J. A. Valdivia

1. Lightning as a Fractal Antenna J. A. Valdivia Collaborators K. Papadopoulos G. Milikh S. Sharma ... … TO PROVIDE THE PHYSICAL INSIGHT REQUIRED FOR THE UNDERSTANDING OF HE HIGH ALTITUDE LIGHTNING PHENOMENA AND THEIR VERY INTERESTING PROPERTIES ...

2. Outline • CONVENTIONAL LIGHTNING • TRADITIONALLY VIEWED as ASSOCIATED with the GROUND • THE NEW FACE OF LIGHTNING • SURPRISE: THE ENERGY COUPLES UPWARDS RED SPRITES Internal Structures Few Km • MODELING RED SPRITES • LIGHTNING as a FRACTAL ANTENNA • FIELD PROPAGATION • HEATING • EMISSIONS and SPECTRUM • CONCLUSIONS

3. Lightning in history LIGHTNING HAS BEEN PRESENT EVEN BEFORE LIFE, IT MAY EVEN BE RESPONSIBLE FOR IT. EARLY THEORIES :Considered GODS as source of lightning Lightning = Flashing of Feathers Thunder = Flapping of Wings • BENJAMIN FRANKLINFirst Realization that lightning is an electrical phenomenon (1750) • Noticed similarity with sparks from rubbing dielectric media • Experiments to show that lightning is electric • Proposed the lightning rod as protection FROM UMAN, 1987

4. A Lightning Discharge ADAPTED FROM UMAN, 1987 STEPPED LEADER STEP ~1 msec PAUSE ~ 50 msec Q ~ 10 C L ~ 50 m RETURN STROKE Last ~ msec I ~ 30 kA V ~ c/10 • FLASH ( ~ 0.5 sec) : FEW STROKES -> STROKE (~ msec) • 109 - 1010 J per FLASH -> 109- 1010W • OBSERVED GLOBAL FLASH RATE -> 100 # / sec (preferentially near equator) • GLOBAL POWER 1011 - 1012 W (US POWER 5x1011 W) • MOST OF THE ENERGY GOES INTO HEAT AND RADIO WAVES

5. NEW “FACE” of LIGHTNING HIGH ALTITUDE LIGHTNING RED SPRITES GAMMA-RAY Flashes FISHMAN et al RADIO pairs [TIPPS] MASSEY & HOLDEN 90 km Internal Structures Few Km CGRO ALEXIS MeV 5-100 MHz IONOSPHERIC DISCHARGES Streamers 50 km BLUE JETS 40 km Gamma Ray Source EMP 30 km (Radio Source?) 10 km ICL GIANT THUNDERSTORM Ground CGL

6. Red Sprites • OPTICAL FLASHES: • OBSERVED with MASSIVE THUNDERSTORMS • DURATION ~ msec • ALTITUDE ~ 60-90 km • OPTICAL INTENSITY ~ 100 kR • (similar to moderate aurora ) ~10-50 kJ (5-25 MW) • PREDOMINANTLY RED • N2(1P) 7.35 eV T~8 usec • O2(B) 1.63 eV T~12 sec (too Long) SENTMAN et al, GRL 1994 • OBSERVED AND PHOTOGRAPHED • Shuttle : Vaughan, Boeck • Airplane : Sentman, Westcott • Ground : Winckler, Lyons • Mende (spectroscopy) SPATIAL STRUCTURE very important

8. Blue Jets • PREDOMINANTLY BLUE • DURATION ~ 100msec • ALTITUDE UP TO 40 - 50 Km • PROPAGATE UPWARDS ~ 100 Km / sec • CONICAL WITH OPTICAL INTENSITY • Base ~ 800 kR • Top ~ 10 kR • TOTAL ENERGY 30 MJ (1% INTO OPTICAL)

10. Gamma rays of atmospheric origin • Measured by CGRO from Earth • (Fishman et al., 1994) • -> produced h > 30 km • Duration msec • Small source of a few km • Correlated with thunderstorm • Equivalent 10-100J ( h ~ 500 km) • Spectrum consistent with Bremsstrahlung (1 MeV) t (msec) CGRO 500 km 30 km source 8 km ULTIMATELY RELATED TO A RUNAWAY AIR BREAKDOWN

