The multiscale nature of streamers

Ebert, Ute; Montijn, Carolynne-Sireeh; Briels, T.M.P.; Hundsdorfer, Willem; Meulenbroek, Bernard; Rocco, Andrea; Veldhuizen, E.M. van

doi:10.1088/0963-0252/15/2/s14

Cited by 214 publications

(291 citation statements)

References 74 publications

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“…First, fully three-dimensional simulations are required to follow streamer evolution after branching. We actually expect the branching time in cylindrical symmetry to be a close upper bound for the actual branching time in the fully three-dimensional situation [48,20]. Second, numerical solutions of our deterministic fluid model show that it is actually admissible for streamer propagation to neglect densities below the threshold of 1 particle per mm 3 where the continuum approximation definitely ceases to hold; we have used this threshold on our computations with refinement.…”

Section: Discussionmentioning

confidence: 99%

“…For the advection part we get a Courant-Friedrichs-Lewy (CFL) restriction 20) and the diffusion part leads to…”

Section: Temporal Discretizationmentioning

confidence: 99%

“…While the physical nature of the Laplacian instability was elaborated in simplified analytical models [13,17,18,19,20], other authors challenged the accuracy of the numerical results [21,22,23,24]. Based on purely numerical evidence, their questions were justified, as all simulations within the minimal model up to now were carried out on uniform grids, and the numerical convergence on finer grids could hardly be tested.…”

Section: Introductionmentioning

confidence: 99%

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An adaptive grid refinement strategy for the simulation of negative streamers

Montijn

Hundsdorfer

Ebert

2006

Journal of Computational Physics

103

178

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The evolution of negative streamers during electric breakdown of a non-attaching gas can be described by a two-fluid model for electrons and positive ions. It consists of continuity equations for the charged particles including drift, diffusion and reaction in the local electric field, coupled to the Poisson equation for the electric potential. The model generates field enhancement and steep propagating ionization fronts at the tip of growing ionized filaments. An adaptive grid refinement method for the simulation of these structures is presented. It uses finite volume spatial discretizations and explicit time stepping, which allows the decoupling of the grids for the continuity equations from those for the Poisson equation. Standard refinement methods in which the refinement criterion is based on local error monitors fail due to the pulled character of the streamer front that propagates into a linearly unstable state. We present a refinement method which deals with all these features. Tests on one-dimensional streamer fronts as well as on three-dimensional streamers with cylindrical symmetry (hence effectively 2D for numerical purposes) are carried out successfully. Results on fine grids are presented, they show that such an adaptive grid method is needed to capture the streamer characteristics well. This refinement strategy enables us to adequately compute negative streamers in pure gases in the parameter regime where a physical instability appears: branching streamers.

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Section: Discussionmentioning

confidence: 99%

“…For the advection part we get a Courant-Friedrichs-Lewy (CFL) restriction 20) and the diffusion part leads to…”

Section: Temporal Discretizationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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An adaptive grid refinement strategy for the simulation of negative streamers

Montijn

Hundsdorfer

Ebert

2006

Journal of Computational Physics

103

178

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“…The electron-neutral collisions, including all relevant elastic, excitation, and ionization collisions, are treated with the Monte Carlo method. Electron-electron or electron-ion processes as well as density changes of the neutral gas are neglected as the degree of ionization stays below 10 −5 even at atmospheric pressure [18,27]. This well-known model will be summarized in section II A.…”

Section: Set-up Of Particle Model and Fluid Model In Local Field mentioning

confidence: 99%

“…Another recent result supporting the fluid approximation for streamers was that even streamer branching [25,26,27] can be understood in terms of an inherent instability of the fully deterministic fluid equations [19,27,28,29,30]. These studies have shown that a streamer in nitrogen can reach a state in which the width of the space charge layer that creates the field enhancement at the streamer tip, is much smaller than the streamer diameters; the streamer then can branch spontaneously due to a Laplacian interfacial instability.…”

Section: Introductionmentioning

confidence: 96%

Deviations from the local field approximation in negative streamer heads

Brok

Ebert

et al. 2007

Journal of Applied Physics

170

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C e n t r u m v o o r W i s k u n d e e n I n f o r m a t i c a Modelling, Analysis and Simulation Modelling, Analysis and SimulationDeviations from the local field approximation in negative streamer heads C. Li, W.J.M. Brok, U. Ebert, J.J.A.M. van der Mullen Deviations from the local field approximation in negative streamer heads ABSTRACT Negative streamer ionization fronts in nitrogen under normal conditions are investigated both in a particle model and in a fluid model in local field approximation. The parameter functions for the fluid model are derived from swarm experiments in the particle model. The front structure on the inner scale is investigated in a 1D setting, allowing reasonable run-time and memory consumption and high numerical accuracy without introducing super-particles. If the reduced electric field immediately before the front is <= 50kV/(cm bar), solutions of fluid and particle model agree very well. If the field increases up to 200kV/(cm bar), the solutions of particle and fluid model deviate, in particular, the ionization level behind the front becomes up to 60% higher in the particle model while the velocity is rather insensitive. Particle and fluid model deviate because electrons with high energies do not yet fully run away from the front, but are somewhat ahead. This leads to increasing ionization rates in the particle model at the very tip of the front. The energy overshoot of electrons in the leading edge of the front actually agrees quantitatively with the energy overshoot in the leading edge of an electron swarm or avalanche in the same electric field. REPORT MAS-E0706 FEBRUARY 2007 Mathematics Subject Classification: 82D10Keywords and Phrases: streamers; ionization front; particle model; local field approximation Note: This work was carried out under project "Multiscale Modelling and Nonlinear Dynamics"-"Electric discharges and plasma technology". The authors acknowledge support by the Dutch national program Bsik, in the ICT project BRICKS, theme MSV1. arXiv:physics/0702129v1 15 Feb 2007Deviations from the local field approximation in negative streamer heads Negative streamer ionization fronts in nitrogen under normal conditions are investigated both in a particle model and in a fluid model in local field approximation. The parameter functions for the fluid model are derived from swarm experiments in the particle model. The front structure on the inner scale is investigated in a 1D setting, allowing reasonable run-time and memory consumption and high numerical accuracy without introducing super-particles. If the reduced electric field immediately before the front is ≤ 50 kV/(cm bar), solutions of fluid and particle model agree very well. If the field increases up to 200 kV/(cm bar), the solutions of particle and fluid model deviate, in particular, the ionization level behind the front becomes up to 60 % higher in the particle model while the velocity is rather insensitive. Particle and fluid model deviate because electrons with high energies do not yet fully run away from the front, ...

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Infrasonic acoustic waves generated by fast air heating in sprite cores

Silva

Pasko

2014

Geophysical Research Letters

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Acceleration, expansion, and branching of sprite streamers can lead to concentration of high electrical currents in regions of space, that are observed in the form of bright sprite cores. Driven by this electrical current, a series of chemical processes take place in the sprite plasma. Excitation, followed by quenching of excited electronic states leads to energy transfer from charged to neutral species. The consequence is heating and expansion of air leading to emission of infrasonic acoustic waves. Results indicate that ≳0.01 Pa pressure perturbations on the ground, observed in association with sprites, can only be produced by exceptionally strong currents in sprite cores, exceeding 2 kA.

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The multiscale nature of streamers

Cited by 214 publications

References 74 publications

An adaptive grid refinement strategy for the simulation of negative streamers

An adaptive grid refinement strategy for the simulation of negative streamers

Deviations from the local field approximation in negative streamer heads

Infrasonic acoustic waves generated by fast air heating in sprite cores

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