Power spectrum calculation for the Cornell Wiggler A SASE experiment at BNL

Recently, we showed (Yu, Phys. Rev. E 58 (1998) 4991) that the widely used simulation code TDA3D, even though a single-frequency code, can be used to determine the power spectrum in the SASE process with excellent approximation in the exponential growth regime. In this paper, we apply this method to the BNL Cornell Wiggler A SASE experiment as an example. When the gain is not very high, there are many modes in the radiation, which seems to make the analytical calculation very difficult. However, we show that the increment of the radiation due to SASE over the spontaneous radiation can be expanded in terms of guided modes with rapid convergence. Thus when the spontaneous radiation is subtracted from the SASE power during the calculation, there is a good agreement between the analytical theory and the numerical simulation.