Effects of a tapered undulator in a free-electron laser oscillator with two electron beams

We have analyzed the effects for a tapered undulator in a free-electron laser (FEL) oscillator by using two electron beams of different energies based on the proposed FEL facility that is to be operated in the far-infrared and infrared regions. The effects of the tapered undulator in a free-electron laser oscillator with two electron beams on the electron beam's emittance, the offset misalignment errors, the energy spreads, and the higher-order modes were studied using a twodimensional (2D) FEL code with two electron beams that we had developed. The effects of the variations in the radiation amplitude on the electron beam's emittance, the offset misalignment errors, and the energy spreads with a tapered undulator and with an untapered undulator were also calculated for the multi-particle and the multi-pass number by using a 2D code. The results for the gains of a higher energy beam with and without a tapered undulator in the two-beam system were compared to the results obtained using a single electron beam with and without tapering. The mode construction was studied for higher-order modes with a tapered undulator, and the results for the emittance and the offset misalignment errors were compared to those of an untapered undulator.