Simulating streamer discharges in 3D with the parallel adaptive Afivo framework

We present an open-source plasma fluid code for 2D, cylindrical and 3D simulations of streamer discharges, based on the Afivo framework that features adaptive mesh refinement, geometric multigrid methods for Poisson's equation, and OpenMP parallelism. We describe the numerical implementation of a fluid model of the drift-diffusion-reaction type, combined with the local field approximation. Then we demonstrate its functionality with 3D simulations of long positive streamers in nitrogen in undervolted gaps, using three examples. The first example shows how a stochastic background density affects streamer propagation and branching. The second one focuses on the interaction of a streamer with preionized regions, and the third one investigates the interaction between two streamers. The simulations run on up to $10^8$ grid cells within less than a day. Without mesh refinement, they would require $4\cdot 10^{12}$ grid cells

Afivo: a framework for quadtree/octree AMR with shared-memory parallelization and geometric multigrid methods

Afivo is a framework for simulations with adaptive mesh refinement (AMR) on quadtree (2D) and octree (3D) grids. The framework comes with a geometric multigrid solver, shared-memory (OpenMP) parallelism and it supports output in Silo and VTK file formats. Afivo can be used to efficiently simulate AMR problems with up to about $10^{8}$ unknowns on desktops, workstations or single compute nodes. For larger problems, existing distributed-memory frameworks are better suited. The framework has no built-in functionality for specific physics applications, so users have to implement their own numerical methods. The included multigrid solver can be used to efficiently solve elliptic partial differential equations such as Poisson's equation. Afivo's design was kept simple, which in combination with the shared-memory parallelism facilitates modification and experimentation with AMR algorithms. The framework was already used to perform 3D simulations of streamer discharges, which required tens of millions of cells

Reply to comment on "Improvements for drift-diffusion plasma fluid models with explicit time integration"

This is a reply to the comment of Jiayong Zou on the paper "Improvements for drift-diffusion plasma fluid models with explicit time integration". The criticism in the comment, namely that the current-limited approach is inconsistent with the underlying partial different equations, seems to be invalid. However, this criticism raises an interesting question about the behavior of the current-limited scheme for a given time step, which is discussed in this reply

Improvements for drift-diffusion plasma fluid models with explicit time integration

Drift-diffusion plasma fluid models are commonly used to simulate electric discharges. Such models can computationally be very efficient if they are combined with explicit time integration. This paper deals with two issues that often arise with such models. First, a high plasma conductivity can severely limit the time step. A fully explicit method to overcome this limitation is presented. This method is compared to the existing semi-implicit method, and it is shown to have several advantages. A second issue is specific to models with the local field approximation. Near strong density and electric field gradients, electrons can diffuse parallel to the field, and unphysically generate ionization. Existing and new approaches to correct this behavior are compared. Details on the implementation of the models and the various approaches are provided

A time scale for electrical screening in pulsed gas discharges

The Maxwell time is a typical time scale for the screening of an electric field in a medium with a given conductivity. We introduce a generalization of the Maxwell time that is valid for gas discharges: the \emph{ionization screening time}, that takes the growth of the conductivity due to impact ionization into account. We present an analytic estimate for this time scale, assuming a planar geometry, and evaluate its accuracy by comparing with numerical simulations in 1D and 3D. We investigate the minimum plasma density required to prevent the growth of streamers with local field enhancement, and we discuss the effects of photoionization and electron detachment on ionization screening. Our results can help to understand the development of pulsed discharges, for example nanosecond pulsed discharges at atmospheric pressure or halo discharges in the lower ionosphere

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

The inception of pulsed discharges in air: simulations in background fields above and below breakdown

We investigate discharge inception in air, in uniform background electric fields above and below the breakdown threshold. We perform 3D particle simulations that include a natural level of background ionization in the form of positive and O$_{2}^-$ ions. When the electric field rises above the breakdown and the detachment threshold, which are similar in air, electrons can detach from O$_{2}^-$ and start ionization avalanches. These avalanches together create one large discharge, in contrast to the `double-headed' streamers found in many fluid simulations. On the other hand, in background fields below breakdown, something must enhance the field sufficiently for a streamer to form. We use a strongly ionized seed of electrons and positive ions for this, with which we observe the growth of positive streamers. Negative streamers were not observed. Below breakdown, the inclusion of electron detachment does not change the results much, and we observe similar discharge development as in fluid simulations

Particle based 3D modeling of positive streamer inception

In this report we present a particle based 3D model for the study of streamer inception near positive electrodes in air. The particle code is of the PIC-MCC type and an electrode is included using the charge simulation method. An algorithm for the ada

A Computational Study of Negative Surface Discharges: Characteristics of Surface Streamers and Surface Charges

We investigate the dynamics of negative surface discharges in air through numerical simulations with a 2D fluid model. A geometry consisting of a flat dielectric embedded between parallel-plate electrodes is used. Compared to negative streamers in bulk gas, negative surface streamers are observed to have a higher electron density, a higher electric field and higher propagation velocity. On the other hand, their maximum electric field and velocity are lower than for positive surface streamers. In our simulations, negative surface streamers are slower for larger relative permittivity. Negative charge accumulates on a dielectric surface when a negative streamer propagates along it, which can lead to a high electric field inside the dielectric. If we initially put negative surface charge on the dielectric, the growth of negative surface discharges is delayed or inhibited. Positive surface charge has the opposite effect.Comment: 8 page