Geoscience Reference
In-Depth Information
be a perfect conductor. This implies that the vertical component of the net electric
iD1
4
field taken along the
z
-axis is given by E
z
D
E
z
i
, where
q
i
.
z
z
i
/
4"
0
r
i
C
E
z
i
E
z
i
D
(3.2)
inside the charged balls and
q
i
.
z
z
i
/
4"
0
j
z
z
i
j
3
C
E
z
i
E
z
i
D
(3.3)
outside the balls. Here
q
i
4"
0
.
z
C
z
i
/
2
E
z
i
D
(3.4)
stands for the electric field of mirror electric images of thundercloud charges, and
z
i
denote the coordinates of centers and radii of the charged spherical regions,
respectively. The variations of the net electric field, E
z
, as a function of altitude
z
can be easily calculated after these simplifications.
To illustrate the results of this simulation we made use of the following numerical
parameters
z
i
D
3:7;6:9;12:1;15:7 km, r
i
D
1:0, 2:2, 2:3, 1:3 km and above-
mentioned values of q
i
taken from Krehbiel et al. (
2008
). The results of calculations
shown in Fig.
3.4
with solid line are in qualitative agreement with the vertical
profiles of thunderstorm electric field as measured by balloon equipment (Marshall
et al.
1995
). The first two peaks at the bottom of Fig.
3.4
are basically due to the
field of a pair of charges q
1
D
12:5 C and q
2
D
60 C whereas the two peaks at the
top of Fig.
3.4
are caused by the upper charges q
3
D
40 C and q
4
D
20 C. It should
be noted that both the magnitude and location of the peaks are very sensitive to the
distances between the charges.
3.1.3
Conventional Mechanism for Air Breakdown
and Streamers
The conventional mechanism of air breakdown is due to the thermal ionization
of the air by low energy electrons in the presence of strong electric fields, which
occasionally occurs inside and around thunderclouds. Typical energy of electrons
producing the ionization is about 10-20 eV while the mean electron energy is about
2 eV. According to laboratory tests the breakdown threshold E
c
is approximately
proportional to the gas pressure p at least under condition pd > 10
6
Pa m, where
d is the inter-electrode gap size (e.g., see Raizer
1991
; Lieberman and Lichtenberg
1994
). It follows from the state equation of perfect gas .p
D
k
B
n
m
T/that at constant
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