Geoscience Reference
In-Depth Information
Fig. 3.21
A schematic plot
of sprite originated from a
sprite halo in the presence of
QE field generated above a
thundercloud after
z
Ionosphere
r
CG
lightning (Surkov and
Hayakawa
2012
)
C
z
*
Halo
Electron shock
wave
Initial
streamer
Tendrils
Earth
Their numerical simulations show that (1) several ms after the powerful causative
C
CG lightning a downward-propagating electron density shock wave can develop
in the lower ionosphere, (2) then this wave transforms into the downward self-
propagating narrow filament which can serve as a positive sprite streamer, and (3)
the impact and photo-ionization rates are the highest at the streamer head. In this
model the electron density wave can be considered as a possible candidate for the
visible sprite halo.
To give a qualitative interpretation of these results, we assume that a dipole
approximation could be applied to mesospheric electric field of the thundercloud
charges and of their mirror image in the perfectly conducting ground
C
z
2
/
3=2
1
C
C
z
2
1=2
3
z
2
d
4"
0
.r
2
E
D
;
(3.14)
r
2
where r and
z
are cylindrical coordinates which are shown in Fig.
3.21
. The electric
dipole moment d
D
2qL, where q is the thunderstorm charge and L is the
distance from the thundercloud to the ground. We also assume that the thundercloud
electric field at the front of the electron wave is close to the breakdown threshold.
Substituting Eq. (
3.5
)forE into Eq. (
3.14
) gives the implicit dependence r .
z
/ or
z
.r/, which defines the surface of the wave front. This surface crosses
z
axis at the
point
z
which can be found from the following equation
D
E
0
exp
:
d
2"
0
z
3
z
H
a
(3.15)
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