Geoscience Reference
In-Depth Information
where
ˆ
2
2
|
(
k
,
ω
)
|
d
n
e
η
(
k
)
≡
,
(59)
π
N
e
is an electron scattering efficiency factor (see Milla & Kudeki, 2006) and depends on the
temperature ratio
T
e
/
T
i
and magnetic aspect angle
. A plot of this factor obtained from
our collisional IS model is shown in Figure 11. As we can observe, if the plasma is in thermal
equilibrium (i.e., if
T
e
α
=
T
i
), this factor is 1/2 at all angles
α
and compatible with (28). We
0
◦
increases in proportion to
T
e
/
T
i
. However, at large magnetic
aspect angles, the efficiency factor shows a decrease with increasing
T
e
/
T
i
. In particular, note
that our calculations for
η
(
k
)
α
=
can also see that
at
T
e
/
T
i
)
−
1
, as expected for
moderate values of
T
e
/
T
i
and negligible Debye length (e.g., Farley, 1966). Note that for
90
◦
match the well-known formula
α
=
(
+
1
1
◦
the factor is approximately independent of
T
e
/
T
i
, but otherwise it increases and decreases
with the temperature ratio at small and large aspect angles, respectively.
α
≈
9. Magnetoionic propagation effects on IS spectrum
A radiowave propagating through the ionosphere experiences changes in its polarization
caused by the presence of the Earth's magnetic field. In this section, a model for incoherent
scatter spectrum and cross-spectrum measurements that takes into account magnetoionic
propagation effects is developed.
A mathematical description of radiowave propagation in an inhomogeneous magnetoplasma
based on the Appleton-Hartree solution is presented. The resultant wave propagation
model is used to formulate a soft-target radar equation in order to account for magnetoionic
propagation effects on incoherent scatter spectrum and cross-spectrum models.
9.1 Propagation of electromagnetic waves in a homogeneous magnetoplasma
In the presence of an ambient magnetic field
B
o
, there are two possible and orthogonal modes
of electromagnetic wave propagation in a plasma, and, therefore, any propagating field can be
represented as the weighted superposition of these characteristic modes. Labeling the modes
as ordinary (O) and extraordinary (X), the transverse component of an outgoing (transmitted)
electric wave field, at a distance
r
from the origin, can be written in phasor form as
A
O
ˆ
e
−
jk
o
n
O
r
A
X
ˆ
e
−
jk
o
n
X
r
,
F
O
Y
L
F
X
Y
L
E
t
j
ˆ
j
ˆ
=
θ
−
+
θ
−
φ
φ
(60)
where
A
O
and
A
X
are the amplitudes of the O- and X-mode waves with refractive indices
X
n
2
O
/
X
=
−
1
(61)
−
1
F
O
/
X
specified by Appleton-Hartree equations (e.g., Budden, 1961), in which
Y
T
+
2
Y
T
∓
4
Y
L
(
1
−
X
)
F
O
/
X
=
,
(62)
(
−
)
2
1
X
p
≡
ω
Y
L
≡
Ω
e
ω
and
Y
T
≡
Ω
e
ω
X
2
,
cos
θ
,
sin
θ
.
(63)
ω
