Quantifying electron cascade size in various irradiated materials for free-electron laser applications

Studying electron- and X-ray-induced electron cascades in solids is essential for various research areas at free-electron laser facilities, such as X-ray imaging, crystallography, pulse diagnostics or X-ray-induced damage. To better understand the fundamental factors that define the duration and spatial size of such cascades, this work investigates the electron propagation in ten solids relevant for the applications of X-ray lasers: Au, B₄C, diamond, Ni, polystyrene, Ru, Si, SiC, Si₃N₄ and W. Using classical Monte Carlo simulation in the atomic approximation, we study the dependence of the cascade size on the incident electron or photon energy and on the target parameters. The results show that an electron-induced cascade is systematically larger than a photon-induced cascade. Moreover, in contrast with the common assumption, the maximal cascade size does not necessarily coincide with the electron range. It was found that the cascade size can be controlled by careful selection of the photon energy for a particular material. Photon energy, just above an ionization potential, can essentially split the absorbed energy between two electrons (photo- and Auger), reducing their initial energy and thus shrinking the cascade size. This analysis suggests a way of tailoring the electron cascades for applications requiring either small cascades with a high density of excited electrons or large-spread cascades with lower electron densities.