Determination of bunch asymmetry from coherent radiation in the frequency domain

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Abstract
The coherent far infrared radiation induced from relativistic electron bunches of millimeter and submillimeter length provides a novel way to characterize the bunch shape, and we review this approach here. Although only the intensity of the coherent spectrum is measured, it is measured over the entire frequency range. Because of the completeness of this spectral measurement, it is possible to extract both the amplitude and the phase information of the radiating source by applying a Kramers‐Kronig relation to the spectral form factor to find the minimal phase. The bunch shape is determined from the complete Fourier transform. One potential problem is the uniqueness of the phase. For all reasonably shaped bunches we have shown that the actual phase is well represented by the minimal phase obtained from the Kramers‐Kronig analysis, hence the method can be used to identify the bunch asymmetry. This technique has been used to analyze the shapes of the submillimeter‐long electron bunches at the Cornell linear accelerator.

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