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Leader-streamer model of blue jets - phenomenon of lightning type in the upper atmosphere above thundercloud Yu.P. Raizer 1 , G.M. Milikh 2 and M.N. Shneider 3 The Institute for Problems in Mechanics, Russian Acad. Sci Maryland University, USA Princeton University, USA.

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Leader-streamer model ofblue jets - phenomenon of lightning type in the upper atmosphere above thundercloud

  • Yu.P. Raizer1, G.M. Milikh2 and M.N. Shneider3
  • The Institute for Problems in Mechanics, Russian Acad. Sci
  • Maryland University, USA
  • Princeton University, USA

Blue jets (BJ) were discovered by Wescott, Sentman et al., 1994 , USA

Scheme of BJ observation; Pasko et al., 2002, Puerto-Rico


Video recording BJ by Pasko et al., 2002

Time between frames = 0.033 s; BJ lifetime ~ 0.3 s


Fractal streamer model of BJ

Petrov and Petrova, 1999; Pasko and George 2002.

  • The average field necessary for positive streameris ЕS0≈5 kV/cm for normal air density N0
  • Similarity law is supposed:




  • There is no time in the model
  • But electrons disappear due to attachment to O2,forτа~N-2~10-5s
  • at h =18 kmwhereas BJshould be supplied by currentduring 0.3 с
  • It is impossible to manage by means of the streamers only, without participation of a leader

Leader-streamer model ofblue jets

Raizer, Y.P., G.M. Milikh, and M.N. Shneider;

Geophys. Res. Lett., 2006, 33, L23801;

J. Atmos. & Solar-Terr Phys., 2007, 69, 925-938.

Effect of a leader:

  • transfers the high potential U~30-50 MV outside the cloud up to h ~ 30 km, - hereτа~ 10-2 s>> τа(18km) and plasma conductivityis kept much longer,
  • - streamers requirefield ЕS<< ЕS(h=18 km).

BJ origination inside thundercloud


Distribution of

the cloud and


potentials along

an altitude h

Scheme of the thundercloud


  • In non-conductive cloud BJ leader appears together with another one of the opposite polarity (bi-leader)∙ BJ bi-leaderappears in the point В where a fieldE= -dUc/dh is mах
  • ВJ leader propagates upward from the point B
  • UR = 150 МV for the cloud charge QC = 50 C andits radius RC =3km

Condition of “unlimited” growth of upward streamer in the exponential atmosphere

  • Field necessary for streamer is

(similarity law)

  • Streamer, born at altitudehL, can grow up to “infinity” if its source (leader tip) has potential
  • Streamer can run up to “infinity” from the altitude
  • hL= 25-30km for realU~ 30 – 50 MV
  • Unrealistically high potential U = 350 MV is required for streamer to runaway from the heighth=18 km

Modeling growth of the individual streamer belonging to BJ

The streamerpropagates in theexponentialself-consistent field, created with participation of all BJ streamers

The set of engaging equations:

  • Equations of a streamer channel, as long line without self-inductivity:

U(x,t) –potential, I(x,t) – current, q(x,t) – linear charge, R1(x,t), C1 ≈ const – linear resistance and capacity, U0(x)=U0(0)exp (-x/Δ) –the self-consisted (“external”) potential

rm - streamer radius, μe-electron mobility, ne- electron density, C1≈ 7.9 pF/m



Equations of electron kinetics; the approximate solution:

t = t - ts(x)

  • Equationof streamer tip motion(хS = streamer length):
  • Equations for the streamer velocityvS, tip radiusrmand electron density behind tipne0,following from the streamer theory :
  • vS = 5.3 104Ut m/s, Ut=Ut – U0(xS)[kV]; vS=0 forUt< 5kV
  • rm= 3 10-5Ut (N0 /N) m, ne0 = 1.01020( N / N0)2 m-3

ts(x) –themoment when the streamer tip passes the point x

τa – the characteristic electron attachment time,

β – the coefficient of electron-ion recombination


Set of equations is reduced to the equation of non-linear diffusion of potential

Boundary condition at x=xs: the field at the channel front should maintain current I(xs) = q(xs)vs . Hence:

Boundary condition at x=0: U(0)=U0(0) = the leader tip potential. Initial condition: the short streamer “germ” at x=0 is taken


Results of computations

Checking the similarity law ES/N=const, for the uniform atmosphere


Growth of a streamer in the exponential self-consistent field

withЕ/N= 1.28 10 – 23 kVm2exceeding slightly critical one ES/N

Streamer was born (х=0) at the height 25 kmin the field 11 kV/m, ( ES= 10.4 kV/m), U0(0)=80 MV

Distributions of potential along the streamer at the instants when its lengths are L = 5, 10…50 km.

Distributions of the electron density


Distributions of the charge per unit length

Distributions of the current

  • Essential: although the whole charge of streameris+ its back part is –
  • Cause: impossibility to supply the long streamer by + from outside due to loss of conductivity of its back part
  • But the space charge in the+streamer zone should be+on the average
  • It is achievedbycontinuous emissionof new+streamers in the leader tip

Diagram illustrating overlap of the streamer segments with different states,

in the streamer zone of a positive leaderand blue jets

Schemes show state in streamers emitted at the leader head (x=0) for time

t1─t0 =LS / vS. t1is the moment when the streamer, born at moment t0 , reaches the leading front of the streamer zone (x=LS)

Segments of highand low


Segments of (+) and (–) charge per unit length of a streamer


Thus a leader is an indispensablepart of blue jets:

  • it transfers upward the high potential of the thundercloud
  • it emits streamers with high frequencyand they participate in the generation of the necessaryself-consistent field
  • owing to presence of many streamers of different age + segmentsof the young streamers neutralize (with excess) ─segments of the old streamers

The main problems for theory

  • To describe mathematically how the self-consistent field is formed in the streamer zones of a laboratory leader and blue jets
  • What does determine the blue jets velocity v?
  • One can assume that the observingv ~ 100 km/s isthe known minimal streamer velocity (it should not depend on N). Streamers of the streamer zone of a laboratory leader are weak and have such velocity.
  • This problem is closely connected with the unresolved first one.


Substantiation of the above-presented streamer modeling by comparison of

red spritescomputations with observations

Streamer model of red sprites ( Raizer, Milikh and Shneider, 1998)

  • Red sprites are usually associated with positive cloud-to-ground lightning
  • Cloud charge Q= ─70C at h= 5km and its images generate
  • U0 (5km)= ─240MV and
  • the field E=0.5V/cm at hi =80km (N=4 1014 cm-3) sufficient for ionization
  • Plasma patches generated by electromagnetic pulses of intercloud
  • lightning could serve as streamer nucleoli (Valdivia, Milikh et al, 1997)

The recent high-speed images, Cummer et al., 2005

( The first scientific study – Sentman, Wescott et al.,1994)


Results of computation of the red sprite’s downward streamer

Distributions of potential along streamer

at different instants.

Dashed curve U0– potential of the

external field

Distributions of current

Distributions of linear charge


Distributions of electron density at different instants

Evolution of streamer velocity vS and length l

  • Computed vSmax= 1.2 109 cm/s, maximal length lmax = 32 km, altitude and time of the streamer stop, h =48 km and 6.7 ms, are in agreement with results of the video recording