Instability Growth Rate Calculations for High Energy Storage Rings

Tolerances in the manufacture of rf cavities for high energy electron-positron storage rings lead to a statistical distribution of higher mode resonant frequencies. This distribution and its associated fluctuations are considered in calculations of the growth rate of instabilities. It is found that in some cases the fluctuations can lead to large growth rates and must be accounted for when designing higher mode damping probes. Calculations for the Cornell 50 GeV electron-positron storage ring are used as illustrations.