Nonlinear resonances in a multi-stage free electron laser amplifier

Nonlinear resonances in the longitudional phase-space of a multi-stage free-electron laser for the two-beam accelerator is studied. A large scale primary resonance observed in simulations is found to be modeled by the nonlinear pendulum equation with the macroparticle model. With the perturbation method, we theoretically describe that the resonance-structure depends on RF power-density.