Calculation of the output power in self-amplified spontaneous radiation using scaling of power with number of simulation particles

Recent advances in self-amplified spontaneous emission (SASE) experiments stimulate interest in quantitative comparison of measurements with theory. In this paper we show that the widely used simulation code TDA3D, developed by Tran and Wurtele [Comput. Phys. Commun. 54, 263 (1989)] even though a single frequency code, can be used to determine the output power in the SASE process with excellent approximation in the exponential growth regime. The method applies when the gain is not very high, which is a special advantage, because when the gain is not very high, the analytical calculation is particularly difficult since the exponential growing term does not dominate. The analysis utilizes a scaling relation between the output power and the number of simulation particles in the code TDA3D: $〈P〉{=N}_{\lambda }^{\prime }{/N}_{\lambda }〈P^{\prime }〉,$ where $〈P〉$ is the output power and $N_{\lambda }$ is the line density of the electrons, while $〈P^{\prime }〉$ is the calculated output power using a line density $N_{\lambda }^{\prime }$ of the number of simulation particles in the code TDA3D. Because of the scaling property, the number of simulation particles can be taken to be many orders of magnitude less than the actual experiment. Comparison of our results with experiment yields new insight into the SASE process.