Saw-tooth instability studies at the Stanford Linear Collider damping rings

Saw-tooth instability occurs during high current operation in the Stanford Linear Collider (SLC) damping rings. This instability is single bunch, and it can be cast as a longitudinal microwave instability. It is caused by the beam interaction with short range wakefields in the ring vacuum chamber. The saw-tooth instability manifests itself in the periodic blow-up in quadruple or higher moments in the longitudinal beam distribution. Most of the instability studies have been experimental. Since the measurements of coherent particle motion within a short ultrarelativistic beam are largely unconventional the authors had to develop some original diagnostics. These includes, for example, the down-conversion of the high frequency (∼10 GHz) broad-band beam position monitor (BPM) signals. The authors have also employed a state-of-the-art Hamamatsu streak camera that is capable of resolving the longitudinal beam distribution with sub-picosecond accuracy. As a result of the streak camera experiments the authors have quantitatively described the phase space of unstable bunches. The authors have found the radial structure of the instability mode and established that it only displaces a few percent of the beam particles. In another series of experiments the authors have correlated the instability signals from the beams before the extraction from the damping rings with their trajectories in the linac downstream. This showed that the instability results in a significant transverse beam jitter in the linac which compromises the damping ring performance as an injector. In addition, the authors have studied the instability behavior under the broad range of stored beam parameters using both passive observation and driven excitation. These measurements revealed unexpected beam behavior significantly above the instability threshold. Finally, the authors performed several low current experiments to estimate the damping ring vacuum chamber impedance