Evolution of non-Gaussian electron bunches in ultrafast electron diffraction experiments: Comparison to analytic model

We present a comparison of a three-dimensional analytic Gaussian (AG) model of electron bunch propagation with numerical simulations of quasi- and non-Gaussian distributions. Quasi- and non-Gaussian distributions are a good representation of electron bunches used in ultrafast electron diffraction (UED) experiments, and we show that the AG model is successful in predicting the evolution of such freely propagating bunches. The bunch parameters in our comparisons are the bunch size, the total momentum spread, and the local momentum spread. In the case of the local momentum spread, which is related to the bunch coherence length, we compare the predictions of the AG model with three methods for calculating the local momentum spread from numerical data. This comparison also highlights the difficulties of calculating the evolution of the local momentum parameter from N-body simulations. The AG model shows good agreement with N-body simulations of different distributions for all the bunch parameters and is therefore a convenient tool for refining the UED experimental design.