Start-up and saturation in self-amplified spontaneous emission free-electron lasers using a time-independent analysis

Numerical simulation of self-amplified spontaneous emission (SASE) in free-electron lasers (FELs) is typically performed using time-dependent computer codes, which take large CPU time and require large memory. Recently, Yu [Phys. Rev. E 58, 4991 (1998)] has shown that one can even use a time-independent code for this purpose (where the requirement on CPU time and memory is significantly reduced) by modifying it to include multiple phase-space buckets and using a scaling relation between the output power and the number of simulation particles, which is valid only in the linear regime. In this paper, we take a fresh look at the problem and show that incorporating multiple buckets in TDA3D is not needed to simulate the SASE process. We give a new interpretation of time-independent simulations of the SASE process and present detailed justification for using a single-frequency steady-state simulation code for the study of evolution of shot noise. We further extend the simulation studies to the nonlinear regime by modifying the code TDA3D to take the incoherent input power. We use this technique to study the start-up and saturation of the TTF-II FEL at DESY and discuss the results.