Emittance growth caused by phase modulation in bunched electron beam cooling

The demand for electron coolers operating at much higher energies than previously achieved necessitates the use of radio-frequency (RF) fields for electron acceleration resulting in the bunched electron beams. Differences in the time structure of ion and electron bunches and variations in their relative timing significantly affect the cooling process. Experiments on ion beam cooling with a short electron bunch have been carried out in the CSRm storage ring at IMP (Lanzhou). Longitudinal painting by the electron bunch phase modulation is found leading to a significant ion beam loss. We show that the space charge field variations of the bunched electron beam play a major role in the ion beam emittance growth while cooling. In this paper, we study the dependency of the ion beam emittance growth on the electron beam parameters and present results of numerical simulation which support experimental observations.