The Comparison of Different Mechanisms of High-AltitudeElectric Discharges: Implications for The Micro-Satellite

CHIBIS-M Mission

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

Nuclear Research Nuclear UniversityMoscow Physics Engineering Institute (MEPhI)

Space Research Institute of the RAS (IKI)

1. Introduction

Schematic showing of the morphology of the lightning-related transient luminous events (TLEs) including Blue Jets, Red Sprites, Elves, Halo, Gigantic Jets.

Fig. 1.

Currents and charges associated with the Blue Jet.

Ionosphere

In the model [Pasko et al., 1996] the Blue Jet is considered as a result of positive streamer type ionization channel.

H,km

10

20

30

40

50

js

jf

vs

jf

Earth

Q=300400 C

Fig. 5.

js is the streamer body current,jf is fair weather current,vs100 km/s is the streamer velocity

2.1.1. Blue Jet model

jf is the current associated with the separation of charges inside the thundercloud.

This figure is partly adopted from [Pasko et al., 1996].

2.1.2. Ionization and attachment

ei a e

dNN

dt

The effective ionization i and attachment a coefficients are used to calculate electron number density changes via

The conventional breakdown threshold electric field, E* , at which i = a is given by [Papadopoulos et al., 1994]

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.

(2)

(1)

25 30 0, where 3 4 MV/m, 2.7 10 mc cE E N N E N

37 kV/cm,

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.

H,km

30

40

50

Is

vs

rs

vd

Behind the front of Blue Jet E E* . The electron drift velocity

The total current, Is, in the Jet is assumed to be conserved along the Jet

,d ev E

where the electron mobility for E E* is [Davies, 1983]

2 20 , =4 10 m / s Ve c cN N

(3)

(4)

It follows from Eqs. (5), (6) and (7) that vd is a constant, i.e.

120 160 km/s,d c cv E

Whence it follows that 2 constant.e sN H r H Fig. 6.

2.1.3. Geometrical shape and velocity of Blue Jet

(5)

(6)

(7)

2 .s e d sI eN H v r H ~

  

Taken from www.usatoday.com/tech/columnist/...st_x.htm

2 7 km, 40 130 km/ss sr v

s

a

H

Hs

a is the conductivity of the ambient

atmosphere, Hs is the streamer stopping

altitude, which corresponds to a s .50 kmsH

Fig. 8.

Fig. 9.

(14)

(15)

is the stopping altitude

Ne N sr 1 2N

0s s

h s s

E v

E r

1 2N 0.1 sv

Results of extensive modeling [e.g., Vitello et al., 1994] indicate that for well developed streamer s behind the streamer front remains approximately constant.

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

Fe=eE

FfrEz

than the electrons will accelerate, that is, they become runaway electrons.

freE F

Taken from www.ess.washington.edu/Space/Atm...nfo.html

The dynamical friction force (electron energy loss) versus electron energy

Ffr

c

Fmin

If

(1) The electric field must exceed the breakdown value E > Ec.

3.2.1. Necessary conditions for runway breakdown in the atmosphere

(2) The spatial scale, L, of the region where E > Ec must be much greater

than la, that is, .alL

z, km

E, V/m

L

20 ms

10 ms5 ms

(3) Fast seed electrons exist with energy E

cmE ecc 2

2

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.

3.2. Sprite as a runaway breakdown in the atmosphere?

2.16 2.16exp , kV/cmcE P z h

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.

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.

z, km

E, V/m

L

20 ms

10 ms5 ms

Fig. 14.

Adopted from Mareev and Trakhtengerts (2007)

Ec

3.2.2. Breakdown threshold field

As E > Ec, the number of the runaway electrons increases

The runaway electron avalanche increases exponentially over the characteristic

length la, which can be estimated as follows [Gurevich and Zybin, 2001]

(32)

(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.

3.2.3. Characteristic length to increase avalanche of runaway electrons

22 19 3

4

2.7 10 cm50 m

2

e c ca

m m

m c E El

N Ze E E N

0 exp aN N z le

Fig. 15.

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 m2s1.

S100 km2 and t1 ms N108.

3.2.4. Fast seed electrons

Fig. 16.Interactions between downward-propagating fast electrons and atomic nucleuses can play a crucial role in formation of upward-propagating fast electrons.

Upward-directed fast seed electrons resulted from cosmic ray shower. Taken from www.ess.washington.edu/Space/Atm...nfo.html

4. Discussion and Conclusions

(Adopted from Nikolai G. Lehtinen, Stanford Electrical Engineering, 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 his phenomena are strongly correlated to thunderstorm activity.strongly correlated to thunderstorm activity.

Duration ranges from 1 to 10 ms.Duration ranges from 1 to 10 ms.Spectrally harder than cosmic gamma ray Spectrally harder than cosmic gamma ray bursts.bursts.

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)

Sketch of TGFs generationFig. 18.

Fig. 17.

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.

Taken from Cummer et al., 2005

Fig. 19.

It was shown that even the biggest TGF-associated strokes are smaller than theory by 100 times.

Perhaps TGFs are not related to sprites.

(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.

(5) Another interesting area of sprite theory is the observed structure.

(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.

Taken from T. Neubert, National Space Institute. Technical University of Denmark, 2007.

Fig. 20.

(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?