Measurement of the longitudinal asymmetry of a charged particle bunch from the coherent synchrotron or transition radiation spectrum

The shapes of submillimeter long electron bunches at the Cornell linear accelerator have been determined by measuring the coherent far-ir synchrotron and transition radiation spectrum produced by the charge distribution. With the aid of a Kramers-Kronig analysis of the spectral data, we show that the longitudinal bunch shape including the asymmetry can be accurately determined.