Can One Hear Whistler Waves?

• Published in: Communications in mathematical physics 2015-09, Vol.338 (2), p.641-703
• Main Author: Cheverry, Christophe
• Format: Article
• Language: English
• Subjects: Analysis of PDEs; Classical and Quantum Gravitation; Complex Systems; Mathematical and Computational Physics; Mathematical Physics; Mathematics; Physics; Physics and Astronomy; Quantum Physics; Relativity Theory; Theoretical
• ISSN: 0010-3616; 1432-0916
• DOI: 10.1007/s00220-015-2389-6

The aim of this article is to propose a mathematical framework giving access to a better understanding of whistler-mode chorus emissions in space plasmas. There is a general agreement that the emissions of whistler waves involve a mechanism of wave-particle interaction that can be described in the framework of the relativistic Vlasov-Maxwell equations. In dimensionless variables, these equations involve a penalized skew-symmetric term where the inhomogeneity of the strong exterior magnetic field B ~ e ( x ) plays an essential part. The description of the related phenomena is achieved in two stages. The first is based on a new approach allowing one to extend in longer times the classical insights on fast rotating fluids [Chemin et al. (Mathematical geophysics, volume 32 of Oxford Lecture Series in Mathematics and its Applications. The Clarendon Press Oxford UniversityPress, Oxford, 2006 ), Cheverry et al. (Duke Math J 161(5):845–892, 2012 ), Frénod and Sonnendrücker (Math Models Methods Appl Sci 10(4):539–553, 2000 ), Gallagher and Saint-Raymond (SIAM J Math Anal 36(4):1159–1176, 2005 )]; it justifies the existence and the validity of long time gyro-kinetic equations; it furnishes criterions to impose on a magnetic field B ~ e ( · ) in order to obtain the long time dynamical confinement of plasmas. The second stage is based on a study of oscillatory integrals implying special phases; it deals with the problem of the creation of light inside plasmas.