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