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

Adaptive multiscale methods for 3D streamer discharges in air

We discuss spatially and temporally adaptive implicit-explicit (IMEX) methods for parallel simulations of three-dimensional fluid streamer discharges in atmospheric air. We examine strategies for advancing the fluid equations and elliptic transport equations (e.g. Poisson) with different time steps, synchronizing them on a global physical time scale which is taken to be proportional to the dielectric relaxation time. The use of a longer time step for the electric field leads to numerical errors that can be diagnosed, and we quantify the conditions where this simplification is valid. Likewise, using a three-term Helmholtz model for radiative transport, the same error diagnostics show that the radiative transport equations do not need to be resolved on time scales finer than the dielectric relaxation time. Elliptic equations are bottlenecks for most streamer simulation codes, and the results presented here potentially provide computational savings. Finally, a computational example of 3D branching streamers in a needle-plane geometry that uses up to 700 million grid cells is presented.Comment: 17 pages, 5 figure

A 3D kinetic Monte Carlo study of streamer discharges in CO2

We theoretically study the inception and propagation of positive and negative streamers in CO2. Our study is done in 3D, using a newly formulated kinetic Monte Carlo discharge model where the electrons are described as drifting and diffusing particles that adhere to the local field approximation. Our emphasis lies on electron attachment and photoionization. For negative streamers we find that dissociative attachment in the streamer channels leads to appearance of localized segments of increased electric fields, while an analogous feature is not observed for positive-polarity discharges. Positive streamers, unlike negative streamers, require free electrons ahead of them in order to propagate. In CO2, just as in air, these electrons are supplied through photoionization. However, ionizing radiation in CO2 is absorbed quite rapidly and is also weaker than in air, which has important ramifications for the emerging positive streamer morphology (radius, velocity, and fields). We perform a computational analysis which shows that positive streamers can propagate due to photoionization in CO2. Conversely, photoionization has no effect on negative streamer fronts, but plays a major role in the coupling between negative streamers and the cathode. Photoionization in CO2 is therefore important for the propagation of both positive and negative streamers. Our results are relevant in several applications, e.g. CO2 conversion and high-voltage technology (where CO2 is used in pure form or admixed with other gases). Keywords: 3D, streamer, CO2publishedVersio

Genesis of column sprites: Formation mechanisms and optical structures

Sprite discharges are electrical discharges that initiate from the lower ionosphere during intense lightning storms, manifesting themselves optically as flashes of light that last a few milliseconds. This study unravels sprite initiation mechanisms and evolution into distinctive morphologies like glows and beads, using direct 3D numerical simulations that capture the intricate electrical discharge processes. We clarify various morphological aspects of sprites such as the halo dynamics, column glows, branching, streamer reconnection, and bead formation. The results advance our understanding of sprites and their connection to thunderstorm dynamics, and puts quantitative analysis of their effect on Earth's climate within reach.publishedVersio

3D fluid modeling of positive streamer discharges in air with stochastic photoionization

Streamer discharges are thin plasma channels that precede lightning and sparks. They usually evolve in bundles as stochastic tree-like structures and are inherently difficult to model due to their multiscale nature. In this paper, we perform a computer investigation of positive streamer discharges in air using contemporary photoionization models. We report on three-dimensional computer simulations under conditions that are available in laboratory spark-gap experiments. The solutions demonstrate a multiscale morphology consisting of streamer fluctuations, branching, and the formation of a discharge tree. Some branches are comparatively thick and noisy, while others are thin, smooth, and carry electric fields exceeding $250\,\textrm{kV/cm}$ at their tips. Our results are consistent with past experiments and clarify the puzzling branching dynamics and stochastic morphology of positive streamer discharges.Comment: 14 pages, 3 figures, 2 movie

Genesis of column sprites: Formation mechanisms and optical structures

Sprite discharges are electrical discharges that initiate from the lower ionosphere during intense lightning storms, manifesting themselves optically as flashes of light that last a few milliseconds. This study unravels sprite initiation mechanisms and evolution into distinctive morphologies like glows and beads, using direct 3D numerical simulations that capture the intricate electrical discharge processes. We clarify various morphological aspects of sprites such as the halo dynamics, column glows, branching, streamer reconnection, and bead formation. The results advance our understanding of sprites and their connection to thunderstorm dynamics, and puts quantitative analysis of their effect on Earth's climate within reach.Comment: 19 pages, 18 figure

