Abstract
Current modulations, current spikes, and current horns, are observed in a range of accelerator physics applications including strong bunch compression in Free Electron Lasers and linear colliders, trains of microbunching for terahertz radiation, microbunching instability and many others. This paper considers the fundamental mechanism that drives intense current modulations in dispersive regions, beyond the common explanation of nonlinear and higher-order effects. Under certain conditions, neighboring electron trajectories merge to form caustics, and often result in characteristic current spikes. Caustic lines and surfaces are regions of maximum electron density, and are witnessed in accelerator physics as folds in phase space of accelerated bunches. We identify the caustic phenomenon resulting in cusplike current profiles and derive an expression which describes the conditions needed for particle-bunch caustic formation in dispersive regions. The caustic expression not only reveals the conditions necessary for caustics to form but also where in longitudinal space the caustics will form. Particle-tracking simulations are used to verify these findings. We discuss the broader implications of this work including how to utilize the caustic expression for manipulation of the longitudinal phase space to achieve a desired current profile shape.
Highlights
Caustics are a common occurrence in optics, describing the bright lines seen in a well-lit coffee cup, or the dancing networks of light at the bottom of swimming pools on a sunny day [1,2]
We have identified the current spike formations often seen in Free Electron Lasers (FELs) as caustic formations of electron trajectories
These caustics are witnessed in a wide range of accelerator applications, and the methods presented here are adapted to such scenarios
Summary
Caustics are a common occurrence in optics, describing the bright lines seen in a well-lit coffee cup, or the dancing networks of light at the bottom of swimming pools on a sunny day [1,2]. High-current portions of the bunch can produce intense coherent synchrotron radiation (CSR) and result in CSR-induced emittance growth [10,11] This current profile is reminiscent of single-spike profiles found at some FEL facilities [22,23,24] or ramped profiles produced using a superconducing radio frequency linear accelerator operating at two frequencies [25]. VI discusses some of the broader implications of the present work, including how we may be able to utilize this knowledge of caustics to avoid current horn formation in strong bunch compression
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