Geoscience Reference
In-Depth Information
Fig. 3.7
Model calculation
of current moment of a return
stroke versus time
30
25
20
15
10
5
0
0
0.1
0.2
0.3
0.4
0.5
t
, ms
The two last terms on the right-hand side of Eq. (
3.6
), that is I
3
exp .
!
3
t/
C
I
4
exp .
!
4
t/, describe the CC, which is responsible for the final decay of the
electrostatic field of the stroke. As we have noted above, a
CG stroke transfers
the negative electric charge to the ground and the lightning current is thus pointed
upward. It follows from the model that the total lightning charge equals
6:3 C,
and about 50% of this charge is carried by the weak CC, which is described by the
component I
4
and, in part, by the component I
3
. Below we show that these terms
make a main contribution to the ULF range of the lightning spectrum.
Far from the lightning discharge the ULF electromagnetic field can be charac-
terized by the current moment of the stroke as the product of the discharge current
and the length of the current channel, i.e., m.t/
D
I .t/l .t/. One more important
lightning characteristic is the charge moment, which is equal to the product of the
total charge transferred from the thundercloud to the ground and the final length of
the current channel.
In the theory the lightning channel length, l, is assumed to be governed by an
exponential law dl=dt
D
V
0
exp .
t/, where V
0
is the current wave velocity at
the ground level (see Ogawa
1995
). In another words, the vertical current channel
grows upward with exponentially attenuated velocity. In this case
m.t/
D
MF
1
.t/
mD1
4
(3.7)
I
m
jI
1
j
F
1
.t/
D
Œ1
exp .
t/
exp .
!
m
t/
where M
Dj
I
1
j
l and l
D
V
0
= is the final channel length.
For illustrative purposes, a model calculation of the lightning current moment is
shown in Fig.
3.7
as a function of time. In making the plot of m.t/ we have used
the following numerical values of parameters: the maximum of lightning channel
velocity is V
0
D
8
10
4
km/s and the inverse time parameter is
D
2
10
4
s
1
.
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