Atmospheric Electricity - Ultra and Extremely Low Frequency Electromagnetic Fields - page 67

0.024

0.022

0.02

0.018

0.016

0.014

0.012

0 10 20 30 40 50

f , Hz

Fig. 3.8 Model calculation of the absolute value of current moment spectrum of an individual
return stroke

Whence it follows that the final channel length is l D V 0 = D 4 km (see, e.g.,
Berger et al. 1975 ; Nickolaenko and Hayakawa 1998 , 1999 , 2002 ; Visacro et al.
2004 ). As is seen from Fig. 3.7 , the current moment magnitude is about 27 kA km
for these parameters.
The spectrum of the current moment M .t/ can be written as

X

4

I m
.! m i!/.! m C i!/

m.!/ D MF 1 .!/ D V 0 (3.8)

mD1

As illustrated in Fig. 3.8 the absolute value of the return stroke spectrum by Eq. ( 3.8 )
is practically constant within the ULF band. It is not surprising since in this case
! ! m and thus the frequency-dependent terms in the denominator of Eq. ( 3.8 )
are negligible.

3.1.5 Multiple Return Stroke

As we have noted above, a typical CG lightning discharge consists of n D 2 6
return strokes. More frequently there are 3-4 return strokes with characteristic
duration of about 100s (Uman 1987 ;Ogawa 1995 ; Lyons 1997 ; McGorman and
Rust 1998 ;Borovsky 1998 ). The mean interval between them is of the order of
t 0 D 40 ms. The current profile of the individual strokes can be different.
Now we consider a simple model of multiple return stroke proposed by Jones
( 1970 ). The final/peak length of each return stroke is assumed to increase with its