Asymptotic-Preserving methods and multiscale models for plasma physics

The purpose of the present paper is to provide an overview of As ymptotic- Preserving methods for multiscale plasma simulations by ad dressing three sin- gular perturbation problems. First, the quasi-neutral lim it of fluid and kinetic models is investigated in the framework of non magnetized as well as magne- tized plasmas. Second, the drift limit for fluid description s of thermal plasmas under large magnetic fields is addressed. Finally efficient nu merical resolutions of anisotropic elliptic or diffusion equations arising in ma gnetized plasma simu- lation are reviewed

An Asymptotic Preserving Scheme for the Euler equations in a strong magnetic field

This paper is concerned with the numerical approximation of the isothermal Euler equations for charged particles subject to the Lorentz force. When the magnetic field is large, the so-called drift-fluid approximation is obtained. In this limit, the parallel motion relative to the magnetic field direction splits from perpendicular motion and is given implicitly by the constraint of zero total force along the magnetic field lines. In this paper, we provide a well-posed elliptic equation for the parallel velocity which in turn allows us to construct an Asymptotic-Preserving (AP) scheme for the Euler-Lorentz system. This scheme gives rise to both a consistent approximation of the Euler-Lorentz model when epsilon is finite and a consistent approximation of the drift limit when epsilon tends to 0. Above all, it does not require any constraint on the space and time steps related to the small value of epsilon. Numerical results are presented, which confirm the AP character of the scheme and its Asymptotic Stability

Numerical approximation of the Euler-Maxwell model in the quasineutral limit

International audienceWe derive and analyze an Asymptotic-Preserving scheme for the Euler-Maxwell system in the quasi-neutral limit. We prove that the linear stability condition on the time-step is independent of the scaled Debye length $\lambda$ when $\lambda \to 0$. Numerical validation performed on Riemann initial data and for a model Plasma Opening Switch device show that the AP-scheme is convergent to the Euler-Maxwell solution when $\Delta x/ \lambda \to 0$ where $\Delta x$ is the spatial discretization. But, when $\lambda /\Delta x \to 0$, the AP-scheme is consistent with the quasi-neutral Euler-Maxwell system. The scheme is also perfectly consistent with the Gauss equation. The possibility of using large time and space steps leads to several orders of magnitude reductions in computer time and storage

Three-dimensional lanthanide-organic frameworks based on di-, tetra-, and hexameric clusters

Three-dimensional lanthanide-organic frameworks formulated as (CH3)2NH2[Ln(pydc)2] · 1/2H2O [Ln3+ ) Eu3+ (1a) or Er3+ (1b); pydc2- corresponds to the diprotonated residue of 2,5-pyridinedicarboxylic acid (H2pydc)], [Er4(OH)4(pydc)4(H2O)3] ·H2O (2), and [PrIII 2PrIV 1.25O(OH)3(pydc)3] (3) have been isolated from typical solvothermal (1a and 1b in N,N-dimethylformamide - DMF) and hydrothermal (2 and 3) syntheses. Materials were characterized in the solid state using single-crystal X-ray diffraction, thermogravimetric analysis, vibrational spectroscopy (FT-IR and FT-Raman), electron microscopy, and CHN elemental analysis. While synthesis in DMF promotes the formation of centrosymmetric dimeric units, which act as building blocks in the construction of anionic ∞ 3{[Ln(pydc)2]-} frameworks having the channels filled by the charge-balancing (CH3)2NH2 + cations generated in situ by the solvolysis of DMF, the use of water as the solvent medium promotes clustering of the lanthanide centers: structures of 2 and 3 contain instead tetrameric [Er4(μ3-OH)4]8+ and hexameric |Pr6(μ3-O)2(μ3-OH)6| clusters which act as the building blocks of the networks, and are bridged by the H2-xpydcx- residues. It is demonstrated that this modular approach is reflected in the topological nature of the materials inducing 4-, 8-, and 14-connected uninodal networks (the nodes being the centers of gravity of the clusters) with topologies identical to those of diamond (family 1), and framework types bct (for 2) and bcu-x (for 3), respectively. The thermogravimetric studies of compound 3 further reveal a significant weight increase between ambient temperature and 450 °C with this being correlated with the uptake of oxygen from the surrounding environment by the praseodymium oxide inorganic core

A HYBRID METHOD FOR ANISOTROPIC ELLIPTIC PROBLEMS BASED ON THE COUPLING OF AN ASYMPTOTIC-PRESERVINGMETHOD WITH THE ASYMPTOTIC LIMIT MODEL

International audienceThis paper presents a hybrid numerical method to solve efficiently a class of highly anisotropic elliptic problems. The anisotropy is aligned with one coordinate axis and its strength is described by a parameter ε ∈ (0, 1], which can largely vary in the study domain. Our hybrid model is based on asymptotic techniques and couples (spatially) an asymptotic-preserving model with its asymptotic limit model, the latter being used in regions where the anisotropy parameter ε is small. Adequate coupling conditions link the two models. The aim of this hybrid procedure is to reduce the computational time for problems where the region of small ε-values extends over a significant part of the domain, and this is due to the reduced complexity of the limit model

SPARSE GRID RECONSTRUCTIONS FOR PARTICLE-IN-CELL METHODS

In this article, we propose and analyse Particle-In-Cell (PIC) methods embedding sparse grid reconstruction as those introduced in [1, 2]. The sparse grid reconstructions offer a significant improvement on the statistical error of PIC schemes as well as a reduction in the complexity of the problem providing the electric field. Main results on the convergence of the electric field interpolant and conservation properties are provided in this paper. Besides, tailored sparse grid reconstructions, in the frame of the offset combination technique, are proposed to introduce PIC methods with improved efficiency. The methods are assessed numerically and compared to existing PIC schemes thanks to classical benchmarks with remarkable prospects for three dimensional computations

Application of sparse grid combination techniques to low temperature plasmas particle-in-cell simulations. I. Capacitively coupled radio frequency discharges

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Acceleration of Particle-In-Cell Simulations using Sparse Grid Algorithms: I. Application to Dual Frequency Capacitive Discharges

International audienceThe use of sparse particle-in-cell (PIC) algorithms to accelerate the standard explicit PIC scheme has recently been successfully applied in the context of single-frequency capacitively coupled plasma discharges [Garrigues et al., J. Appl. Phys. 129, 153303 (2021)]. We have extended the sparse PIC scheme to model dual-frequency capacitive discharges. Comparisons between standard and sparse PIC algorithms show that the plasma properties as well as the electron and ion distribution functions can be retrieved with a maximum error of 2%. This work opens the interest of using the sparse PIC algorithm to perform 2D and 3D simulations under real operating conditions of capacitively coupled plasma discharges