Parameter optimization and start-to-end simulation for the phase-merging enhanced harmonic generation free electron laser

Recently, a novel scheme called the phase-merging enhanced harmonic generation (PEHG) free-electron laser (FEL) has been developed to achieve higher harmonic bunching in a single stage set up. However, previous studies of the PEHG mechanism ignored the practical lattice configuration, leaving out the impact of the intrinsic beam divergence on the phase-merging effect. In this paper, a new method based on the beam transport matrix is proposed to comprehensively study the optimization conditions of the harmonic generation FELs. On the basis of this method, the new optimization conditions of the PEHG are obtained by taking into account both the intrinsic horizontal beam size and the intrinsic horizontal beam divergence. The parameter optimization and three dimensional start-to-end simulations are carried out using the typical beam parameters of the Shanghai Soft X-ray Free Electron Laser user facility. The simulation results are in agreement with the theoretical analysis and demonstrate the validity of the PEHG-FEL.