The physics of streamer discharge phenomena

In this review we describe a transient type of gas discharge which is commonly called a streamer discharge, as well as a few related phenomena in pulsed discharges. Streamers are propagating ionization fronts with self-organized field enhancement at their tips that can appear in gases at (or close to) atmospheric pressure. They are the precursors of other discharges like sparks and lightning, but they also occur in for example corona reactors or plasma jets which are used for a variety of plasma chemical purposes. When enough space is available, streamers can also form at much lower pressures, like in the case of sprite discharges high up in the atmosphere. We explain the structure and basic underlying physics of streamer discharges, and how they scale with gas density. We discuss the chemistry and applications of streamers, and describe their two main stages in detail: inception and propagation. We also look at some other topics, like interaction with flow and heat, related pulsed discharges, and electron runaway and high energy radiation. Finally, we discuss streamer simulations and diagnostics in quite some detail. This review is written with two purposes in mind: First, we describe recent results on the physics of streamer discharges, with a focus on the work performed in our groups. We also describe recent developments in diagnostics and simulations of streamers. Second, we provide background information on the above-mentioned aspects of streamers. This review can therefore be used as a tutorial by researchers starting to work in the field of streamer physics.Comment: 89 pages, 29 figure

An adaptive Cartesian embedded boundary approach for fluid simulations of two- and three-dimensional low temperature plasma filaments in complex geometries

We review a scalable two- and three-dimensional computer code for low-temperature plasma simulations in multi-material complex geometries. Our approach is based on embedded boundary (EB) finite volume discretizations of the minimal fluid-plasma model on adaptive Cartesian grids, extended to also account for charging of insulating surfaces. We discuss the spatial and temporal discretization methods, and show that the resulting overall method is second order convergent, monotone, and conservative (for smooth solutions). Weak scalability with parallel efficiencies over 70\% are demonstrated up to 8192 cores and more than one billion cells. We then demonstrate the use of adaptive mesh refinement in multiple two- and three-dimensional simulation examples at modest cores counts. The examples include two-dimensional simulations of surface streamers along insulators with surface roughness; fully three-dimensional simulations of filaments in experimentally realizable pin-plane geometries, and three-dimensional simulations of positive plasma discharges in multi-material complex geometries. The largest computational example uses up to $800$ million mesh cells with billions of unknowns on $4096$ computing cores. Our use of computer-aided design (CAD) and constructive solid geometry (CSG) combined with capabilities for parallel computing offers possibilities for performing three-dimensional transient plasma-fluid simulations, also in multi-material complex geometries at moderate pressures and comparatively large scale.Comment: 40 pages, 21 figure

Spatially hybrid computations for streamer discharges: II. Fully 3D simulations

We recently have presented first physical predictions of a spatially hybrid model that follows the evolution of a negative streamer discharge in full three spatial dimensions; our spatially hybrid model couples a particle model in the high field region ahead of the streamer with a fluid model in the streamer interior where electron densities are high and fields are low. Therefore the model is computationally efficient, while it also follows the dynamics of single electrons including their possible run-away. Here we describe the technical details of our computations, and present the next step in a systematic development of the simulation code. First, new sets of transport coefficients and reaction rates are obtained from particle swarm simulations in air, nitrogen, oxygen and argon. These coefficients are implemented in an extended fluid model to make the fluid approximation as consistent as possible with the particle model, and to avoid discontinuities at the interface between fluid and particle regions. Then two splitting methods are introduced and compared for the location and motion of the fluid-particle-interface in three spatial dimensions. Finally, we present first results of the 3D spatially hybrid model for a negative streamer in air

Modeling of plasma dynamics and pattern formation during high pressure microwave breakdown in air

