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Simulation of streamer propagation using a PIC-MCC code. Application to Sprite discharges .

Simulation of streamer propagation using a PIC-MCC code. Application to Sprite discharges. Olivier Chanrion and Torsten Neubert Danish National Space Center - Juliane Maries Vej 30, DK-2100 Copenhagen Ø, chanrion@ spacecenter .dk. Outline. Discharge model. Numerical model.

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Simulation of streamer propagation using a PIC-MCC code. Application to Sprite discharges .

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  1. Simulation of streamer propagation using a PIC-MCC code.Application to Sprite discharges. Olivier Chanrion and Torsten Neubert Danish National Space Center - Juliane Maries Vej 30, DK-2100 Copenhagen Ø, chanrion@spacecenter.dk

  2. Outline • Discharge model. • Numerical model. • Negative streamer simulation. • Negative and positive streamer simulation. The multiscale nature of sparks precursors and high altitude lightning. May 9-13, 2005, Leiden

  3. The Discharge Model The model : - Electrons move and suffer collisions with neutrals. - Ions ( produced by ionisation ) are assumed immobile. - Non relativistic kinetic for electrons. - Electrostatic model. The multiscale nature of sparks precursors and high altitude lightning. May 9-13, 2005, Leiden

  4. Kinetic Equations for particles ( Vlasov-Boltzmann ) Collision terms : Fields Equation for the electric potential ( Poisson ) ( with convenient boundary conditions ) Densities given by : Governing Equations The multiscale nature of sparks precursors and high altitude lightning. May 9-13, 2005, Leiden

  5. Numerical Methods The multiscale nature of sparks precursors and high altitude lightning. May 9-13, 2005, Leiden

  6. Numerical Methods Based on a standard PIC-MCC method. [Birdshall, IEEE TPS, 1991] 1 - Push ( trajectories ) : Leap-Frog scheme. 2 - Collisions : Monte Carlo, [Nambu, JJAP,94] scheme based on the cross section of each scattering process. - subcycling if the collision frequency is high. - resampling to limit the particle number increase. 3 - Weighting ( density ) : PIC ( particle in cell ) scheme. 4 - Field : Solved on a Cartesian mesh with finite element. - FE array inverted with a direct ( Choleski ) or indirect ( SOR ) method. The multiscale nature of sparks precursors and high altitude lightning. May 9-13, 2005, Leiden

  7. Calculation of typical swarm parameters for gas discharge physics , ( Mobility ) defined by Vd / E where Vd is the mean speed of electrons,and E the external field. , ( Effective ionisation coefficient ) with : , ( Electronic temperature ), due to collisions in the background electric field E. Comparison with a Boltzmann solver ( Boeuf / Pitchford ) Code Validation , ( Townsend ionisation coefficient ) =/ Vd where is the ionisation frequency. , ( attachment coefficient ) = / Vd where is the attachment frequency. kTe The multiscale nature of sparks precursors and high altitude lightning. May 9-13, 2005, Leiden

  8. Initial conditions • - Neutral density : • Initial field Em : • - Initiated by a Gaussian electron bead. ( as initiated by a single electron at t=0) Electron Avalanche Transition Into a Streamer - No background ionisation - No photo ionisation. => typical characteristics of negative streamer propagation : - electron avalanche / negative streamer head propagate upward. - self-consistent electric field. The multiscale nature of sparks precursors and high altitude lightning. May 9-13, 2005, Leiden

  9. Branching Streamer • Cylindrical computation • Initial conditions chosen close to air at altitude ~70km, after a +CG lightning. • - Neutral gaz density : • - Initial electric field : The multiscale nature of sparks precursors and high altitude lightning. May 9-13, 2005, Leiden

  10. Electron Distribution Function. - plot of the reduced distribution functioninside the head of the streamer. The multiscale nature of sparks precursors and high altitude lightning. May 9-13, 2005, Leiden

  11. Photoionization Model The photoionization model is the particle version of the model used in [Liu & Pasko, JGR, 2004] The emissivity of photons that will ionize oxygen is assumed to be proportional to the ionization rate: The coefficient is assumed to be a function of E/p[Zheleznyak, High Temp, 1982]. => In our code, when an ionization occurs, we create a photon of frequency chosen randomly in if a random number The mean free path for this photon to ionize oxygen is given in by A ion-electron pair is then created at a distance from the preliminary ionization event chosen randomlyaccordingly this mean free path. where p and pq are resp. the gas pressure and the quenching pressure of N2 is the excitation frequency ( which lead to ionizing radiation ) the ionization frequency, the probability to ionize through absorption, and the ionization rate calculated by our MCC scheme. The multiscale nature of sparks precursors and high altitude lightning. May 9-13, 2005, Leiden

  12. - Neutral gaz density : • - Initial electric field : Negative and Positive Streamers Propagation • Cylindrical computation with photoionization • Test case from [Liu & Pasko, JGR, 2004] • Initiated by a Gaussian electron bead of peak density 5.1011 m-3and of characteristic length 3 m. The multiscale nature of sparks precursors and high altitude lightning. May 9-13, 2005, Leiden

  13. - Neutral gaz density : • - Initial electric field : Negative and Positive Streamers Propagation • Cylindrical computation with photoionization • Test case from [Liu & Pasko, JGR, 2004] • Initiated by a Gaussian electron bead of peak density 5.1011 m-3and of characteristic length 3 m. The multiscale nature of sparks precursors and high altitude lightning. May 9-13, 2005, Leiden

  14. - Neutral gaz density : • - Initial electric field : Negative and Positive Streamers Propagation • Cylindrical computation with photoionization • Test case from [Liu & Pasko, JGR, 2004] • Initiated by a Gaussian electron bead of peak density 5.1011 m-3and of characteristic length 3 m. The multiscale nature of sparks precursors and high altitude lightning. May 9-13, 2005, Leiden

  15. The Rescaling Technique To avoid the exponential growth of the particle number we use a rescaling technique from [Kunhardt & Tzeng, Phys Rev A, 1998]. => have to be improved ... The multiscale nature of sparks precursors and high altitude lightning. May 9-13, 2005, Leiden

  16. MCC => production rates of different excitation states of N2 or N2+ due to collisions. Spontaneous emissions of photons come from transition between different excitation states. Optical Emissions => Differential system solved using a exponential scheme. The multiscale nature of sparks precursors and high altitude lightning. May 9-13, 2005, Leiden

  17. Conclusions • We have : • 1D/2D/2D cylindric Parallel PIC-MCC model of discharge. • Simulation of negative streamer propagation until branching point. • Simulation of the beginning of the positive streamer propagation. • Calculation of some optical emissions. • We do not have : • Relativistic description of electrons. • Magnetic field interactions. • Future needs : • Validation of the streamer dynamics. • Validation of the photoionization model. • Improve the resampling of particles. The multiscale nature of sparks precursors and high altitude lightning. May 9-13, 2005, Leiden

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