Can One Hear Whistler Waves?

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) over tilde (e)(x) plays an essential part. The description of the related phenomena is achieved in two stages. The first is based on a newapproach 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), Frenod and Sonnendrucker (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) over tilde (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.