The measurements recently performed by the Viking spacecraft have shown that, in addition to being cold plasma depleted, the source regions of the Auroral Kilometric Radiation (A.K.R.) are characterized by a relatively denser, more energetic electron component (a few particle by cm-3, ≈ 5 KeV). In order to properly study the Cyclotron Maser Instability (C.M.I.) which is thought to be responsible for the A.K.R. generation, it is thus necessary to include relativistic corrections in both the hermitian and the antihermitian parts of the dielectric tensor characterizing the linear properties of the plasma. Here one presents an analytical study of the corresponding dispersion equation which aims to describe stable and unstable waves having frequencies lying very close to the electronic gyrofrequency and propagating across the geomagnetic field with a perpendicular refractive index less than a few units (n⊥1 and &khgr; small), the growth rate could maximize at the cut-off frequency of the relativistic X mode.

It can be quite large: Im(&ohgr;)mm≈Δ&ohgr;c (10-2 &ohgr;c for electrons of 5 Kev). Moreover, for small &khgr;, the relativistic X mode is connected to freely propagating modes which guarantees an easy access of the electromagnetic energy to free space. ¿ American Geophysical Union 1989