Dans cette thèse, un modèle de la dynamique du plasma après un claquage microonde dans l'air à pression atmosphérique a été développé. Ce modèle a permis d'expliquer pour la première fois la formation et la dynamique de structures filamentaires auto-organisées lors du claquage microonde. Le claquage microonde dans l'air à pression atmosphérique a été récemment observé au MIT dans des expériences mettant en œuvre une source microonde de puissance et des caméras rapides. Les mesures montrent que, lors du claquage, un ensemble structuré de filaments de plasma se forme et se dirige vers la source à une vitesse de plusieurs km/s. Les mécanismes de formation et de propagation de ces structures auto-organisées de plasma ne sont pas bien compris et l'objectif de cette thèse a été de mettre en évidence et de modéliser les phénomènes physiques de base qui en sont responsables. Dans le but de décrire la dynamique du plasma après claquage, les équations de Maxwell ont été couplées à un modèle simple de plasma et résolues numériquement. Le modèle de plasma suppose la quasineutralité et décrit l'évolution de la densité de plasma sous l'effet de la diffusion, de l'ionisation, de l'attachement et de la recombinaison électron-ion. L'ionisation et l'attachement sont supposés dépendre du champ électrique effectif local. La vitesse moyenne électronique est déduite d'une équation de transport de quantité de mouvement simplifiée. La diffusion des particules chargées est ambipolaire au sein du plasma mais devient libre dans le front où la densité chute à zéro. Une expression heuristique de la transition entre diffusion ambipolaire dans le corps du plasma et diffusion libre sur les bords a été établie et validée à l'aide d'un modèle mono-dimensionnel de type dérive-diffusion-Poisson que nous avons développé et dans lequel on ne suppose pas la quasineutralité du plasma. Le modèle plasma-Maxwell quasineutre a ensuite été utilisé pour étudier la dynamique du plasma après claquage dans les conditions des expériences du MIT. Les résultats numériques montrent la formation de structures filamentaires auto-organisées de plasma en excellent accord qualitatif avec les observations expérimentales. Ces structures auto-organisées sont liées aux structures du champ électrique diffracté par le plasma. De nouveaux filaments se forment de façon continue dans le front du plasma par des phénomènes de diffusion-ionisation. Le modèle montre que la formation d'un réseau de filaments de plasma auto-organisé est dû à l'apparition des maxima de champ électrique de l'onde stationnaire formée dans le front du plasma. Dans la dernière partie de la thèse, la formation d'un filament de plasma isolé (ou streamer microonde) au maximum de champ formé à l'intersection de deux faisceaux microondes est analysée à l'aide du modèle. Le streamer microonde s'allonge parallèlement à la direction du champ en raison du renforcement du champ à ses pôles (phénomène de polarisation). L'intensité du champ aux extrémités du filament est modulée dans le temps en raison de phénomènes de résonance pour des longueurs de filaments voisines de multiples de la demi longueur d'onde.In this thesis, a model for the plasma dynamics after microwave breakdown at atmospheric pressure in air has been developed. The model has been able to explain for the first time the formation and dynamics of self-organized structures during microwave breakdown. Microwave breakdown in air at atmospheric pressure has been recently observed at MIT with high power microwave sources and fast CCD cameras. The measurements show that a self-organized multi-streamer array forms and propagates towards the incident microwave source with a high velocity (several km/s) during the discharge. The detailed dynamics of the self-organized streamer structures during microwave breakdown is still not well understood and the objective of this thesis was to clarify the physics of the plasma dynamics and self-organization during and after microwave breakdown. In order to study the plasma dynamics in microwave breakdown, Maxwell's equations have been coupled to a simple plasma model and solved numerically. The plasma model assumes quasineutrality and describes the evolution of the plasma due to diffusion, ionization, attachment and recombination. Ionization and attachment are supposed to depend on the local effective field. The electron mean velocity is obtained from a simplified momentum equation. The diffusion coefficient must be ambipolar in the plasma bulk but should be equal to the free electron diffusion on the edge of the plasma since the plasma density decays to zero in the front. A heuristic expression of the transition from ambipolar diffusion in the bulk plasma to free diffusion at the edges has been derived and validated with a non-neutral one-dimensional (1D) model based on drift-diffusion and Poisson's equations. The 1D and 2D plasma-Maxwell models have been used to study the plasma dynamics after breakdown in the conditions of the MIT experiments. The numerical results show the formation of self-organized structures or patterns that are in excellent qualitative agreement with the MIT measurements. The formation of the self-organized dynamical pattern can be attributed to the scattering of the microwave field by the plasma. New filaments continuously form in the plasma front due to diffusion-ionization mechanisms. The model shows that the formation of the filamentary plasma array is associated with the standing wave pattern formed by the microwave field scattered by the plasma. In the last part of the thesis we analyze the formation of a single, isolated microwave filament or streamer at the antinode of a standing wave formed at the intersection of two microwave beams. The microwave streamer stretches in a direction parallel to the electric field because of polarization effects. The model results show that the field is strongly enhanced at the tips of the microwave filament and that the field intensity is modulated in time as the streamer length increases. This modulation is associated with resonant effect when the filament length reached values that are close to multiples of the half wavelength

