Dispersion relations in cold magnetized plasmas

Abstract

Starting from kinetic models of cold magnetized collisionless plasmas, we provide a complete description of the characteristic variety sustaining electromagnetic wave propagation. As in [ 4 , 13 , 17 ], the 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. The method is inspired from geometric optics [ 29 , 33 ]. It allows to unify all the preceding results [ 8 , 12 , 38 , 31 , 37 , 40 ], while incorporating new aspects. Specifically, the non trivial effects [ 5 , 9 , 10 , 24 ] 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 [ 7 , 28 , 30 ].