Mathematical models and methods for plasma physics. Volume 1. Fluid models
type: Item
instance of: scholarly article
title: Mathematical models and methods for plasma physics. Volume 1. Fluid models
zbMATH Open document ID: 1286.82001
DOI: 10.1007/978-3-319-03804-9
author: R. Sentis
published in: Modeling and Simulation in Science, Engineering and Technology
publication date: 2014-01-08T00:00:00Z
review text: The first volume of this monograph is devoted to fluid models in plasma physics. The author says to have about two motivations for undertaking this work: to understand and justify from the mathematical point of view the derivations of some classical-specific models from more general ones, and to give the precise statements of the PDFs systems with the appropriated boundary conditions which are necessary to perform efficient numerical simulations mainly in multi-dimensional cases. The short Chapter 1, after a historical information, gives some classic characteristic quantities appearing in plasma physics. In Chapter 1, the massless-electron approximation is justified from the general ion-electron electrodynamic model. The quasi-neutrality approximation is presented as the essence of most fluid models considered further. This approximation is rigorously proved by an asymptotic analysis where a small parameter related to the Debye length tends to zero. Then the two-temperature Euler system is considered as the basic model for quasi-neutral plasmas, presented in this framework with thermal conduction and radiative coupling. The known model of electron magnetohdrodynamics (MHD) is introduced as the fundamental model for all magnetized plasmas. In a conclusion section the analyses of the hyperbolic part for (E2T) and (MHD) systems is given. Chapter 3 contains most of the fundamental concepts for the laser-plasma interaction. The paraxial approximation for the laser propagation is derived from the full Maxwell equations by using a time envelope model and performing the Wenzel-Kramer-Brillouin (WKB) expansion. Here, the geometrical optics approximation and the paraxial approximations are compared. Then the Brillouin instability corresponding to a coupling of the laser waves and an ion acoustic wave are considered that lead to the three-wave coupling system introduced by Kadomtsev. Some crucial mathematical properties of this system are deduced for the better understanding o…
Mathematics Subject Classification ID: 82-02
Mathematics Subject Classification ID: 82D10
Mathematics Subject Classification ID: 00A79
Mathematics Subject Classification ID: 76W05
Mathematics Subject Classification ID: 78A60
Mathematics Subject Classification ID: 78A05
zbMATH DE Number: 6243678
zbMATH Keywords: kinetic models of plasma physics
zbMATH Keywords: magnetohydrodynamics
zbMATH Keywords: laser propagation
zbMATH Keywords: coupling with ion acoustic waves
zbMATH Keywords: Zakharov equations
zbMATH Keywords: Langmuir waves
zbMATH Keywords: coupling electron waves and laser waves
zbMATH Keywords: models with several spaces
reviewed by: Boris V. Loginov
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1007/978-3-319-03804-9
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description: scientific article; zbMATH DE number 6243678