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].