Simulation study of electron cloud induced instabilities and emittance growth for the CERN Large Hadron Collider proton beam

The electron cloud may cause transverse single-bunch instabilities of proton beams such as those in the Large Hadron Collider (LHC) and the CERN Super Proton Synchrotron (SPS). We simulate these instabilities and the consequent emittance growth with the code HEADTAIL, which models the turn-by-turn interaction between the cloud and the beam. Recently some new features were added to the code, in particular, electric conducting boundary conditions at the chamber wall, transverse feedback, and variable beta functions. The sensitivity to several numerical parameters has been studied by varying the number of interaction points between the bunch and the cloud, the phase advance between them, and the number of macroparticles used to represent the protons and the electrons. We present simulation results for both LHC at injection and SPS with LHC-type beam, for different electron-cloud density levels, chromaticities, and bunch intensities. Two regimes with qualitatively different emittance growth are observed: above the threshold of the transverse mode-coupling (TMC) type of instability there is a rapid blowup of the beam, while below this threshold a slow, long-term, emittance growth remains. The rise time of the TMC instability caused by the electron cloud is compared with results obtained using an equivalent broadband resonator impedance model, demonstrating reasonable agreement.