Unstable electron distribution measured by FAST in the Earth auroral region (Ergun et al. 2000). This kind of distribution is typical in the auroral regions emitting radio emissions. It consists in a cold (a few eV) Gaussian distribution with a warmer (a few hundred eV) halo which is shifted in energy by a few keV and whose pitch angle is scattered due to magnetic mirroring. We assumed a distribution function of that kind in our modelling of the beaming angle from auroral cavities. Velocity dispersion, corresponding to the cold and halo temperature (ϵ_c and ϵ_h), and velocity shift, corresponding to the beam energy (ϵ_b), are shown. The resonant electron velocity (v_r) and the equivalent “thermal” velocity (v_th) are also shown.