Hybrid resonance of Maxwell's equations in slab geometry

Bruno Després; Lise Marie Imbert-Gérard; Ricardo Weder

doi:10.1016/j.matpur.2013.10.001

Hybrid resonance of Maxwell's equations in slab geometry

Bruno Després
, Lise Marie Imbert-Gérard
, Ricardo Weder

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

19 Scopus citations

Abstract

Hybrid resonance is a physical mechanism for the heating of a magnetic plasma. In our context hybrid resonance is a solution of the time harmonic Maxwell's equations with smooth coefficients, where the dielectric tensor is a non-diagonal Hermitian matrix. The main part of this work is dedicated to the construction and analysis of a mathematical solution of the hybrid resonance with the limit absorption principle. We prove that the limit solution is singular: it consists of a Dirac mass at the origin plus a principal value and a smooth square integrable function. The formula obtained for the plasma heating is directly related to the singularity.

Original language	English (US)
Pages (from-to)	623-659
Number of pages	37
Journal	Journal des Mathematiques Pures et Appliquees
Volume	101
Issue number	5
DOIs	https://doi.org/10.1016/j.matpur.2013.10.001
State	Published - May 2014
Externally published	Yes

Keywords

Anisotropic dielectric tensor
Hybrid resonance
Limit absorption principle
Maxwell equations
Resonant heating

ASJC Scopus subject areas

General Mathematics
Applied Mathematics

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10.1016/j.matpur.2013.10.001

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title = "Hybrid resonance of Maxwell's equations in slab geometry",

abstract = "Hybrid resonance is a physical mechanism for the heating of a magnetic plasma. In our context hybrid resonance is a solution of the time harmonic Maxwell's equations with smooth coefficients, where the dielectric tensor is a non-diagonal Hermitian matrix. The main part of this work is dedicated to the construction and analysis of a mathematical solution of the hybrid resonance with the limit absorption principle. We prove that the limit solution is singular: it consists of a Dirac mass at the origin plus a principal value and a smooth square integrable function. The formula obtained for the plasma heating is directly related to the singularity.",

keywords = "Anisotropic dielectric tensor, Hybrid resonance, Limit absorption principle, Maxwell equations, Resonant heating",

author = "Bruno Despr{\'e}s and Imbert-G{\'e}rard, \{Lise Marie\} and Ricardo Weder",

note = "Funding Information: The collaboration leading to this article was started during a visit of Ricardo Weder to INRIA Paris-Rocquencourt. Ricardo Weder thanks Patrick Joly for his kind hospitality. This research was partially supported by Consejo Nacional de Ciencia y Tecnolog{\'i}a (CONACYT) under project CB2008-99100-F . 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.",

year = "2014",

month = may,

doi = "10.1016/j.matpur.2013.10.001",

language = "English (US)",

volume = "101",

pages = "623--659",

journal = "Journal des Mathematiques Pures et Appliquees",

issn = "0021-7824",

publisher = "Elsevier Masson SAS",

number = "5",

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T1 - Hybrid resonance of Maxwell's equations in slab geometry

AU - Després, Bruno

AU - Imbert-Gérard, Lise Marie

AU - Weder, Ricardo

N1 - Funding Information: The collaboration leading to this article was started during a visit of Ricardo Weder to INRIA Paris-Rocquencourt. Ricardo Weder thanks Patrick Joly for his kind hospitality. This research was partially supported by Consejo Nacional de Ciencia y Tecnología (CONACYT) under project CB2008-99100-F . 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.

PY - 2014/5

Y1 - 2014/5

N2 - Hybrid resonance is a physical mechanism for the heating of a magnetic plasma. In our context hybrid resonance is a solution of the time harmonic Maxwell's equations with smooth coefficients, where the dielectric tensor is a non-diagonal Hermitian matrix. The main part of this work is dedicated to the construction and analysis of a mathematical solution of the hybrid resonance with the limit absorption principle. We prove that the limit solution is singular: it consists of a Dirac mass at the origin plus a principal value and a smooth square integrable function. The formula obtained for the plasma heating is directly related to the singularity.

AB - Hybrid resonance is a physical mechanism for the heating of a magnetic plasma. In our context hybrid resonance is a solution of the time harmonic Maxwell's equations with smooth coefficients, where the dielectric tensor is a non-diagonal Hermitian matrix. The main part of this work is dedicated to the construction and analysis of a mathematical solution of the hybrid resonance with the limit absorption principle. We prove that the limit solution is singular: it consists of a Dirac mass at the origin plus a principal value and a smooth square integrable function. The formula obtained for the plasma heating is directly related to the singularity.

KW - Anisotropic dielectric tensor

KW - Hybrid resonance

KW - Limit absorption principle

KW - Maxwell equations

KW - Resonant heating

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U2 - 10.1016/j.matpur.2013.10.001

DO - 10.1016/j.matpur.2013.10.001

M3 - Article

SN - 0021-7824

VL - 101

SP - 623

EP - 659

JO - Journal des Mathematiques Pures et Appliquees

JF - Journal des Mathematiques Pures et Appliquees

IS - 5

ER -

Hybrid resonance of Maxwell's equations in slab geometry

Abstract

Keywords

ASJC Scopus subject areas

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