Singularities of particle trajectory caustics and beam shaping in bunch compressors

Caustics are a common occurrence in optics, describing the bright lines seen in a well-lit coffee cup or the dancing networks of light seen at the bottom of a swimming pool on a sunny day. Recently, caustic formation in electron trajectories was identified as the mechanism driving strong current modulations in accelerated charged-particle beams. Under certain conditions, neighboring electron trajectories coalesce to form caustics, resulting in current spikes. Caustic lines and surfaces are regions of maximum electron density, and are often witnessed in accelerator physics as folds in the transverse or longitudinal phase space distribution. Knowledge of caustics can allow us to shape the longitudinal beam shape to our advantage.