Geoscience Reference
In-Depth Information
Although the arisen layer of the ionization stops shining, the long existence of
its high ionization level influences the distribution of the electric field and further
events.
5.4
Mechanism of the Occurrence of “Sprites”
The front of the avalanche of ionization is unstable with respect to large-scale
perturbances of its surface (Khodataev
1995
). Any asperity on a flat surface of a
capacitor plate results in an increase of electric field on the asperity. The speed of
the ionization avalanche is defined by Eq.
5.27
:
V
fr
D
2
p
D
e
.
i
a
/;
(5.27)
where
D
e
is the coefficient of free electron diffusion (Khodataev and Gorelik
1997
);
a
D
K
a
E
N.
z
/
N.
z
/
(5.28)
is the frequency of the dissociative attachment; and
i
D
K
i
E
N.
z
/
N.
z
/
(5.29)
is the frequency of the ionization by electron impact. The greater the asperity, the
faster it grows. Because the frequency of the ionization is a growing function of the
electric field, the speed of the exserted part of the front exceeds the speed of the
not-exserted part.
For estimation, we approximate the form of the asperity by half of the ellipsoid of
revolution with the symmetry axis directed normally to the surface of the ionization
avalanche front (Fig.
5.24
a).
The conductivity of the layer, as the foregoing calculations show, is high enough
for full shielding of the electric field during the time of the order of microseconds.
Therefore, for estimation of the field increase at the top of the asperity, it is possible
to consider the layer and the asperity as ideally conducting and to apply the known
formula for the ideally conducting ellipsoid of revolution located in the external
field represented by Eq.
5.30
:
8
<
q
1
a
2
; a>b
2e
long
1e
long
1
ln
1
C
e
long
1
;e
long
D
E
m
E
0
D
2e
long
Q.a;b/
e
long
q
a
2
:
e
flat
1
e
flat
arctg.e
flat
/
;
flat
D
1; a < b
(5.30)
e
flat
1
C
