Particle and fluid models for Particle and fluid models for streamers: comparison and streamers: comparison and

spatial couplingspatial couplingLi Chao1

in cooperation with:, U. Ebert1,2, W. Hundsdorfer1, W.J.M. Brok2 and J.J.A.M. van der Mullen2

1. Centrum voor Wiskunde en Informatica (CWI) A’dam2. Eindhoven University of Technology (TU/E) Eindhoven

Simulation models: advantages and disadvantages

Fluid model•Particles : electrons and ions

•Deterministic free flight between Monte Carlo Collisions

Particle model

Efficient computations in continuum approximation.

Full physics;but too many particles for CPU

Drift Diffusion Ionizationreaction

E

1. The propagation of streamers (velocity, width, field enhancement, etc.)

2. The branching of streamers

3. Interaction of streamers (see talk of A. Luque)

4. Role of photo-ionization in positive streamer

5. Interaction with electrodes, walls etc.

Problems that can be studied with fluid models:

Problems that can not be studied with the fluid models, for example,

1. Inception from few free electrons

1. The propagation of streamers (velocity, width, field enhancement, etc.)

2. The branching of streamers

3. Interaction of streamers

4. Role of photo-ionization in positive streamer

5. Interaction with electrodes, walls etc.

Problems that can be studied with fluid models, for example,

The avalanche from one electron near anode (real motion of real electrons) :

Setup: needle-plane electrodes, 1 bar in air, 10kV at anode, free electrons 1/mm3 Time: 0.3ns

Problems that can not be studied with the fluid models, for example,

1. Inception from few free electrons

2. The fluctuation of individual particles

1. The propagation of streamers (velocity, width, field enhancement, etc.)

2. The branching of streamers

3. Interaction of streamers

4. Role of photo-ionization in positive streamer

5. Interaction with electrodes, walls etc.

Problems that can be studied with fluid models, for example,

Planar front in particle model:

E=E+

E=0

Periodic boundary condition

Charge layer with charge:

Streamer front

planar approximation

z

E=E+

E=0

Periodic boundary condition

Charge layer with charge:

Streamer front

planar approximation

z

Particle planar front simulation at 3Ek

E=E+

E=0

Periodic boundary condition

Charge layer with charge:

Streamer front

planar approximation

z

Negative ionization front propagates into a field of 6 Ek

Problems that can not be studied with the fluid models, for example,

1. Inception from few free electrons

2. The fluctuation of individual particles

3. How branching is influenced by particle fluctuation

4. The runaway electrons and X-rays generation (see talk of Vuong Nguyen).

5. Spectroscopic signal, chemistry

1. The propagation of streamers (velocity, width, field enhancement, etc.)

2. The branching of streamers

3. Interaction of two streamers

4. Role of photo-ionization in positive streamer

5. Interaction with electrodes, walls etc.

Problems that can be studied with fluid models, for example,

Runaway electrons from streamers have been studied in

[G.D. Moss, V.P. Pasko, N. Liu, G. Veronis, J. GeoPhys. Res. 111, 2006]

(1) simplified condition (1D with simplified electric field)

(2) with super-particles

Runaway electrons are also studied in

[O. Chanrion, T. Neubert, J. Comput. Phys., In press. ]

(1) 2D axisymmetrical particle model

(2) with super-particles.

But: real particle versus super-particle simulation:

[C. Li et al. IEEE TPS. 2008]

Negative streamer at background field of 100 kV/(cm bar) or ~3Ek

** 1super particle = 256 real particles

How to solve?Fluid model

•Particles : electrons and ions

•Deterministic free flight between Monte Carlo Collisions

Particle model

Efficient computations in continuum approximation.

Full physics ;but too many particles for CPU

Compare and combine models!

Drift Diffusion Ionizationreaction

E

Aim: a 3D spatially hybrid model contains the important physics while the density approximation efficiency remains.

1. The speeds are almost same.2. The densities differ by 20%. Effect becomes stronger at higher fields.

Planar front simulation results comparison at 100 kV/cm

Comparison of particle model with fluid model:

higher electron energy in the front larger ionization rate in the front higher density behind

Particle model:

[C. Li et al. J. Appl. Phys. 2007 ]

Comparison of particle model with fluid model:

Note that in our hybrid simulation: 1) particle model is applied in the most active region;2) model interface moves with the front;3) particles are real electrons rather than super-particles;4) interaction of two models is dealt with carefully.

We have constructed a hybrid model:

Questions:• Can the fluid model be improved?• Where to put the model interface?• How to realize a correct flux at model interface?

We have constructed a hybrid model:

[C. Li et al. Phys. D 2008, and in preparation]Solved, see

ConclusionConclusion

• Density approximation does not include particle physics in leading edge:a) correct energy distributionb) run away electronsc) perturbations for branchingd) discrete particles in low density regione) Excited species, spectral emission, chemistry

• Pure Particle simulation is computational very costly, and super-particles create numerical artifacts.

Spatial computing of fluid and particle models

1) realized in 1D

2) to be extended to 3D

Computationally efficient and reliable tool to study electron energies etc.