11. Radio Bursts • PAIRS OF RADIO BURSTS • SATELLITE (25-100 Mhz) • IMPULSIVE ~ 3-5 msec • DELAY ~ 20-60 msec • MASSEY & HOLDEN, 1995 • DISPERSED -> IONOSPHERIC ORIGIN • STRONGER THAN CONVENTIONAL • LIGHTNING • ENERGY ~ 1J, FLUENCE 10-13 J/m2 • REFLECTION ALEXIS 800 km F Region Mhz 300 km ? 5 km

12. Red Sprites • OPTICAL FLASHES: • OBSERVED with MASSIVE THUNDERSTORMS • DURATION ~ msec • ALTITUDE ~ 60-90 km • OPTICAL INTENSITY ~ 100 kR • (similar to moderate aurora ) ~10-50 kJ (5-25 MW) • PREDOMINANTLY RED • N2(1P) 7.35 eV T~8 usec • Problems • SPATIAL STRUCTURE very important • Dipole models don’t provide enough emissions SENTMAN et al, GRL 1994

13. The model of red sprites: is based on the fact that lightning radiates as a fractal antenna and includes models for the fractal lightning discharge, propagation of radiated electric fields, and the nonlinear interaction with the ionosphere. The model explains the main features and the energetics of the sprite phenomena. • EMISSIONS (+SPECTRA) • INTERACTION OF ELECTRONS WITH NEUTRALS • ELECTRON ENERGIZATION • FOKKER-PLANCK CODE • PROPAGATION OF EM FIELDS INCLUDING SELF ABSORPTION • SOURCE IS FRACTAL LIGHTNING • HORIZONTAL & DENDRITIC h = 80 km EM FIELDS h =5 km

14. Other theories Electromagnetic dipole model of lightning 1- no spatial structure (like a monopole) 2- not enough emissions Quasi-electrostatic (QS) field relaxation in the ionosphere after discharge in thunder cloud 1- no spatial structure (like a monopole) 2- not enough emissions Supplemented with streamer model in the presence of QS fields 3-what is the seed for the streamers? Electric field imbalance

15. Lightning as a Fractal antenna • TORTUOSITY: NATURAL FOR A DISCHARGE • - Le Vine and Meneghini [1978] • - Williams [1988] • Discharge as a DLA process • - Niemeyer et al., [1984] • - Sanders [1986] + - LICHTENBERG PATTERN Niemeyer et al., 1984

16. Coherence and Gain TORTUOSITY: Radiates every change in direction as a phase array COHERENCE Discontinuity in derivative couples to radiation pattern -> FRACTAL INCOHERENT INTERFERENCE COHERENCE IN SOME DIRECTION

17. DischargeModel INCLUDES BRUNCHING and TORTUOSITY Assume dielectric discharges is an equipotential (high s) Solve discretized LAPLACE’S EQUATION (i,j) Discharge Boundary PROPAGATES: To adjacent points (i,j) Brunching point: Satisfy current conservation and distribute proportional to total length Li of ith brunching arm } D = D(h) h -> 0 2D Disc h -> large 1D Dipole

18. 10 Y (km) 0 -10 0 10 X (km) Fractal Lightning D = 1.4 L = 10 km l = 100 m Radiated Fields Array factor in ionosphere Horizontal size 15 - 60 km Fractal field gain

19. D = 1.61 h = 1.0 10 ln N(e) Y (km) 1000 0 100 10 100 -10 0 10 ln e X (km)

20. D = 1.4 h = 2.0 10 ln N(e) Y (km) 1000 0 100 10 1 10 100 -10 0 10 ln e X (km)

21. Discharge Dimension THE FRACTAL DIMENSION D IS THE MOST RELEVANT STRUCTURAL PARAMETER DESCRIBING THE DISCHARGE D(h) h

22. Electromagnetic Fields CURRENT PULSEPropagates along discharge rn I L(n+1) L(n) LINE ELEMENTS HERTZ VECTOR -> Time Fourier SOLUTION OF MAXWELL’S EQNS

23. Fokker Planck • ELECTRIC FIELD CHANGES THE TRANSPORT PROPERTIES • REQUIRE A SELF-CONSISTENT SOLUTION FOR THE ELECTRON DISTRIBUTION • FUNCTION IN THE PRESENCE OF A VARYING ELECTRIC FIELD • -> FOKKER-PLANCK EQUATION • (A LINEARIZATION OF THE BOLTZMANN TRANSPORT EQUATION) • IT INCLUDES: • Acceleration by varying electric field • Diffusion due to collisions • Inelastic loss terms • WE OBTAIN: • Distribution function of electrons • Transport coefficients - > Collisional frequency • Excitation rates - > N2 (1P), N2(2P), ... • So on!

