Frequency-Domain Picture

We start with the ‘Schottky’ signals induced by a beam coasting in the storage ring: The current, detected by a longitudinal (sum) pickup, due to a single particle going around at constant revolution frequency can be represented as a sum of a short pulse at each traversal which can be Fourier analysed into harmonics of the revolution frequency ω rev =2πf rev . The single turn self-effect is evaluated as the sum of the self-effects occurring at each revolution harmonic contained in the system frequency band. In addition to the self-effect (also called coherent effect) random and unwanted effects are explained which are caused by neighboring particles as well as by white noise from preamplifiers (the latter 2 are called incoherent effects).