Analytic model of electron pulse propagation in ultrafast electron diffraction experiments

We present a mean-field analytic model to study the propagation of electron pulses used in ultrafast electron diffraction experiments (UED). We assume a Gaussian form to characterize the electron pulse, and derive a system of ordinary differential equations that are solved quickly and easily to give the pulse dynamics. We compare our model to an N -body numerical simulation and are able to show excellent agreement between the two result sets. This model is a convenient alternative to time consuming and computationally intense N -body simulations in exploring the dynamics of UED electron pulses, and as a tool for refining UED experimental designs.