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.
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
k B T av
Mm n g 7:4 km;
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
dh D S UV N.h/ J ;
where S UV () is the cross section of photo-ionization.