
The maximum ion production rate is defined as
q
0
=
φ(
∞
)η
He
,
(45)
where
φ(
∞
)
solar flux density outside the atmosphere (in photons/area),
η
number of ion pairs produced per proton,
e
base of natural exponential function.
To obtain the altitude of maximum ion production rate
h
max
, the Chapman function
Eq. (
44
) is differentiated. This yields
h
max
=
h
0
+
Hz
max
with
z
max
=
ln sec
χ.
(46)
The maximum of the ion production is obtained from
q
max
=
χ.
q
0
cos
(47)
