Geoscience Reference
In-Depth Information
to the distribution of random velocities of the electrons in the radar frame of reference in
accordance with a two-way Doppler effect.
The “incoherent scatter” concept refers, in essence, to a scattering scenario where each of
the Thomson scattering electrons would have statistically independent random motions. The
total scattered power would then be reduced to a simple sum (see below) of the return power
of individual electrons in the radar field of view treated as hard targets in terms of a standard
radar equation
, i.e.,
P
t
G
t
A
r
(
P
r
=
2
σ
e
,
(1)
4
π
r
2
)
with
transmitted power
and
gain P
t
and
G
t
, respectively, effective area
A
r
of the receiving
antenna, radar range
r
, and backscatter
radar-cross-section
(RCS) of an individual electron,
σ
e
≡
)
−
1
10
−
15
r
e
, where
r
e
=
e
2
π
o
mc
2
4
π
(
4
≈
2.181
×
misthe
classical electron radius
.
Ionospheric electron motions are not fully independent — i.e., particle trajectories are partially
correlated — however, and, as a consequence, the scattered radar power from the ionosphere
deviates form such a simple sum in a manner that depends on several factors including the
radar frequency, electron and ion temperatures, as well as ambient magnetic field of the
ionospheric plasma. This deviation is just one of many manifestations of the correlations
— also known as “collective effects” — between ionospheric charge carriers, including the
deviation of the Doppler frequency spectrum of the scattered fields from a simple Gaussian
shape (of thermal velocity distribution of electrons) implied by the ideal incoherent scatter
scenario. It turns out that the “complications” introduced by the collective effects in the
Doppler spectrum of this “not-exactly-incoherent-scatter” from the ionosphere amount to a
wealth of information that can be extracted from the ISR spectrum given its proper forward
model. This model will be described in the following sections.
Historical note:
When ISR's were first proposed (Gordon, 1958), it was expected that
ionospheric scattering from free electrons would be fully incoherent. First ISR measurements
(Bowles, 1958) showed that not to be the case. Realistic spectral models compatible with
the measurements and correlated particle motions were developed subsequently. Rapid
theoretical progress took place in the 1960's, but issues related to ISR response at small
magnetic aspect angles were resolved only very recently (e.g., Milla & Kudeki, 2011) as
explained in Section 8.
3. From Thomson scatter to the general formulation of ISR spectrum
Since oscillating free electrons radiate like Hertzian dipoles, it can be shown, using elementary
antenna theory, that the backscattered field amplitude
1
from an electron at a distance
r
to a
radar antenna is (using phasor notation)
r
e
r
e
r
e
−
jk
o
r
E
i
=
−
r
E
o
e
−
j
2
k
o
r
,
E
s
=
−
(2)
E
o
e
−
jk
o
r
is the incident field phasor and
k
o
=
ω
o
/
c
is the wavenumber of the
incident wave with a carrier frequency
where
E
i
=
ω
o
. It follows that a collection of scattering electrons
1
Since transmitted and scattered fields are co-polarized we can avoid using a vector notation here.
