Vlasov Theory of Signal Suppression for Bunched Beams Interacting with a Stochastic Cooling Feedback Loop

We develop a self-consistent Vlasov theoretic description of the dynamic distortion of incoherent Schottky signals from a bunched beam undergoing stochastic cooling, arising from beam feedback. In the situation of non-overlapping synchrotron bands, explicit expressions for the signal suppression factors are derived and evaluated numerically for a prototype high-energy storage ring.