Atmospheric Electricity - Ultra and Extremely Low Frequency Electromagnetic Fields - page 65

25

20

15

10

5

0

0 0.1 0.2 0.3 0.4 0.5

t , ms

Fig. 3.6 Model calculation of the return stroke current versus time

It is thought that about 5-10 % of global CG lightning activity is composed of
positive cloud-to-ground ( C CG) lightning, which transfers the positive charge to the
ground (Rakov 2003 ). A positive flash usually consists of a single stroke followed by
a CC that typically lasts for several tens or hundreds ms. The amplitude of positive
CC current varies from several kA to tens kA, an order of magnitude larger than
that for the CG (Rakov 2003 ; Rakov and Uman 2003 ). The reader is referred to
the extensive special literature for details about CG and IC lightning discharges
(e.g., see Krider 1986 ; Uman 1987 ; Raizer 1991 ; Lyons 1997 ; McGorman and Rust
1998 ; Rakov and Uman 2003 and references therein).
There are a number of relevant models, which can serve as “engineering” models
of lightning stroke (Rakov and Uman 1998 ). According to the known models for a
CG lightning, the current at the base of the stroke is described by a combination
of a power function and several exponents with different relaxation times (e.g., see
Nickolaenko and Hayakawa 2002 ). More usually we choose four items in this model
(e.g., see Jones 1970 ; Taylor 1972 ; Uman and Krider 1982 ; Uman 1987 )

X

4

I .t/ D I m exp . ! m t/ (3.6)

m D 1

where ! m are inverse time constants. Since the current given by Eq. ( 3.6 ) is equal
to zero at the initial moment t D 0, the amplitudes I m of individual current terms
must satisfy the condition

mD1

4

I m D 0. Following Jones ( 1970 ) we use the following
values of the parameters, which are typical for the models of return strokes I 14 D
28:45, 23:0, 5:0, 0:45 (in kA) and ! 14 D 6:0 10 5 , 3:0 10 4 , 2:0 10 3 , 147:0
(in s 1 ). Figure 3.6 shows the temporal variation of the return stroke current for
these parameters.