Longitudinal beam-transfer-function measurements at the SLC damping rings

A longitudinal single-bunch instability in the damping rings at the Stanford Linear Collider (SLC) is thought to contribute to pulse-to-pulse orbit variations in downstream accelerator sections. To better understand this instability, we measured the beam phase and bunch length under harmonic modulations of the RF phase and RF voltage. For small phase-modulations the measured response can be explained by interaction of the beam with the cavity fundamental mode. For larger excitations, we observed bifurcation and hysteresis effects. The response to an RF voltage modulation revealed two peaks near the quadrupole-mode frequency, one of which appears to be related to the longitudinal instability. In this paper we present the experimental results