Geoscience Reference

In-Depth Information

Based on obtained results, to present a possible scenario of sprite development

proved by quantitative estimations

The calculations and estimations as carried out have allowed to obtain a clear

picture of the phenomenon “elf-sprites” at the quantitative level, having constructed

the elementary model suitable for further specifications and complications.

5.2

The Elementary Model of Atmosphere Ionization

by Solar UV Radiation (Layer E and Lower)

The calculations carried out earlier for determination of altitudes where the electric

field generated by lightning discharges can exceed a critical value (a value at which

excess the avalanche ionization takes place) assume an absence of conductivity

below the ionosphere. At the same time it is known that a regular current with the

average density of
10
-16
A/cm
2
flows through the atmosphere from the terrestrial

surface to the ionosphere; it assumes the presence of electric conductivity. Its

presence can have an essential effect on a spatial-temporal distribution of the electric

field above the storm cloud.

For the determination of conductivity distribution over altitude in the atmosphere,

we use an elementary model of an ionization balance at which UV radiation of the

sun and cosmic rays are present as sources of the ionization.

Let us assume that a distribution of air molecule concentration
N
(
h
) over altitude

h
is described by the barometric formula (we neglect variation of air temperature

with altitude for simplicity):

N.h/
D
N
0
exp

;
0
D

h

h
0

k
B
T
av

Mm
n
g
7:4 km;

(5.1)

Here
m
n
D
mass of a neutron;
M
D
29, the molecular weight of the air mixture,

which structure is almost constant up to the altitude of 200 km;
g
D
acceleration of

gravity;
k
B
D
the Boltzmann constant; and
T
av
D
245 K, the average air temperature

at altitudes 0-120 km. Equation
5.1
approximates air density dependence on altitude

for relatively standard atmosphere data with accuracy better than
˙
50% for altitudes

less than 120 km. It is quite enough for our investigation.

Absorption of the sun radiation
J
with a wavelength in the atmosphere caused

by photo-ionization is described by the equation

dJ

dh
D
S
UV
N.h/
J
;

(5.2)

where
S
UV
() is the cross section of photo-ionization.