Solutions to the cold plasma model at resonances

Després, Bruno; Imbert-Gérard, Lise-Marie; Lafitte, Olivier

Journal de l’École polytechnique — Mathématiques, Tome 4 (2017), pp. 177-222.

La théorie mathématiques des équations de Maxwell avec le tenseur du plasma froid en présence d’une résonance cyclotron ou hybride est peu développée. Ces équations sont présentes pour modéliser la propagation d’une onde électromagnétique dans un plasma magnétique tel que celui d’un Tokamak et les solutions peuvent être très différentes de la propagation dans le vide. Ce travail contribue principalement à la théorie locale de la résonance hybride avec des formules originales de représentation à partir de fonctions spéciales. Ces formules sont obtenues au moyen d’une équation eikonale et d’un traitement spécifique de la singularité.

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 differently 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.

Classification : 34M03, 78A25, 34C11
Keywords: Cold plasma model, resonant Maxwell’s equations, hybrid resonance, eikonal equation, singular solutions of ODEs
Mot clés : Modèle du plasma froid, équations de Maxwell résonantes, résonance hybride, équation eikonale, solutions singulières d’EDO

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