Studies of longitudinal single bunch stability

The goal of this MD was to study a single bunch longitudinal instability observed during the acceleration ramp in the LHC in 2010 for bunches with nominal intensity and small injected longitudinal emittance. During this MD there were two fills, the first without acceleration and the second with acceleration. In the first each ring was filled with 8 high intensity bunches with small longitudinal emittance. During the second 8 high intensity bunches were injected into each ring with longitudinal emittances varying from 0.9 eVs to 0.3 eVs. Two longitudinal instability modes (dipole and quadrupole) were observed in different parts of the cycle with both beams. Measurements of phase and bunch length oscillations, as well as data extracted from bunch profile acquisitions during the cycle, are presented in this Note together with an analysis of the growth rate dependence on bunch emittances and intensity.