Controlled Hopf Bifurcation of a storage-ring free-electron laser

Local bifurcation control is a topic of fundamental importance in the field of nonlinear dynamical systems. We discuss an original example within the context of storage-ring free-electron laser physics by presenting a new model that enables analytical insight into the system dynamics. The transition between the stable and the unstable regimes, depending on the temporal overlapping between the light stored in the optical cavity and the electrons circulating into the ring, is found to be a Hopf bifurcation. A feedback procedure is implemented and shown to provide an effective stabilization of the unstable steady state.