Hybrid resonance of Maxwell's equations in slab geometry

被引：18

作者：

Despres, Bruno ^{[1
]}

Imbert-Gerard, Lise-Marie ^{[1
]}

Weder, Ricardo ^{[2
]}

机构：

[1] Univ Paris 06, Lab Jacques Louis Lions, F-75252 Paris 05, France

[2] Univ Nacl Autonoma Mexico, Inst Invest & Matemat Aplicadas & Sistemas, Dept Fis Matemat, Mexico City 01000, DF, Mexico

来源：

JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES | 2014年 / 101卷 / 05期

关键词：

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

D O I：

10.1016/j.matpur.2013.10.001

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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. (C) 2013 Elsevier Masson SAS. All rights reserved.

引用

页码：623 / 659

页数：37

共 38 条

[1]

Abramowitz M., 1972, Handbook on Mathematical Functions with Formulas, Graphs, and Mathematical Tables

[2]

[Anonymous], 1992, Boundary problems of function theory and their application to mathematical physics

[3]

[Anonymous], 1953, Grundzuge einer allgemeinen Theorie der linearen Integralgleichungen

[4]

Bart G. R., 1973, SIAM Journal on Mathematical Analysis, V4, P609, DOI 10.1137/0504053

[5]

Bateman H., 1953, Higher Transcendental Functions: Volume 1, 2

[6] RADIATION CONDITION FOR A NON-SMOOTH INTERFACE BETWEEN A DIELECTRIC AND A METAMATERIAL [J].

Bonnet-Ben Dhia, Anne-Sophie ;

Chesnel, Lucas ;

Claeys, Xavier .

MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES, 2013, 23 (09) :1629-1662

[7]

Bouche D., 1996, ASYMPTOTIC METHODS E

[8]

Brambilla M., 1998, INT SER MONOGR PHYS

[9]

Budden K.G., 1961, Radio Waves in the Ionosphere, Vfirst

[10] PLASMA OSCILLATIONS [J].

CASE, KM .

ANNALS OF PHYSICS, 1959, 7 (03) :349-364

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