Geoscience Reference
In-Depth Information
2 Ionosphere Refractive Index
The ionosphere is a dispersivemediumwith respect tomicrowave signals. Thismeans
that the propagation of microwave signals through the ionosphere depends on the
frequency of the signals. In order to quantify these effects, the refractive index of the
ionosphere must be specified. For a general derivation of the refractive index
n
in
the ionosphere, we refer to Budden (
1985
). If the collision effects of the particles are
ignored, the formula for the phase ionospheric refractive index can be presented as
X
n
ph
=
1
−
2
1
/
2
,
(16)
X
4
Y
4
sin
4
2
Y
2
sin
2
θ
1
Y
2
cos
2
1
−
±
θ
+
θ(
1
−
X
)
1
−
X
1
−
where
2
0
ω
=
ω
=
ω
H
ω
X
2
,
Y
,
N
e
e
2
ε
0
m
e
,
B
0
|
|
m
e
,
e
ω
0
=
2
π
f
0
=
H
=
2
π
f
H
=
n
complex refractive index
N
e
electron density
ω
=
2
π
f
(radial frequency)
f
wave frequency
ω
0
electron plasma frequency
ω
H
electron gyro frequency
ε
0
permittivity of free space
B
0
magnitude of the magnetic field vector
B
0
θ
angle between the ambient magnetic
e
electron charge
field vector and the wave vector
m
e
electron mass
Equation
16
is called the Appleton-Hertree formula for the ionospheric refractive
index of phase. To evaluate the ionospheric effects more easily, various approxima-
tions of Eq.
16
were proposed. According to Tucker and Fanin (
1968
) and Hartmann
and Leitinger (
1984
) the traditional way of deriving approximate expressions of the
refractive index is by assuming that the magnetic field is associated with the propaga-
tion direction, with sin
0. Without taking any assumptions about the propagation
direction, Brunner and Gu (
1991
) preferred to use the order of magnitude of the vari-
ous terms in Eq.
16
in deriving a suitable approximate expression for the ionospheric
refractive index and their result is identical to the quasi-longitudinal refractive index
expression derived by Budden (
1985
).
θ
≈
X
2
8
.
X
2
±
XY
2
n
ion
ph
=
1
−
cos
θ
−
(17)
Following Brunner and Gu (
1991
), it is convenient to define the constants
C
X
and
C
Y
as
