Dipole instability of a circulating beam due to the ion cloud in an electron cooling system

We consider the dipole instability of the circulating beam in a storage ring in presence of a cooling electron beam and an “ion cloud” captured in the potential well of the electron beam. The coherent interaction between the centers of gravity of three species (circulating beam, cooling electrons and accumulated ions) is described by a four-dimensional transfer matrix with elements depending on frequency. The interaction becomes dangerous when the frequency of the dipole oscillations for the circulating beam coincides with the coherent frequency of the ion cloud. The theory is applied to the planned antiproton storage ring HESR (High Energy Storage Ring), which is part of the GSI future project. Calculations show that in the HESR, comparatively small ion traces (with a neutralization factor 0.2%) can increase the instability increment by 1–2 orders of magnitude compared with the case without ions.