@article{d15e19ffc9674e2182c98b77efb7ada5,
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",
issn = "2429-7100",
publisher = "Ecole Polytechnique",
}