Geoscience Reference
In-Depth Information
The spectrum of lightning discharge is given by m.!/
D
MF .!/, where M is the
“magnitude” of the current moment and the function F .!/ describes a shape of the
spectrum. Here we have made the following abbreviations
Z
i
0
Ǜ
H
LF .!/
2
cosh .kh/
sinh .kd/
kJ
1
.kr/
qLJ
3
g
r
D
dk;
(5.56)
0
Z
0
F .!/
2
cosh
f
k.d
h/
g
sinh .kd/
g
'
D
kJ
1
.kr/dk
(5.57)
0
Z
LJ
1
Ǜ
H
v
'
Ǜ
2
H
C
Ǜ
P
C
LJ
1
Ǜ
P
v
r
kJ
1
.kr/
qLJ
3
w
r
D
dk
(5.58)
0
where the functions , LJ
3
, and q are given in Eqs. (
5.30
), (
5.31
), and (
5.34
),
respectively, J
1
.kr/ is the Bessel function of the first kind and the first order.
As is seen from Eqs. (
5.54
)-(
5.58
), only the radial component ıB
r
includes the
resonance factor q, while the perpendicular component ıB
'
does not exhibit the
resonance properties. The resonance factor q in turn depends on the “wave numbers”
2
2
x
0
for the ground,
ionosphere, and magnetosphere, respectively. The factor LJ
3
in denominators of the
functions g
r
and
w
r
describes the field damping with distance due to the presence
of exponential functions. The latter factor is a function of d and ; that is, a function
of the atmospheric and ground parameters.
The radial component given by Eq. (
5.54
) consists of two terms. The first
one describes the IAR excitation due to the CG lightning discharge whereas the
second term is caused by the neutral gas flow inside the E-layer. Alternatively, the
perpendicular component (
5.55
) can be excited by only the lightning discharges.
However, the last statement holds true only in the case of axial-symmetrical
distribution of the neutral wind velocities in the ionosphere.
D
k
2
i
0
!
g
,
I
D
k
2
L
2
x
0
, and
2
M
D
k
2
L
2
5.3.4
A Model Calculation of the IAR Spectra
To study the contribution of a solitary lightning discharge to the SRS of the IAR, we
now shall ignore the neutral gas flow in the E layer, so that the neutral wind velocity
is assumed to be zero. Figure
5.12
shows a model calculation of the lightning-
generated spectra of the resonance component ıB
r
for the typical nighttime
parameters of the mid-latitude ionosphere. The lightning flash contains three CG
return strokes. The discharge shape and the spectrum, F .!/, are approximated
by Eqs. (
3.7
) and (
3.8
). The numerical parameters of the lightning discharge used
in making this plot are given in Chap.
3
. The numerical values for the various
magnetospheric, ionospheric, and other parameters are: V
AI
D
500 km/s, V
AM
D
5
10
3
km/s, L
D
500 km, d
D
100 km,
z
D
d, h
D
0,
g
D
2
10
3
S/m,
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