1. 1 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 1.The Institute for Problems in Mechanics, Russian Acad. Sci 2.Maryland University, USA 3.Princeton University, USA

2. 2 Blue jets (BJ) were discovered by Wescott, Sentman et al., 1994, USA Scheme of BJ observation; Pasko et al., 2002, Puerto-Rico

3. 3 Video recording BJ by Pasko et al., 2002 Time between frames = 0.033 s; BJ lifetime ~ 0.3 s

4. 4 Fractal streamer model of BJ Petrov and Petrova, 1999; Pasko and George 2002. The average field necessary for positive streamer is Е S0 ≈5 kV/cm for normal air density N 0 There is no time in the model But electrons disappear due to attachment to O 2, for τ а ~N -2 ~ 10 -5 s at h =18 km whereas BJ should be supplied by current during 0.3 с Similarity law is supposed: Δ≈7.2km Е S ~N ~ e -h/Δ, It is impossible to manage by means of the streamers only, without participation of a leader

5. 5 Leader-streamer model of blue 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. -transfers the high potential U~30-50 MV outside the cloud up to h ~ 30 km, - here τ а ~ 10 -2 s >> τ а (18km) and plasma conductivity is kept much longer, - streamers require field Е S << Е S (h=18 km). Effect of a leader:

6. 6 BJ origination inside thundercloud Scheme of the thundercloud charges Distribution of the cloud and “bi-leader” potentials along an altitude h In non-conductive cloud BJ leader appears together with another one of the opposite polarity ( bi-leader ) ∙ BJ bi-leader appears in the point В where a field E= -dU c /dh is mах ВJ leader propagates upward from the point B U R = 150 МV for the cloud charge Q C = 50 C and its radius R C =3 km h

7. 7 Condition of “unlimited” growth of upward streamer in the exponential atmosphere Field necessary for streamer is Streamer, born at altitude h L, can grow up to “infinity” if its source (leader tip) has potential Streamer can run up to “infinity” from the altitude Unrealistically high potential U = 350 MV is required for streamer to runaway from the height h=18 km h L = 25-30 km for real U ~ 30 – 50 MV (similarity law)

8. 8 Modeling growth of the individual streamer belonging to BJ The streamer propagates in the exponential self-consistent field, created with participation of all BJ streamers Equations of a streamer channel, as long line without self-inductivity: U(x,t) –potential, I(x,t) – current, q(x,t) – linear charge, R 1 (x,t), C 1 ≈ const – linear resistance and capacity, U 0 (x)=U 0 (0) exp (-x/Δ) –the self-consisted (“external”) potential The set of engaging equations: r m - streamer radius, μ e -electron mobility, n e - electron density, C 1 ≈ 7.9 pF/m

9. 9 Equations of electron kinetics; the approximate solution: t = t - t s (x) = Equations for the streamer velocity v S, tip radius r m and electron density behind tip n e0, following from the streamer theory : v S = 5.3 10 4  U t m/s,  U t =U t – U 0 (x S )[kV]; v S =0 for  U t < 5kV r m = 3 10 -5  U t (N 0 /N) m, n e0 = 1.0 10 20 ( N / N 0 ) 2 m -3 Equation of streamer tip motion (х S = streamer length): t s (x) –the moment when the streamer tip passes the point x τ a – the characteristic electron attachment time, β – the coefficient of electron-ion recombination

10. 10 Set of equations is reduced to the equation of non-linear diffusion of potential Boundary condition at x=x s : the field at the channel front should maintain current I(x s ) = q(x s )v s. Hence: Boundary condition at x=0: U(0)=U 0 (0) = the leader tip potential. Initial condition: the short streamer “germ” at x=0 is taken

11. 11 Results of computations Checking the similarity law E S /N=const, for the uniform atmosphere

12. 12 Growth of a streamer in the exponential self-consistent field with Е/N= 1.28 10 – 23 kV m 2 exceeding slightly critical one E S /N Streamer was born (х=0) at the height 25 km in the field 11 kV/m, ( E S = 10.4 kV/m), U 0 (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

13. 13 Distributions of the current Essential: although the whole charge of streamer is + 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 achieved by continuous emission of new + streamers in the leader tip Distributions of the charge per unit length

14. 14 Diagram illustrating overlap of the streamer segments with different states, in the streamer zone of a positive leader and blue jets Schemes show state in streamers emitted at the leader head (x=0) for time t 1 ─t 0 =L S / v S. t 1 is the moment when the streamer, born at moment t 0, reaches the leading front of the streamer zone (x=L S ) Segments of (+) and (–) charge per unit length of a streamer Segments of high and low conductivity

15. 15 Thus a leader is an indispensable part of blue jets: it transfers upward the high potential of the thundercloud it emits streamers with high frequency and they participate in the generation of the necessary self-consistent field owing to presence of many streamers of different age + segments of the young streamers neutralize (with excess) ─ segments of the old streamers

16. 16 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 observing v ~ 100 km/s is the 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.

17. 17 Appendix Substantiation of the above-presented streamer modeling by comparison of red sprites computations 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 U 0 (5km) = ─240MV and the field E=0.5V/cm at h i =80km (N=4 10 14 cm -3 ) sufficient for ionization Plasma patches generated by electromagnetic pulses of intercloud lightning could serve as streamer nucleoli ( Valdivia, Milikh et al, 1997)

18. 18 The recent high-speed images, Cummer et al., 2005 ( The first scientific study – Sentman, Wescott et al.,1994)

19. 19 Results of computation of the red sprite’s downward streamer Distributions of potential along streamer at different instants. Dashed curve U 0 – potential of the external field Distributions of current Distributions of linear charge

20. 20 Evolution of streamer velocity v S and length l Distributions of electron density at different instants Computed v Smax = 1.2 10 9 cm/s, maximal length l max = 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