SUPERRADIANT FREE-ELECTRON LASERS IN THE HIGH-GAIN STRONG PUMP REGIME

Time-dependent high-gain free-electron laser equations are generalized to the strong pump regime where fast, 2pi/k(w), spatial oscillations can no longer be eliminated by spatial averages, and evolution of the radiation phase needs to be taken into account. The equations are solved numerically along the characteristics of the beam and the laser field for superradiant solutions in the strong pump regime using the parameters of the Electron Laser Facility (ELF) of the Lawrence Livermore National Laboratory, [Phys. Rev. Lett. 54, 889 (1985); Nucl. Instrum. Methods A 250, 144 (1986); 285, 217 (1989); Phys. Rev. A 35, 2184 (1987)]. With beam pulses short compared to the wiggler length and long compared to the cooperation length, numerical solutions show that the initial laser fields get amplified to the steady-state level intensity in only a few bucket distances in the slippage region along the beam characteristics. The underlying mechanism for this superradiant gain gradient is due to the amplification of the incoming fields by the electrons prebunched by the earlier outgoing fields. Contrary to the earlier results, no spikes on the laser amplitude is observed in the slippage region. On the other hand, the solutions do show spikes on the relative laser phase. However, it is not clear on the credibility and the significance of these spikes, whether in amplitude or in phase.