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The Comparison of Different Mechanisms of High-Altitude
Electric Discharges: Implications for The Micro-Satellite
CHIBIS-M Mission
S.V.Goncharov, V.V.Surkov, Pilipenko V.A.
Nuclear Research Nuclear University
Moscow Physics Engineering Institute (MEPhI)
Space Research Institute of the RAS (IKI)
1. Introduction
Fig. 1. Schematic showing of the morphology of the lightning-related transient
luminous events (TLEs) including Blue Jets, Red Sprites, Elves, Halo, Gigantic
2.1.1. Blue Jet model
jf is the current associated with
the separation of charges inside
the thundercloud.
In the model [Pasko et al., 1996]
the Blue Jet is considered as a
result of positive streamer type
ionization channel.
js is the streamer body current,
jf is fair weather current,
vs100 km/s is the streamer
Q=300400 C
Fig. 5.
Currents and charges
associated with the Blue Jet.
This figure is partly adopted from
[Pasko et al., 1996].
2.1.2. Ionization and attachment
The effective ionization i and attachment a coefficients are used to calculate
electron number density changes via
dN e
  i   a  N e
The conventional breakdown threshold electric field, E* , at which i = a
is given by [Papadopoulos et al., 1994]
E  Ec N N 0 ,
w h ere E c  337 4kV/cm,
M V /m , N 0  2 .7  1 0
Here N is the atmospheric neutral density.
For E >E* , Ne grows exponentially in time with rate (i  a ) > 0 determined
as a function of E.
It should be noted that the Jet differs from point-to-plane corona discharge in the
geometry and size. The altitude variations of atmospheric neutral density N and
of atmospheric conductivity affect the Blue Jet parameters.
2.1.3. Geometrical shape and velocity of Blue Jet
where the electron mobility for E  E* is
[Davies, 1983]
Behind the front of Blue Jet E  E* . The electron
drift velocity
vd   e E ,
e  c N 0 N ,
 c = 4  10
m / s  V 
It follows from Eqs. (5), (6) and (7) that vd is a
constant, i.e.
v d   c E c  120  160 km /s,
The total current, Is, in the Jet is assumed to be
conserved along the Jet
I s ~ eN e  H  v d  rs  H  .
Fig. 6.
Whence it follows that
N e  H  rs
 H   constant. (7)
Results of extensive modeling [e.g., Vitello et al., 1994]
indicate that for well developed streamer s behind the
streamer front remains approximately constant.
Ne  N
Fig. 8.
Taken from
vs 0
rs  s
 N 1 2
 0.1  vs  N 1 2
rs  2  7 km ,
Fig. 9.
v s  40  130 km /s (15)
a is the conductivity of the ambient
atmosphere, Hs is the streamer stopping
altitude, which corresponds to a  s .
Hs is the stopping altitude
H s  50 km
2.1.4. Brief discussion
(1) The “streamer”/thermal breakdown model reproduces the dynamics and the
general shape of the Blue Jets as observed in video.
(2) The model predicts that the velocity of upward propagation of jets is about 100
km/s in agreement with observations.
(3) The model can explain the value of the stopping altitudes (about 50 km).
(4) The streamer model naturally explains the blue color of jets as observed in video
as emission of N2 expected upon electron impact.
(5) It follows from the theory that Blue jets are not necessarily associated with
lightning discharges and may appear only in relatively rare cases of large ( 300 
400 C) thundercloud charge accumulation at high ( 20 km) altitude.
It seems that the “streamer” theory cannot explain a number of phenomena associated
with TLEs that involves
bursts of X and -rays (TGFs),
electron acceleration up to relativistic energies (up to 30 MeV).
On the other hand, the runaway electron mechanism appears attractive since it has a
threshold field which is  10 times lower than the conventional breakdown E* .
3. Runaway electron breakdown
If eE  F fr  
than the electrons will
accelerate, that is,
they become
runaway electrons.
The dynamical friction force (electron
energy loss) versus electron energy
Taken from
3.2. Sprite as a runaway breakdown in the atmosphere?
3.2.1. Necessary conditions for runway
breakdown in the atmosphere
(1) The electric field must exceed the breakdown value E > Ec.
