Geoscience Reference
In-Depth Information
5.3
Dynamics of an Electric Field Above a Storm Cloud
Slow increase of the cloud charge causes a polarization in the stratosphere,
mesosphere, and ionosphere. We present a cloud as a charged disk with radius
L
c
located above the surface of the ground at altitude
h
0
. The lightning discharge occurs
on the axis of the cloudy disk (Fig.
5.14
). The field of the cloud is determined by
the sum of the cloud charge and its reflection under its terrestrial surface. The cloud
and the ground are considered to conduct well.
The potential of the charged disk of radius
R
c
with charge
q
in emptiness is
defined by Eq.
5.16
:
0
@
1
A
t
q
R
c
arctg
2R
c
.r;
z
/
D
q
r
2
: (5.16)
R
c
C
z
2
2
r
2
R
c
C
z
2
C
C
4R
c
z
2
The potential of the charged disk located above the conducting plane at altitude
h
0
is equal to
.r;
z
/
D
.r;
z
h
0
/
.r;
z
C
h
0
/:
(5.17)
The module of the electric field is described by Eq.
5.18
:
r
@ .r;
z
/
@
z
2
@ .r;
z
/
@r
2
C
E
cloud
.r;
z
/
D
E
0
r
@ .0;0/
@
z
2
:
(5.18)
2
@ .0;0/
@r
C
where
E
0
is the field at the ground under the cloud.
The formula of Eq.
5.18
at
r
D
0 with good accuracy is approximated by the
expression
L
C
h
0
E
0
Fig. 5.14
A cloud and its
“reflection”
