Electron cloud wakefields in bunch trains

Electron cloud is a concern for many modern and future accelerator facilities. There are a number of undesired effects attributed to the presence of electron clouds. Among them are coherent instabilities, emittance growth, cryogenic heat load, synchronous phase shift and pressure rise. In long bunch trains one can observe the emittance growth getting faster along the bunch train. The interaction between the beam and the electron cloud is a two-stream interaction. The prameters of the electron cloud wakefields depend on the beam intensity, beam centroid perturbations, and on the electron density and perturbations. If the electron cloud forgets the bunch centroid perturbation very fast, the buildup itself, via growing density, becomes a way of coupling between the bunches. In the present paper we address how the bunch perturbation shape affects the multi-bunch wakefields under the conditions similar to the CERN LHC and SPS. We study the interplay between the single-bunch and multi-bunch electron cloud wakefields. The effect of the dipole magnetic field on the multi-bunch wakefields is studied.