Estimation of collective instabilities in RHIC

We have estimated the broadband impedance in RHIC to be |Z/n|<1.2 Ω for frequencies above 100 MHz. The Z/n threshold is set for Au⁺⁷⁹ ions at transition with an estimated 10% growth in emittance for Z/n=1.5 Ω. We summarize the sources of broad and narrow band impedances in RHIC and investigate the multibunch instability limits throughout the machine cycle. The largest contribution to the broadband impedance comes from the abort and injection kickers. Since RHIC is designed to accelerate fully stripped ions from H⁺ up to Au⁺⁷⁹ we give results for both protons and gold ions; other ions should give results somewhere between these two extremes. All ion species are expected to be stable during storage. At lower energies damping systems and chromaticity corrections will limit any growth to acceptable levels during the short time it takes to inject and accelerate the beams