Longitudinal Motion of the Beam in the Fermilab Booster

When the Fermilab Booster Accelerator is operated at or above 1.5 × 1012 protons per pulse (extraction current about 155 mA) large amplitude coupled bunch longitudinal dipole oscillations occur between transition and extraction times. The oscillations do not contribute to beam loss in the booster but, because the beam is transferred synchronously into preexisting buckets in the Main Ring, the oscillations contribute to a deterioration of beam quality in the main ring. Two mode numbers have been established for the instabilities and the primary source frequencies have been isolated, although the offending objects have not. Operation of one of the eighteen accelerating cavities at a harmonic number one unit lower than the operating value (83 instead of 84) effectively damps the motion by the introduction bunch to bunch synchrotron tune spread.