Dispersion relations in cold magnetized plasmas

Christophe Cheverry (1) , Adrien Fontaine (1)

1 IRMAR - Institut de Recherche Mathématique de Rennes

Starting from kinetic models of cold magnetized collisionless plasmas, we provide a complete description of the characteristic variety sustaining electromagnetic wave propagation. Our analysis is based on some asymptotic calculus exploiting the presence at the level of dimensionless relativistic Vlasov-Maxwell equations of a large parameter: the electron gyrofrequency. Our method is inspired from geometric optics. It allows to unify preceding results, while incorporating new aspects. Specifically, the non trivial effects of the spatial variations of the background density, temperature and magnetic field are exhibited. In this way, a comprehensive overview of the dispersion relations becomes available, with important possible applications in plasma physics.

Mots clés: Electromagnetic wave propagation; characteristic variety; Dispersion relations; Relativistic Vlasov-Maxwell equations; Cold magnetized plasmas; Plasma phenomena out of equilibrium; Appleton-Hartree equations; eikonal equations

Domaines: Equations aux dérivées partielles [math.AP]

Christophe Cheverry, Adrien Fontaine. Dispersion relations in cold magnetized plasmas. Kinetic and Related Models , 2017, 10 (2), pp.373-421. ⟨10.3934/krm.2017015⟩. ⟨hal-01243495⟩