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Caustics: Singularities in particle trajectory densities 

Abstract:

On occasion, phenomena encountered in other fields of physics find themselves an equivalence in accelerator physics. Caustics are one such example. Within the fields of X-ray optics and electron microscopy, caustics are commonly recognized and are well-understood. The same effect can be seen in various accelerator physics scenarios. Caustics are a form of ‘natural focusing’, whereby particle trajectories coalesce to form regions of greatly enhanced charge density.  By their nature, caustics