A comparison of 3D particle, fluid and hybrid simulations for negative streamers

In the high field region at the head of a discharge streamer, the electron energy distribution develops a long tail. In negative streamers, these electrons can run away and contribute to energetic processes such as terrestrial gamma-ray and electron flashes. Moreover, electron density fluctuations can accelerate streamer branching. To track energies and locations of single electrons in relevant regions, we have developed a 3D hybrid model that couples a particle model in the region of high fields and low electron densities with a fluid model in the rest of the domain. Here we validate our 3D hybrid model on a 3D (super-)particle model for negative streamers in overvolted gaps, and we show that it almost reaches the computational efficiency of a 3D fluid model. We also show that the extended fluid model approximates the particle and the hybrid model well until stochastic fluctuations become important, while the classical fluid model underestimates velocities and ionization densities. We compare density fluctuations and the onset of branching between the models, and we compare the front velocities with an analytical approximation

An efficient and accurate MPI based parallel simulator for streamer discharges in three dimensions

We propose an efficient and accurate message passing interface (MPI) based parallel simulator for streamer discharges in three dimensions using the fluid model. First, we propose a new second-order semi-implicit scheme for the temporal discretization of the model, which relaxes the dielectric relaxation time restriction. Moreover, it solves the Poisson equation only once at each time step, while classical second-order semi-implicit and explicit schemes typically need twice. Second, we introduce a geometric multigrid preconditioned FGMRES solver, which dramatically improves the efficiency of solving the Poisson equations with either constant or variable coefficients. It is numerically shown that the solver is faster than other Krylov subspace solvers, and it takes no more than 4 iterations for the Poisson solver to converge to a relative residual of $10^{-8}$ during streamer simulations. Last but not the least, all the methods are implemented using MPI, and the good parallel efficiency of the code and great performance of the numerical algorithms are demonstrated by a series of numerical experiments, using up to 2560 cores on the Tianhe2-JK clusters. A double-headed streamer discharge as well as the interaction of two streamers is studied, using up to 10.7 billion mesh cells

Numerical simulation of ignition of premixed air/fuel mixtures by microwave streamer discharge

A subcritical microwave streamer discharge is used to initiate ignition of premixed air/fuel mixture. The streamer is arising on the internal surface of the dielectric tube using a passive vibrator in a single-pulse regime at atmospheric pressure and temperature. The propagation speed of the combustion front in the quartz cylindrical tube filled by the air/propane mixture is analyzed numerically. The performed studies showed that the streamer discharge, which creates a multitude of ignition points, provides practically instantaneous ignition of the mixture in the entire volume of the tube, where the streamers reach. The results of numerical simulation are compared with the experimental data. Increasing the length of streamer discharge leads to increasing the flame propagation speed