Wake-field and fast head-tail instability caused by an electron cloud

In positron and proton storage rings, electrons produced by photoemission, ionization, and secondary emission accumulate in the vacuum chamber during multibunch operation with close spacing. A positron or proton bunch passing through this “electron cloud” experiences a force similar to a short-range wake field. This effective wake field can cause a transverse-mode-coupling instability, if the electron-cloud density exceeds a threshold value. In this report, we compute the electron-cloud induced wake in a region without external magnetic field both analytically and via computer simulation, for parameters representing the low-energy positron ring of KEKB and the LHC proton beam in the CERN SPS. We study the linearity and time dependence of the wake function and its variation with the size of the electron cloud. Using a broadband resonator model for the electron-cloud wake field, we then evaluate theoretical expressions for the transverse-mode-coupling instability based on the linearized Vlasov equation, and for the instability threshold of fast transverse blow up including its dependence on chromaticity.