Atmospheric Electricity - Ultra and Extremely Low Frequency Electromagnetic Fields - page 59

Fig. 3.3 A simplified model
of electric charge distribution
in a thundercloud. The spatial
charge densities are constant
inside the spherical regions
whose centers are located on
the z -axis at different altitudes
and z 1 ; z 2 ; z 3 ,and z 4 (Surkov
and Hayakawa 2012 )

z

z 4

q 4

z 3

q 3

z 2

q 2

z 1

q 1

0

earth

charged particles is thought to be due to slow hydrodynamics processes inside
the thundercloud. It appears that upward air fluxes drag small and light positively
charged ice fragments, whereas heavy negatively charged hailstones predominantly
fall downward due to the gravity (Lyons et al. 2003 ; Lyons 2006 ; Krehbiel et al.
2008 ;Pasko 2010 ). Since the current is upward inside the thundercloud and
approximately zero outside, charges pile up at the thundercloud boundaries as
shown in Fig. 3.2 .Here j g is updrafts- and gravity-driven current density inside the
thundercloud. This current causes the charge separation in the thundercloud and thus
it plays a role of a battery/source for the generation of upward or downward-directed
lightning discharges. j f denotes the so-called fair weather current. The lightning can
be operative as long as the current j g can separate the charges and provide the top
of the thundercloud with sufficient amount of positive charges.
The charge density, , which is usually observed under the fine weather condition
is about 0:01 nC/m 3 . In stratocumulus clouds the charge density increases up to
0:1 nC/m 3 . In cumulonimbus clouds under the downpour the mean charge density
is about D 0:3-10 nC/m 3 while in the thunderclouds D 3-30 nC/m 3 (Imyanitov
et al. 1971 ).
Notice that the electrical structure/charge distribution of actual thunderclouds is
much more complicated as compared to the above model. Moreover a certain charge
imbalance may persist in a thunderstorm, which leads to strong variations of the
electric field with altitude. The electrical structure of a standard thundercloud can
be described via a stratiform/multilayered thundercloud model in which the charged
regions are situated at different altitudes (Krehbiel et al. 2008 ;Rioussetetal. 2010a ).
The spatial distribution of these charges was assumed to obey a Gaussian law
and was not spherically symmetric. To simplify the problem and to interpret this
model, we assume that all the charges are uniformly distributed in spherical regions
shown in Fig. 3.3 . A normally electrified storm, which corresponds to a typical CG
lightning, was characterized by the following numerical values q i D 12:5, 60, 40,
and 20 C, where i D 1;2;3;4 (Krehbiel et al. 2008 ). The Earth is considered to