Experiments with undulator radiation of a single electron

A single electron circulating in a storage ring is a very peculiar object. Permanent emission of synchrotron radiation offers the possibility to observe the electron but also causes the “natural bunch length”. In the quasiclassical treatment uncertainties in the electron position arise from the averaging of the energy and position of the point-like electron over many turns in the storage ring. Nevertheless the question about the electron localization remains open. The radiation from a long undulator permits one to obtain “snapshots” of the electron longitudinal distribution. Experiments with a single electron on the VEPP-3 optical klystron are discussed.