Locally Controlled Coherence in the Longitudinal Dynamics of Electron Bunches in Particle Accelerators

The possibility to generate and control coherent states for a charged particle bunch in a circular accelerating machine in the presence of radiation damping and quantum excitation is investigated in the framework of the Thermal Wave Model. It is proven that in correspondence of arbitrary time-variations of a radio-frequency (RF) strength, a Schroedinger-like equation predicts the h a l equilibrium state, toward which the system spontaneously goes, where a sort of mesoscopical coherence is reached. This state corresponds to an example of the Glauber-Klauder-Sudarshan (GKS) coherent states widely considered in quantum optics and optical fibers. In addition, it is shown that for suitable time-varying RF strength, coherent states are possible in each time (locally controlled coherence) during the evolution toward the above asymptotic equilibrium, and the possibility that allows for carrying these analytical predictions in particle accelerators out is discussed