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

2  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 References

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

4 Geometry Schema 90Km Perfect Conductors 60 km Gaussian distribution Lightning : Exponential decline of the charge Time ≈ 1ms

5 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 : Nitrogen’s Cross Section : Elastic, First state excitation and First ionization Homogeneous ambient medium = vacuum :  =1  =0 S/m

6 Ambient electrical properties Ion conductivity profile Neutral density profileElectron density profile G. Bainbridge and U. S. Inan Atmospheric Handbook 1984 V.P. Pasko, U.S. Inan and T.F. Bell

7 Ambient electrical properties N 0 and N are from Neutral density profile N 0 = Neutral density at the ground

8 Expected results - Ambient E field t = 0,5 s lightning t = 0,501 s sustained field after 1ms t = 1 s relaxed 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 Last results

9 PIC-MonteCarlo modeling Macro particles and Microscopic process a

10 Particle In Cell Discretization PIC = Particle In Cell

11 Meshing Central difference formula Temporal mesh Spatial mesh

12 Cycle of the Calculations Coupling Maxwell-Lorentz Self-consistently

13 Monte Carlo simulation Random Collision rate Scattering

14 Cross section Adaptation to the VLF project Nitrogen, Oxygen and Argon Cross Section : Elastic, Several level of excitation and ionization Recombination, Attachment Argon’s rateNitrogen’s rateOxygen’s 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)

15 Results : plane electrodes Drift Velocity Townsend Coefficient Longitudinal and Transversal coefficients

16 Numerical Modeling VLF propagation in the earth-Ionosphere waveguide Transient Luminous Events Electromagnetic simulations : Trimpis, Tweek Works of Cummer, Poulsen, Johnson, … Works of Pasko, Liu, Moss, … PIC Monte Carlo simulations : Streamers and Runaway electrons

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20 Brouillon Ionospheric D region electron density profiles derived from the measured interference pattern of VLF waveguide modes G. Bainbridge and U. S. Inan

21 Discretized equations Equation de Faraday Central difference formula