Abstract
The coherent synchrotron radiation of a bunch in a bunch compressor may lead to the microwave instability producing longitudinal modulation of the bunch. This modulation generates coherent radiation with the wave length small compared to the bunch length. It can also be a source of an undesirable emittance growth in the compressor. We derive and analyze the equation that describes linear evolution of the microwave modulation. Numerical solution of this equation for the LCLS bunch compressor reveals such an instability, in qualitative agreement with numerical simulations.
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