Effects of phase noise in heavily beam loaded storage rings

Synchrotron oscillations in a storage ring can be driven by noise in the storage ring RF system. For phase noise in the master oscillator, which falls off exponentially with frequency, we show that beam oscillations can become significant in cases of moderate to heavy beam loading. We derive the transfer function for generator phase to beam phase and calculate the beam motion using the measured phase noise in several master oscillator sources. This is compared with measurements of the beam noise made at the Advanced Light Source, a 1.5-1.9 GeV electron storage ring.