The Physics of high altitude lightning

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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
...
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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

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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 FRANKLIN First 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
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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 -gt STROKE
  ( msec)
• 109 - 1010 J per FLASH -gt 109- 1010W
• OBSERVED GLOBAL FLASH RATE -gt 100 / sec
  (preferentially near equator)
• GLOBAL POWER 1011 - 1012 W (US POWER 5x1011
  W)
• MOST OF THE ENERGY GOES INTO HEAT AND RADIO WAVES

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NEW FACE of LIGHTNING HIGH
ALTITUDE LIGHTNING
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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 T8 usec
• O2(B) 1.63 eV T12 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
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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)

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Gamma rays of atmospheric origin

• Measured by CGRO from Earth
• (Fishman et al., 1994)
• -gt produced h gt 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
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Radio Bursts

• PAIRS OF RADIO BURSTS
• SATELLITE (25-100 Mhz)
• IMPULSIVE 3-5 msec
• DELAY 20-60 msec
• MASSEY HOLDEN, 1995
• DISPERSED -gt IONOSPHERIC ORIGIN
• STRONGER THAN CONVENTIONAL
• LIGHTNING
• ENERGY 1J, FLUENCE 10-13 J/m2
• REFLECTION

ALEXIS
800 km
F Region
Mhz
300 km
?
5 km
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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 T8 usec
• Problems
• SPATIAL STRUCTURE very important
• Dipole models dont provide enough emissions

SENTMAN et al, GRL 1994
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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
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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
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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
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Coherence and Gain
TORTUOSITY Radiates every change in direction as
a phase array
COHERENCE
Discontinuity in derivative couples to radiation
pattern -gt FRACTAL
INCOHERENT
INTERFERENCE
COHERENCE IN SOME DIRECTION
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Discharge Model
INCLUDES BRUNCHING and TORTUOSITY Assume
dielectric discharges is an equipotential (high
s) Solve discretized LAPLACES 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 -gt 0 2D Disc h -gt large 1D Dipole
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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
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D 1.61 h 1.0
10
ln N(e)
Y (km)
1000
0
100
10
100
-10
0
10
ln e
X (km)
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D 1.4 h 2.0
10
ln N(e)
Y (km)
1000
0
100
10
1
100
10
-10
0
10
ln e
X (km)
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Discharge Dimension
THE FRACTAL DIMENSION D IS THE MOST RELEVANT
STRUCTURAL PARAMETER DESCRIBING THE DISCHARGE
D(h)
h
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Electromagnetic Fields
CURRENT PULSE Propagates along discharge
rn
I
L(n1)
L(n)
LINE ELEMENTS
HERTZ VECTOR -gt Time Fourier
SOLUTION OF MAXWELLS EQNS
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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
• -gt 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 - gt Collisional frequency
• Excitation rates - gt N2 (1P), N2(2P), ...
• So on!

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Propagation and absorption

• SOLVE MAXWELLS EQUATIONS
• FOR PROPAGATING EM FIELDS
• Heat electrons
• Followed by collisions with neutrals
• KINETIC TREATMENT -gt FOKKER PLANCK
• Get K(z,E2)
• Get excitation rates

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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)
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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

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

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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

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New issues
New results show STREAMERS down from main body of
sprite (diameter lt 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?
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New issues
A discharge from the cloud tops moving upwards
was photographed recently Coupling to the space
environment -gt Magnetosphere ELF/ULF/VLF in
conjunctions with the sprites
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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
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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 -gt e 2O -gt O O2 -gt O3 ) Nitrogen
Fixation ( e N2 -gt e 2N -gt N O2 -gt NO2
) Catalytic ozone destruction NO2 O -gt NO
O2 NO O3 -gt 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)
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THE END