Gaussian random field generator for simulating partially coherent undulator radiation

Abstract

Wavefront propagation codes play pivotal roles in the design of optics at synchrotron radiation sources. However, they usually do not account for the stochastic behavior of the radiation field originating from shot noise in the electron beam. We propose a computationally efficient algorithm to calculate a single statistical realization of partially coherent synchrotron radiation fields at a given frequency. This field can be consequently propagated from the source position downstream through an optical beamline to the sample position. The proposed algorithm relies on a method for simulating Gaussian random fields. We initially generate the radiation field as Gaussian white noise and then restrict it in both real and inverse space domains for a given radiation size and divergence. We exploit the assumption of quasi-homogeneity of the source. However, we show that the method is applicable with reasonable accuracy outside of this assumption. The proposed algorithm is consistent with other well-established approaches, and, in addition, it possesses an advantage in terms of computational efficiency. It can be extended to other types of sources that follow Gaussian statistics. Finally, the demonstration of the algorithm is well suited for educational purposes.