Multiphysics simulations of collisionless plasmas

Collisionless plasmas, mostly present in astrophysical and space environments, often require a kinetic treatment as given by the Vlasov equation. Unfortunately, the six-dimensional Vlasov equation can only be solved on very small parts of the considered spatial domain. However, in some cases, e.g. magnetic reconnection, it is sufficient to solve the Vlasov equation in a localized domain and solve the remaining domain by appropriate fluid models. In this paper, we describe a hierarchical treatment of collisionless plasmas in the following way. On the finest level of description, the Vlasov equation is solved both for ions and electrons. The next courser description treats electrons with a 10-moment fluid model incorporating a simplified treatment of Landau damping. At the boundary between the electron kinetic and fluid region, the central question is how the fluid moments influence the electron distribution function. On the next coarser level of description the ions are treated by an 10-moment fluid model as well. It may turn out that in some spatial regions far away from the reconnection zone the temperature tensor in the 10-moment description is nearly isotopic. In this case it is even possible to switch to a 5-moment description. This change can be done separately for ions and electrons. To test this multiphysics approach, we apply this full physics-adaptive simulations to the Geospace Environmental Modeling (GEM) challenge of magnetic reconnection.Comment: 13 pages, 5 figure

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

Coupled Vlasov and two-fluid codes on GPUs

We present a way to combine Vlasov and two-fluid codes for the simulation of a collisionless plasma in large domains while keeping full information of the velocity distribution in localized areas of interest. This is made possible by solving the full Vlasov equation in one region while the remaining area is treated by a 5-moment two-fluid code. In such a treatment, the main challenge of coupling kinetic and fluid descriptions is the interchange of physically correct boundary conditions between the different plasma models. In contrast to other treatments, we do not rely on any specific form of the distribution function, e.g. a Maxwellian type. Instead, we combine an extrapolation of the distribution function and a correction of the moments based on the fluid data. Thus, throughout the simulation both codes provide the necessary boundary conditions for each other. A speed-up factor of around 20 is achieved by using GPUs for the computationally expensive solution of the Vlasov equation and an overall factor of at least 60 using the coupling strategy combined with the GPU computation. The coupled codes were then tested on the GEM reconnection challenge

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

Kinetic Solvers with Adaptive Mesh in Phase Space

An Adaptive Mesh in Phase Space (AMPS) methodology has been developed for solving multi-dimensional kinetic equations by the discrete velocity method. A Cartesian mesh for both configuration (r) and velocity (v) spaces is produced using a tree of trees data structure. The mesh in r-space is automatically generated around embedded boundaries and dynamically adapted to local solution properties. The mesh in v-space is created on-the-fly for each cell in r-space. Mappings between neighboring v-space trees implemented for the advection operator in configuration space. We have developed new algorithms for solving the full Boltzmann and linear Boltzmann equations with AMPS. Several recent innovations were used to calculate the discrete Boltzmann collision integral with dynamically adaptive mesh in velocity space: importance sampling, multi-point projection method, and the variance reduction method. We have developed an efficient algorithm for calculating the linear Boltzmann collision integral for elastic and inelastic collisions in a Lorentz gas. New AMPS technique has been demonstrated for simulations of hypersonic rarefied gas flows, ion and electron kinetics in weakly ionized plasma, radiation and light particle transport through thin films, and electron streaming in semiconductors. We have shown that AMPS allows minimizing the number of cells in phase space to reduce computational cost and memory usage for solving challenging kinetic problems

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

Hydrodynamic model for picosecond propagation of laser-created nanoplasmas

The interaction of a free-electron-laser pulse with a moderate or large size cluster is known to create a quasi-neutral nanoplasma, which then expands on hydrodynamic timescale, i.e., $>1$ ps. To have a better understanding of ion and electron data from experiments derived from laser-irradiated clusters, one needs to simulate cluster dynamics on such long timescales for which the molecular dynamics approach becomes inefficient. We therefore propose a two-step Molecular Dynamics-Hydrodynamic scheme. In the first step we use molecular dynamics code to follow the dynamics of an irradiated cluster until all the photo-excitation and corresponding relaxation processes are finished and a nanoplasma, consisting of ground-state ions and thermalized electrons, is formed. In the second step we perform long-timescale propagation of this nanoplasma with a computationally efficient hydrodynamic approach. In the present paper we examine the feasibility of a hydrodynamic two-fluid approach to follow the expansion of spherically symmetric nanoplasma, without accounting for the impact ionization and three-body recombination processes at this stage. We compare our results with the corresponding molecular dynamics simulations. We show that all relevant information about the nanoplasma propagation can be extracted from hydrodynamic simulations at a significantly lower computational cost when compared to a molecular dynamics approach. Finally, we comment on the accuracy and limitations of our present model and discuss possible future developments of the two-step strategy.Comment: 14 pages, 6 figure