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

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

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

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

6. The multiscale nature of sparks precursors and high altitude lightning. May 9-13, 2005, Leiden Numerical Methods 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. Based on a standard PIC-MCC method. [Birdshall, IEEE TPS, 1991]

7. The multiscale nature of sparks precursors and high altitude lightning. May 9-13, 2005, Leiden Code Validation 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 ) kTe, ( Townsend ionisation coefficient ) = / Vd where is the ionisation frequency., ( attachment coefficient ) = / Vd where is the attachment frequency.

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

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

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

11. The multiscale nature of sparks precursors and high altitude lightning. May 9-13, 2005, Leiden 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: [Zheleznyak, High Temp, 1982] 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 randomly accordingly this mean free path. where p and p q are resp. the gas pressure and the quenching pressure of N 2 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.

12. The multiscale nature of sparks precursors and high altitude lightning. May 9-13, 2005, Leiden Negative and Positive Streamers Propagation - Neutral gaz density : - Initial electric field : -Cylindrical computation with photoionization -Test case from [Liu & Pasko, JGR, 2004] -Initiated by a Gaussian electron bead of peak density 5.10 11 m -3 and of characteristic length 3 m.

13. The multiscale nature of sparks precursors and high altitude lightning. May 9-13, 2005, Leiden Negative and Positive Streamers Propagation - Neutral gaz density : - Initial electric field : -Cylindrical computation with photoionization -Test case from [Liu & Pasko, JGR, 2004] -Initiated by a Gaussian electron bead of peak density 5.10 11 m -3 and of characteristic length 3 m.

14. The multiscale nature of sparks precursors and high altitude lightning. May 9-13, 2005, Leiden Negative and Positive Streamers Propagation - Neutral gaz density : - Initial electric field : -Cylindrical computation with photoionization -Test case from [Liu & Pasko, JGR, 2004] -Initiated by a Gaussian electron bead of peak density 5.10 11 m -3 and of characteristic length 3 m.

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

16. The multiscale nature of sparks precursors and high altitude lightning. May 9-13, 2005, Leiden Optical Emissions 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. => Differential system solved using a exponential scheme.

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