Dynamic filling factor in the Super-ACO free electron laser

Here, the Free Electron Laser evolution before the start-up from the spontaneous radiation of an undulator, is considered. This analysis is carried on through the dynamical behaviour of the Filling-factor, representing the transverse overlap between the light pulse and the electron bunch. In such a framework, the gain optimization before the laser start-up is presented and more generally applied to low-gain storage-ring free electron lasers, such as on Super-ACO.