Observation of a short bunch train longitudinal instability in the Fermilab Main Ring

Longitudinal coupled-bunch instability has been addressed in many papers. Most of them assume that all bunches are distributed equal-distant from each other. Here we present a different case where a train of 13 bunches is followed by a big gap of 1100 empty buckets in the Fermilab Main Ring. No residual wake fields are left after one revolution for a higher order mode of the RF cavity with Q in the few hundreds. The head bunch of the train cannot feel the wake field left by the previous turn, and classic closed loop instability is not possible, though destructive coherent oscillations are observed in later bunches. However, it has been observed that the beam can still be unstable if the beam intensity is high enough (e.g. 1E10 per bunch). In this paper we present some experimental observations along with computer simulation results. They agree with each other quite well. A feedback loop is possible to eliminate these coherent oscillations