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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.
Leader-streamer model ofblue jets - phenomenon of lightning type in the upper atmosphere above thundercloud
Scheme of BJ observation; Pasko et al., 2002, Puerto-Rico
Time between frames = 0.033 s; BJ lifetime ~ 0.3 s
Petrov and Petrova, 1999; Pasko and George 2002.
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:
the cloud and
an altitude h
Scheme of the thundercloud
Condition of “unlimited” growth of upward streamer in the exponential atmosphere
The streamerpropagates in theexponentialself-consistent field, created with participation of all BJ streamers
The set of engaging equations:
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)
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
Checking the similarity law ES/N=const, for the uniform atmosphere
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 current
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
Substantiation of the above-presented streamer modeling by comparison of
red spritescomputations with observations
Streamer model of red sprites ( Raizer, Milikh and Shneider, 1998)
( The first scientific study – Sentman, Wescott et al.,1994)
Distributions of potential along streamer
at different instants.
Dashed curve U0– potential of the
Distributions of current
Distributions of linear charge
Evolution of streamer velocity vS and length l