Parallel electric field amplitude associated with the mode m′ = 2 and calculated from the hybrid simulations. The dotted line corresponds to the theoretical initial amplitude given by Eq. (73), while the dashed line is the analytical estimation of the stationary value given by Eq. (75). The match with the numerical results is quite significant. In this simulation β_e = 6 × 10⁻² and β_p = 10⁻² and the excitation corresponds to a R-mode.