Nonlinear analysis of self-field effects in free-electron lasers

A model of the DC self-fields associated with the electron beam is incorporated into 3-dimensional nonlinear formulations of free-electron lasers. The nonlinear formulations are based upon the ARACHNE and WIGGLIN codes which are slow-time-scale formulations for the evolution of the amplitudes and phases of a multi-mode superposition of vacuum waveguide modes. The electron dynamics in these codes are treated by means of the complete 3-dimensional Lorentz force equations, and the representations for the self-fields are incorporated directly into this formulation. Results of the simulations are compared with experiments at LLNL using a planar wiggler, and at MIT and NRL which used helical wigglers. These experiments exhibited comparable space-charge depressions of Δγself/γ0 0.53-0.78% across the beam. The simulations are in reasonable agreement with the experiments.