An attempt in modeling streamers in sprites

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An attempt in modeling streamers in sprites
Diffuse and streamer regions of sprites V. P.
Pasko - H. C. Stenbaek-Nielsen
Hassen Ghalila Laboratoire de Spectroscopie
Atomique Moléculaire et Applications
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References

• Sprites produced by quasi-electrostatic heating
  and ionization in the lower ionosphere
• V.P. Pasko, U.S. Inan, T.F. Bell and Y.N.
  Taranenko

• Monte Carlo model for analysis of thermal
  runaway electrons in streamer tips in transient
  luminous events and streamer zones of lightning
  leaders
• G. D. Moss, V. P. Pasko,N. Liu and G. Veronis

• Effects of photoionization on propagation and
  branching of positive and negative
• streamers in sprites.
• N. Liu and V. P. Pasko

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Quasi-Electrostatic Field
100Km
Ionosphere
Mesosphere
E
50Km
Streamers
Stratosphere
- - - - - - -
10Km
Troposphere

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Geometry Schema
60 km
Perfect Conductors
90Km
Gaussian distribution
Lightning Exponential decline of the
charge Time 1ms
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Numerical Modeling
Why modeling and why PIC Monte-Carlo ?
PIC code already ready Cylindrical 2D1/2 and
relativistic Interaction of free electrons with
External and Self Electromagnetic field
Monte Carlo partially ready Nitrogens Cross
Section Elastic, First state excitation and
First ionization
Homogeneous ambient medium vacuum ?1 ?0 S/m
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Ambient electrical properties
Neutral density profile
Electron density profile
G. Bainbridge and U. S. Inan - 2003
Atmospheric Handbook 1984
Ion conductivity profile
V.P. Pasko , U.S. Inan and T.F. Bell - 1997
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Ambient electrical properties
N0 and N are from Neutral density profile N0
Neutral density at the ground
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Expected results - Ambient E field
Sprites produced by quasi-electrostatic heating
and ionization in the lower ionosphere V.P.
Pasko, U.S. Inan, T.F. Bell and Y.N. Taranenko
t 0,5 s lightning t 0,501 s sustained field
after 1ms t 1 s relaxed field
Last results
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PIC-MonteCarlo modeling
Macro particles and Microscopic process
a
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Particle In Cell
Discretization
PIC Particle In Cell
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Meshing
Central difference formula
Temporal mesh
Spatial mesh
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Cycle of the Calculations
Coupling Maxwell-Lorentz Self-consistently
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Monte Carlo simulation
Random
Collision rate
Scattering
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Cross section
Adaptation to the VLF project
Nitrogen , Oxygen and Argon Cross Section
Elastic, Several level of excitation and
ionization Recombination, Attachment
Argons rate
Nitrogens rate
Oxygens rate
Compilation of electrons cross section - Lawton
and Phelps, J. Chem. Phys. 69, 1055 (1978) -
Phelps and Pitchford, Phys. Rev. 31, 2932
(1985) - Yamabe, Buckman, and Phelps, Phys. Rev.
27, 1345 (1983)
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Results plane electrodes
Townsend Coefficient
Drift Velocity
Longitudinal and Transversal coefficients
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Numerical Modeling
VLF propagation in the earth-Ionosphere waveguide
Electromagnetic simulations Trimpis, Tweek
Works of Cummer, Poulsen, Johnson,  
Transient Luminous Events
PIC Monte Carlo simulations Streamers and
Runaway electrons
Works of Pasko, Liu, Moss,
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Brouillon
Ionospheric D region electron density profiles
derived from the measured interference pattern
of VLF waveguide modes G. Bainbridge and U. S.
Inan
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Discretized equations
Central difference formula
Equation de Faraday