Lawrence Berkeley National Laboratory

Characterization of single-bunch instabilities in the International Linear Collider (ILC) damping rings (DRs) has been indicated as a high-priority activity toward completion of an engineering design. In this paper we report on a first estimate of the current thresholds for the instability using numerical and analytical models of the wake potentials associated with the various machine components. The numerical models were derived (upon appropriate scaling) from designs of the corresponding components installed in existing machines. The current thresholds for instabilities were determined by numerical solution of the Vlasov equation for the longitudinal dynamics. For the DR baseline lattice as of Feb. 2007 we find the critical current for instability to be safely above the design specifications leaving room for further optimization of the choice of the momentum compaction.