Generation of multiple coherent pulses in a superradiant free-electron laser

We analyze the structure of the tail of a superradiant pulse, which is constituted by a train of trailing-pulses with decaying amplitudes. We show how a trailing pulse, with phase advance from the leading pulse, is generated at the falling edge of the leading pulse, where the corresponding phase space is deeply saturated and the electrons become de-trapped by the reduced ponderomotive potential. Once the trailing pulse gains enough energy, it generates a second trailing pulse, and the process takes place again. By performing detailed simulations of the resulting electron phase space distribution and the FEL pulse spectral and temporal structure with PERSEO, we confirm that the deformation and re-bunching of the longitudinal phase space create a sequence of pulses.