Nonlinear short-pulse propagation in a free-electron laser

With one-dimensional time-dependent Maxwell-Lorentz equations, we have numerically investigated the nonlinear short-pulse propagation in a free-electron laser (FEL). Considering the pulsed electron beam and the cavity detuning, we describe a spiking behavior and the dissipative dynamics in a FEL oscillator. We show that the spiking behavior is well understood by superradiant pulse propagation and its dynamical regimes are closely related to a bifurcation and the chaotic transition in the nonlinear dissipative dynamics. The scaled synchrotron slippage distance (${\mathit{L}}_{\mathrm{syn}}$/${\mathit{L}}_{\mathit{s}}$), where ${\mathit{L}}_{\mathit{s}}$ is the slippage length and ${\mathit{L}}_{\mathrm{syn}}$ is the slippage distance in a synchrotron period, plays an important role in determining the dynamical regimes. Using dimensionless branching parameters, which are the cavity detuning parameter D, the slippage parameter S, and the superradiant parameter K, we describe the bifurcation and the chaotic transitions via a period-doubling cascade, an intermittency, and a quasiperiodicity. The real-time signal, the phase-space plot, and the corresponding power spectrum are used to confirm our results.