Analytical study of the relativistic dispersion: Application to the generation of the auroral kilometric radiation

Publisher Website
Google Scholar
Abstract
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 perticle by cm−3, 〈E〉 ≈ 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⊥0/c)² which is a small number and scales both the temporal growth rate and the bandwidth of the CMI.ii) a parameter characterising the density of the energetic population: P = 1/δ(ωph/ωc)²(ωph being the plasma frequency of the energetic component).iii) the proportion of thermal plasma : χ = nc/nh where nc and nh are the density of the thermal and the hot plasma components respectively.iv) the ratio τ between the peak energy of the DGH and the mean energy of the maxwellian population.Our calculations allow us to simply perform a parametric study of the various regimes presented by the CMI. For the range of parameters inferred from measurements of the Swedish spacecraft Viking: (P>1 and χ small), the growth rate could maximize at the cut‐off frequency of the relativistic X mode. It can be quite large: Im(ω)max ≈ δωc (10−2 ωc for electrons of 5 Kev). Moreover, for small χ, the relativistic X mode is connected to freely propagating modes which guarantees an easy access of the electromagnetic energy to free space.