24. Propagation and absorption • SOLVE MAXWELL’S EQUATIONS • FOR PROPAGATING EM FIELDS • Heat electrons • Followed by collisions with neutrals • KINETIC TREATMENT -> FOKKER PLANCK • Get K(z,E2) • Get excitation rates

25. Radiation and Emissions CONSIDER N2(1P) (Band in the Red) THE EXCITATION RATES : Distribution function reaches steady state EMISSIONS = EXCITATION COMPARE WITH OBSERVATIONS: TIME AVERAGING: Discharge last for about a msec Column integrated (along optical path)

26. RESULTS To run the model: Fractal antenna h = 3 (D = 1.3) Ne nightime profile Io = 200 kA b = 0.025 • SELF-CONSISTENT • FIELD GENERATION • PROPAGATION • ELECTRON ENERGIZATION • EXCITATION & EMISSIONS • N2 (1+) FIRST EXCITEDSTATE

27. To run the model: Fractal antenna h = 3 (D = 1.3) Ne nightime profile Io = 200 kA b = 0.025

30. Dimension Dependence • Fractality is important: Field and emissions dependence • Statistics of Lightning • Io ~ 100 kA 1-5 % • Statistics of Sprites • I ~ 100 kR 1-5 % Optimal D ~ 1.3

31. Spectrum • POPULATION EQUATION • Direct excitation • Cascade excitations • Radiation losses • Collisional quenching • ATMOSPHERIC ATTENUATION • Absorption by ozone • Absorption by oxigen • Absorption by water vapor • Rayleigh scattering • Mie scattering by aerosols

32. Comparisons • CAN CALCULATE LOCAL • FIELD FROM DIFFERENT LINES • e ~ 0.1 eV • E ~ 35 V/m (h = 80 km) • REPEATE FOR HEIGHT • DEPENDENT SPRITE FROM • FRACTAL DISCHARGES • FIRST MODEL OF • SPRITE SPECTRUM • DIRERENT FROM AURORA • High energy electrons excite • N2+(1N) strongly

33. Newissues • New results show STREAMERS down from main body of sprite (diameter < 100 m) • What starts the streamers? • 1- Spatiotemporal E field? • Start from nucleated spatial structure of conductivity after fractal discharge in the presence of a (after discharge) laminar field (quasi-static). • 2- Density fluctuations (gravity waves)? • Neutral density fluctuations require may induce extra emissions and/or ionization • since they depend on E2/N. • Requiere Dn/n ~ 5 % for optimal conditions • 3- Random trigger? • Meteors? • electron runaways?

34. Newissues A discharge from the cloud tops moving upwards was photographed recently Coupling to the space environment -> Magnetosphere ELF/ULF/VLF in conjunctions with the sprites

35. Importance for the Space environment • LARGE AMOUNT OF ENERGY (1011-1012 W) couples to the ionosphere • Mostly in heat and radio waves that can reach into magnetosphere • EFFECTS ON HIGH ALTITUDE FLYING • Sprites streamers 50-90 km • Blue jets and gray runaway electrons 10-50 km • EFFECTS ON LIFE • Proposed for source of molecules required by life • Forests fires maintain the composition in the forests • FAIR WEATHER FIELD • Charge transfer to ionosphere may contribute to this field • ENVIRONMENTAL IMPLICATIONS • Ozone • Chemistry of the Mesosphere • Atmospheric circuit

36. Ozone Layer Runaway pulse releases in the stratosphere 100 J for 2-3 msec close to peak of ozone layer Stimulated processes Ozone production ( e + O2 -> e + 2O -> O + O2 -> O3 ) Nitrogen Fixation ( e + N2 -> e + 2N -> N + O2 -> NO2 ) Catalytic ozone destruction NO2 + O -> NO + O2 NO + O3 -> NO2 + O However ozone production dominates if stimulated by a short pulse . A single runaway pulse could double the ozone abundance in a column of 20 cm2 cross section (or even better)

37. THE END