simulation of streamer propagation using a pic-mcc code. application to sprite discharges
DESCRIPTION
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. - PowerPoint PPT PresentationTRANSCRIPT
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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, [email protected]
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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.
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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.
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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 :
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The multiscale nature of sparks precursors and high altitude lightning. May 9-13, 2005, Leiden
Numerical Methods
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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]
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The multiscale nature of sparks precursors and high altitude lightning. May 9-13, 2005, Leiden
Code ValidationCalculation 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.
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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.
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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 :
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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.
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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:
The coefficient is assumed to be a function of E/p [Zheleznyak, High Temp, 1982][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 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.
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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 5.1011 m-3 and of characteristic length 3 m.
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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 5.1011 m-3 and of characteristic length 3 m.
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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 5.1011 m-3 and of characteristic length 3 m.
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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].
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The multiscale nature of sparks precursors and high altitude lightning. May 9-13, 2005, Leiden
Optical EmissionsMCC => 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.
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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.