Numerical approximation of the Euler-Poisson-Boltzmann model in the quasineutral limit

This paper analyzes various schemes for the Euler-Poisson-Boltzmann (EPB) model of plasma physics. This model consists of the pressureless gas dynamics equations coupled with the Poisson equation and where the Boltzmann relation relates the potential to the electron density. If the quasi-neutral assumption is made, the Poisson equation is replaced by the constraint of zero local charge and the model reduces to the Isothermal Compressible Euler (ICE) model. We compare a numerical strategy based on the EPB model to a strategy using a reformulation (called REPB formulation). The REPB scheme captures the quasi-neutral limit more accurately

Mini-Workshop: Numerics for Kinetic Equations

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Asymptotic-Preserving Particle-In-Cell method for the Vlasov-Poisson system near quasineutrality

International audienceThis paper deals with the numerical resolution of the Vlasov-Poisson system in a nearly quasineutral regime by Particle-In-Cell (PIC) methods. In this regime, classical PIC methods are subject to stability constraints on the time and space steps related to the small Debye length and large plasma frequency. Here, we propose an ``Asymptotic-Preserving" PIC scheme which is not subject to these limitations. Additionally, when the plasma period and Debye length are small compared to the time and space steps, this method provides a consistent PIC discretization of the quasineutral Vlasov equation. We perform several one-dimensional numerical experiments which provide a solid validation of the method and its underlying concepts

Singular Limits for Plasmas with Thermalised Electrons

This work is concerned with the study of singular limits for the Vlasov-Poisson system in the case of massless electrons (VPME), which is a kinetic system modelling the ions in a plasma. Our objective is threefold: first, we provide a mean field derivation of the VPME system in dimensions from a system of N extended charges. Secondly, we prove a rigorous quasineutral limit for initial data that are perturbations of analytic data, deriving the Kinetic Isothermal Euler (KIE) system from the VPME system in dimensions . Lastly, we combine these two singular limits in order to show how to obtain the KIE system from an underlying particle system.This work was supported by the UK Engineering and Physical Sciences Research Council (EPSRC) grant EP/L016516/1 for the University of Cambridge Centre for Doctoral Training, the Cambridge Centre for Analysis; and the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (grant agreement No 726386)

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