Solutions to the cold plasma model at resonances

Bruno Despres; Lise Marie Imbert-Gerard; Olivier Lafitte

doi:10.5802/jep.41

Solutions to the cold plasma model at resonances

Bruno Despres
, Lise Marie Imbert-Gerard
, Olivier Lafitte

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

Abstract

Little is known on the mathematical theory of hybrid and cyclotron solutions of Maxwell’s equations with the cold plasma dielectric tensor. These equations arise in magnetized plasmas to model an electromagnetic wave in a Tokamak. The solutions can behave extremely di erently from those in vacuum. This work contributes to the local theory of the hybrid resonance by means of an original representation formula based on special functions, a certain eikonal equation and with a careful treatment of the singularity.

Original language	English (US)
Pages (from-to)	177-222
Number of pages	46
Journal	Journal de l'Ecole Polytechnique - Mathematiques
Volume	4
DOIs	https://doi.org/10.5802/jep.41
State	Published - 2017
Externally published	Yes

Keywords

Cold plasma model
Eikonal equation
Hybrid resonance
Resonant Maxwell’s equations
Singular solutions of ODEs

ASJC Scopus subject areas

General Mathematics

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10.5802/jep.41

Cite this

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title = "Solutions to the cold plasma model at resonances",

abstract = "Little is known on the mathematical theory of hybrid and cyclotron solutions of Maxwell{\textquoteright}s equations with the cold plasma dielectric tensor. These equations arise in magnetized plasmas to model an electromagnetic wave in a Tokamak. The solutions can behave extremely di erently from those in vacuum. This work contributes to the local theory of the hybrid resonance by means of an original representation formula based on special functions, a certain eikonal equation and with a careful treatment of the singularity.",

keywords = "Cold plasma model, Eikonal equation, Hybrid resonance, Resonant Maxwell{\textquoteright}s equations, Singular solutions of ODEs",

author = "Bruno Despres and Imbert-Gerard, \{Lise Marie\} and Olivier Lafitte",

note = "Funding Information: Lise-Marie Imbert-G{\'e}rard and Bruno Despr{\'e}s acknowledge the support of ANR under contract ANR-12-BS01-0006-01. Moreover, this work was carried out within the framework of the European Fusion Development Agreement and the French Research Federation for Fusion Studies. It is supported by the European Communities under the contract of Association between Euratom and CEA. The views and opinions expressed herein do not necessarily reflect those of the European Commission. Lise-Marie Imbert-G{\'e}rard also acknowledges the support of the Applied Mathematical Sciences Program of the U.S. Department of Energy under contract DEFG0288ER25053.",

year = "2017",

doi = "10.5802/jep.41",

language = "English (US)",

volume = "4",

pages = "177--222",

journal = "Journal de l'Ecole Polytechnique - Mathematiques",

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publisher = "Ecole Polytechnique",

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AU - Despres, Bruno

AU - Imbert-Gerard, Lise Marie

AU - Lafitte, Olivier

N1 - Funding Information: Lise-Marie Imbert-Gérard and Bruno Després acknowledge the support of ANR under contract ANR-12-BS01-0006-01. Moreover, this work was carried out within the framework of the European Fusion Development Agreement and the French Research Federation for Fusion Studies. It is supported by the European Communities under the contract of Association between Euratom and CEA. The views and opinions expressed herein do not necessarily reflect those of the European Commission. Lise-Marie Imbert-Gérard also acknowledges the support of the Applied Mathematical Sciences Program of the U.S. Department of Energy under contract DEFG0288ER25053.

PY - 2017

Y1 - 2017

N2 - Little is known on the mathematical theory of hybrid and cyclotron solutions of Maxwell’s equations with the cold plasma dielectric tensor. These equations arise in magnetized plasmas to model an electromagnetic wave in a Tokamak. The solutions can behave extremely di erently from those in vacuum. This work contributes to the local theory of the hybrid resonance by means of an original representation formula based on special functions, a certain eikonal equation and with a careful treatment of the singularity.

AB - Little is known on the mathematical theory of hybrid and cyclotron solutions of Maxwell’s equations with the cold plasma dielectric tensor. These equations arise in magnetized plasmas to model an electromagnetic wave in a Tokamak. The solutions can behave extremely di erently from those in vacuum. This work contributes to the local theory of the hybrid resonance by means of an original representation formula based on special functions, a certain eikonal equation and with a careful treatment of the singularity.

KW - Cold plasma model

KW - Eikonal equation

KW - Hybrid resonance

KW - Resonant Maxwell’s equations

KW - Singular solutions of ODEs

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DO - 10.5802/jep.41

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AN - SCOPUS:85034069508

SN - 2429-7100

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EP - 222

JO - Journal de l'Ecole Polytechnique - Mathematiques

JF - Journal de l'Ecole Polytechnique - Mathematiques

ER -

Solutions to the cold plasma model at resonances

Abstract

Keywords

ASJC Scopus subject areas

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