The nonlinear evolution of a free electron laser with electromagnetic wigglers

Abstract

The nonlinear evolution of a free electron laser (FEL) with an electromagnetic wiggler in the high gain regime is investigated. Two opposite configurations for the wiggler field propagation direction are considered: the wiggler field propagating counter to the electron beam, which is subject to a depletion in the nonlinear stage, and the one propagating parallel to the electron beam, which is subject to an amplification. Especially for the latter case, the possibility of an explosive instability has been fully investigated. A self-consistent set of equations is derived and solved numerically. In the Compton regime the radiation field saturates at a peak amplitude a2=0.6(ωpb/ω1)4/3a1/3w, where a(aw) is the usual normalized vector potential of the radiation (wiggler) field and ωpb(ω1) is the beam plasma (radiation) frequency in the ponderomotive wave frame. In the Raman regime the FEL instability saturates either by particle trapping or by detuning from the resonance due to the nonlinear frequency of the beam mode, depending on the initial wiggler strength. For the copropagating wiggler field system the explosive behavior can be seen only in an impractically small wiggler strength region. In a parameter regime of practical interest the behavior of the radiation field around the saturation is not affected much by the pump depletion or amplification.