Dispersion relations in hot magnetized plasmas

In the framework of hot magnetized collisionless plasmas, dispersion relations have been extensively studied in the past [2], [12], [13], [24], [33], [34], [38]. This subject is still topical in plasma physics [19], [27], [32], [36], [42]. The aim of this article is to provide a rigorous derivation of the characteristic variety, based on some asymptotic analysis of the relativistic Vlasov-Maxwell system. Special emphasis is made on the modeling of Tokamaks, with spatial variations of the magnetic field and of the equilibrium distribution function. In order to take into account the inhomogeneities, the problem is formulated in terms of geometrical optics [29], [31]. This allows to unify, justify and extend the preceding results. New aspects are indeed included. For instance, the dielectric tensor is defined for real frequencies through singular integrals involving the Hilbert transform.