The Fast Vertical Single-Bunch Instability after Injection into the CERN Super Proton Synchrotron

Since 2003, high-intensity single-bunch proton beams with low longitudinal emittance have been affected by heavy losses after less than one synchrotron period after injection. The effects of the resonance frequency of the responsible impedance, longitudinal emittance and chromaticity on the intensity threshold were already discussed in detail in 2004, comparing analytical predictions with simulation results. In this paper the evolution of the instability between injection and the time of beam loss is our main concern. Measurements are compared with HEADTAIL simulations. A travellingwave pattern propagating along the bunch, which is the signature of a Beam Break-Up or Transverse Mode Coupling Instability (TMCI), is clearly identified. The oscillating frequency, near ~1 GHz, is in good agreement with the usual broad-band impedance model deduced from beam-based measurements like the head-tail growth rate vs. chromaticity.