(2) The spatial scale, L, of the region where E > Ec must be much greater
L  l a
than la, that is,
Ec mec
(3) Fast seed electrons exist with energy    c 
z, km
Fig. 14.
It appears the first two
conditions may occur above
thundercloud for the short
interval about tens ms just
after the intense positive
10 ms
lightning discharge.
5 ms
20 ms
At the altitude 20 km the
parameter L/la 20  40.
E, V/m
3.2.2. Breakdown threshold field
The runaway breakdown field is dependent on atmospheric pressure and height
E c  2.16  P  2.16 exp   z h  , kV/cm
For example, on the ground surface Ec  2.16 kV/cm and Eth  23 kV/cm.
z, km
Positive return strokes tend
to be followed by continuing
currents. Plotted are the
electric field profiles
resulted from the continuing
currents several milliseconds
after the return stroke. L is
the altitude range where
E>Ec. Sprite initiation can
occur in this altitude range.
Fig. 14.
5 ms
10 ms
20 ms
E, V/m
Adopted from Mareev and Trakhtengerts (2007)
3.2.3. Characteristic length to increase avalanche
of runaway electrons
As E > Ec, the number of the runaway electrons increases
Ne  N 0 exp  z l a 
The runaway electron avalanche increases exponentially over the characteristic
length la, which can be estimated as follows [Gurevich and Zybin, 2001]
m c 
la 
2 N m Z e
E c  2.7  10 cm 
 50 m 
E 
On the ground surface la  70 m. The value of the characteristic length increases
with height due to fall off of the neutral’s number density Nm.
The number of slow/thermal electrons increases exponentially as well.
3.2.4. Fast seed electrons
The fast seed electrons can arise from
cosmic rays. At the altitudes 4-8 km the
flux density of the secondary/seed fast
electrons is  103 m2s1.
S100 km2 and t1 ms  N108.
Fig. 15.
Upward-directed fast seed electrons resulted
from cosmic ray shower.
Taken from
Interactions between downward-propagating fast electrons
Fig. 16. and atomic nucleuses can play a crucial role in formation
of upward-propagating fast electrons.
4. Discussion and Conclusions
Fig. 17. The map shows the global thunderstorm
activity, while the crosses reveal where the TGFs
were observed. [Smith et al., 2005]. (Taken from
Gennady Milikh, University of Maryland, 2005)
The theoretical runaway model can explain,
in principle, not only blue jets and sprites
but also such phenomena as bursts of X and
-rays (TGFs). This phenomena are strongly
correlated to thunderstorm activity.
Duration ranges from 1 to 10 ms.
Spectrally harder than cosmic gamma ray
Fig. 18. Sketch of TGFs generation
(Adopted from Nikolai G. Lehtinen, Stanford
Electrical Engineering, 2005)
Some problems of runaway breakdown model of sprites
(1) The theory predicts -emission due to bremsstrahlung but up to now the optic
emission due to sprite and TGFs have not observed simultaneously.
(2) The TGF lightning strokes are not as big as expected.
It was shown that
even the biggest
strokes are smaller
than theory by 100
Perhaps TGFs are not
related to sprites.
Fig. 19.
Taken from Cummer
et al., 2005
(1) Compared to thermal breakdown theory, the runaway breakdown theory
requires a weaker vertical electric field to produce sprite. So we need
information about the electric field inside the sprite body.
(2) It is possible that thermal/streamer breakdown and runaway breakdown
could occur at the same time.
(3) TGFs cannot be generated by a thermal breakdown model while runaway
model can explain it, in principle. The problem is that the measured lightning
charge moment changes are about 100 times smaller than suggested by
runaway theory.
(4) Both theories predict wide band
electromagnetic emission at the initial stage of
sprite formation. But the spectrum due to
thermal breakdown has to differ from that due
to runaway breakdown. How estimate these
spectra theoretically and how distinguish
them experimentally?
(5) Another interesting area of sprite theory
is the observed structure.
Taken from T. Neubert, National Space Institute.
Technical University of Denmark, 2007.
Fig. 20.
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