Estimates of CSR Instability Thresholds for Various Storage Rings

We review the key predictions and conditions by several authors for the onset of longitudinal instabilities due to coherent synchrotron radiation (CSR), and evaluate them numerically for various storage rings, namely the KEKB High Energy Ring (HER) & Low Energy Ring (LER), SuperKEKB HER & LER, old and new designs of the SuperKEKB Damping Ring (DR), SuperB HER & LER, CLIC DR (2009 and 2010 design parameters), SLC DR, and ATF DR. We show that the theoretical uncertainty in the instability onset is at least at the level of 20-30% in bunch intensity. More importantly, we present some doubts about the general applicability for many of these storage rings of some commonly used formulae. To cast further light on these questions, an experiment at lower beam energy on the ATF Damping Ring is proposed.