1. S.V.Goncharov, V.V.Surkov, Pilipenko V.A.
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)

2. 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 Jets.

3. 2.1.1. Blue Jet model Fig. 5. Ionosphere H, km 10 20 30 40 50 js jfvs jf
Earth
Q=300400 C
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 velocity
Fig. 5.
Currents and charges associated with the Blue Jet.
This figure is partly adopted from [Pasko et al., 1996].

4. 2.1.2. Ionization and attachment
The effective ionization i and attachment a coefficients are used to calculate electron number density changes via
(1)
The conventional breakdown threshold electric field, E* , at which i = a is given by [Papadopoulos et al., 1994]
37 kV/cm,
(2)
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.

5. 2.1.3. Geometrical shape and velocity of Blue JetIs vs rs vd H, km
Behind the front of Blue Jet E  E* . The electron drift velocity
(3) 50
where the electron mobility for E  E* is [Davies, 1983]
(4) 40
It follows from Eqs. (5), (6) and (7) that vd is a constant, i.e.
(5) 30
The total current, Is, in the Jet is assumed to be conserved along the Jet ~
(6)
Whence it follows that
(7)
Fig. 6.

6.  Ne  N Fig. 8.  0.1 v Þ s a  H Hs Fig. 9.
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. 
0.1 s v Þ
(14)
Taken from
/columnist/...st_x.htm
(15) s a  H Hs
Fig. 9.
a is the conductivity of the ambient atmosphere, Hs is the streamer stopping altitude, which corresponds to a  s .
is the stopping altitude

7. 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* .

8. 3. Runaway electron breakdown
Fe=eE
Ffr E z
Taken from
The dynamical friction force (electron energy loss) versus electron energy
Ffr 
Fmin If
than the electrons will accelerate, that is, they become runaway electrons.

9. 3.2. Sprite as a runaway breakdown in the atmosphere?
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 than la, that is,
(3) Fast seed electrons exist with energy
z, km
E, V/m L
20 ms
10 ms
5 ms
Fig. 14.
It appears the first two conditions may occur above thundercloud for the short interval about tens ms just after the intense positive lightning discharge.
At the altitude 20 km the parameter L/la 20  40.

10. 3.2.2. Breakdown threshold field
The runaway breakdown field is dependent on atmospheric pressure and height
(31)
For example, on the ground surface Ec  2.16 kV/cm and Eth  23 kV/cm.
z, km
E, V/m L
20 ms
10 ms
5 ms
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. Ec
Adopted from Mareev and Trakhtengerts (2007)

11. 3. 2. 3. Characteristic length to increase avalanche
Characteristic length to increase avalanche of runaway electrons
As E > Ec, the number of the runaway electrons increases e
(32)
The runaway electron avalanche increases exponentially over the characteristic length la, which can be estimated as follows [Gurevich and Zybin, 2001] 
(33)
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.

12. 3.2.4. Fast seed electrons Fig. 15. Fig. 16.
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 and atomic nucleuses can play a crucial role in formation of upward-propagating fast electrons.
Fig. 16.

13. 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 bursts.
Fig. 18.
Sketch of TGFs generation
(Adopted from Nikolai G. Lehtinen, Stanford Electrical Engineering, 2005)

14. Fig. 19. Some problems of runaway breakdown model of sprites
The theory predicts -emission due to bremsstrahlung but up to now the optic emission due to sprite and TGFs have not observed simultaneously.
The TGF lightning strokes are not as big as expected.
It was shown that even the biggest TGF-associated strokes are smaller than theory by 100 times.
Perhaps TGFs are not related to sprites.
Fig. 19.
Taken from Cummer et al., 2005

15. 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.