A 3D kinetic Monte Carlo study of streamer discharges in CO2_2

We theoretically study the inception and propagation of positive and negative streamers in CO$_2$. Our study is done in 3D, using a newly formulated kinetic Monte Carlo discharge model where the electrons are described as drifting and diffusing particles that adhere to the local field approximation. Our emphasis lies on electron attachment and photoionization. For negative streamers we find that dissociative attachment in the streamer channels leads to appearance of localized segments of increased electric fields, while an analogous feature is not observed for positive-polarity discharges. Positive streamers, unlike negative streamers, require free electrons ahead of them in order to propagate. In CO$_2$, just as in air, these electrons are supplied through photoionization. However, ionizing radiation in CO$_2$ is absorbed quite rapidly and is also weaker than in air, which has important ramifications for the emerging positive streamer morphology (radius, velocity, and fields). We perform a computational analysis which shows that positive streamers can propagate due to photoionization in CO$_2$. Conversely, photoionization has no affect on negative streamer fronts, but plays a major role in the coupling between negative streamers and the cathode. Photoionization in CO$_2$ is therefore important for the propagation of both positive and negative streamers. Our results are relevant in several applications, e.g., CO$_2$ conversion and high-voltage technology (where CO$_2$ is used in pure form or admixed with other gases).Comment: 19 pages, 17 figure

Stochastic and self-consistent 3D modeling of streamer discharge trees with Kinetic Monte Carlo

This paper contains the foundation for a new Particle-In-Cell model for gas discharges, based on Ito diffusion and Kinetic Monte Carlo (KMC). In the new model the electrons are described with a microscopic drift-diffusion model rather than a macroscopic one. We discuss the connection of the Ito-KMC model to the equations of fluctuating hydrodynamics and the advection-diffusion-reaction equation which is conventionally used for simulating streamer discharges. The new model is coupled to a particle description of photoionization, providing a non-kinetic all-particle method with several attractive properties, such as: 1) Taking the same input as a fluid model, e.g. mobility coefficients, diffusion coefficients, and reaction rates. 2) Guaranteed non-negative densities. 3) Intrinsic support for reactive and diffusive fluctuations. 4) Exceptional stability properties. The model is implemented as a particle-mesh model on cut-cell grids with Cartesian adaptive mesh refinement. Positive streamer discharges in atmospheric air are considered as the primary application example, and we demonstrate that we can self-consistently simulate large discharge trees.Comment: 29 pages, 16 figure

Stochastic and self-consistent 3D modeling of streamer discharge trees with Kinetic Monte Carlo

This paper contains the foundation for a new Particle-In-Cell model for gas discharges, based on Îto diffusion and Kinetic Monte Carlo (KMC). In the new model the electrons are described with a microscopic drift-diffusion model rather than a macroscopic one. We discuss the connection of the Îto-KMC model to the equations of fluctuating hydrodynamics and the advection-diffusion-reaction equation which is conventionally used for simulating streamer discharges. The new model is coupled to a particle description of photoionization, providing a non-kinetic all-particle method with several attractive properties, such as: 1) Taking the same input as a fluid model, e.g. mobility coefficients, diffusion coefficients, and reaction rates. 2) Guaranteed non-negative densities. 3) Intrinsic support for reactive and diffusive fluctuations. 4) Exceptional stability properties. The model is implemented as a particle-mesh model on cut-cell grids with Cartesian adaptive mesh refinement. Positive streamer discharges in atmospheric air are considered as the primary application example, and we demonstrate that we can self-consistently simulate large discharge trees.Stochastic and self-consistent 3D modeling of streamer discharge trees with Kinetic Monte CarlopublishedVersio

What Determines the Parameters of a Propagating Streamer: A Comparison of Outputs of the Streamer Parameter Model and of Hydrodynamic Simulations

Electric streamer discharges (streamers) in the air are a very important stage of lightning, taking place before formation of the leader discharge, and with which an electric discharge starts from conducting objects which enhance the background electric field, such as airplanes. Despite years of research, it is still not well understood what mechanism determines the values of a streamer’s parameters, such as its radius and propagation velocity. The novel Streamer Parameter Model (SPM) was made to explain this mechanism, and to provide a way to efficiently calculate streamer parameters. Previously, we demonstrated that SPM results compared well with a limited set of experimental data. In this article, we compare SPM predictions to the published hydrodynamic simulation (HDS) results. Keywords: atmospheric electricity; electric streamer discharges; streamer theory; streamer parameters; plasma instabilities; partially-ionized plasmaspublishedVersio