Phase problem associated with the determination of the longitudinal shape of a charged particle bunch from its coherent far-ir spectrum

Abstract

The coherent far-infrared radiation induced from relativistic electron bunches of submillimeter length provides a way to characterize the bunch shape. Once the spectrum of the bunch form factor is measured, one can apply the Kramers-Kronig relations to the spectral form factor to find the minimal phase and then calculate the bunch shape from the complete Fourier transform. One potential problem is the uniqueness of the phase so determined since, in general, the phase shift associated with the Blaschke product must also be included. Here we examine a variety of possible asymmetric bunch shapes in order to identify any errors inherent in this approach.