Quiet start method in HGHG FEL simulation

Quiet start scheme is broadly utilized in self amplified spontaneous radiation (SASE) FEL simulations, which is proven to be correct and efficient. Nevertheless, due to the energy modulation and the dispersion section, the high gain harmonic generation (HGHG) FEL simulation will not be improved by the traditional quiet start method. A new approach is presented to largely decrease the number of macro-particles per slice that can be implemented in both time-independent and time-dependent simulation, accordingly expedites the high order harmonic cascade simulation and makes the multi-parameter scanning be possible.