Phase modulation of the bucket stops bunch oscillations at the Fermilab Tevatron

Bunches in the Tevatron are known to exhibit longitudinal oscillations which persist indefinitely. These oscillations are colloquially called ``dancing bunches.'' Although the dancing proton bunches do not cause single bunch emittance growth or beam loss at injection, they lead to bunch lengthening at collisions. In Tevatron operations, a longitudinal damper has been built which stops this dance and damps out coupled bunch modes. Recent theoretical work predicts that the dance can also be stopped by an appropriate change in the bunch distribution. This paper describes the Tevatron experiments which support this theory.