Simulation study of the horizontal head-tail instability observed at injection of the CERN Proton Synchrotron

For many years, a horizontal head-tail instability has been observed at the CERN Proton Synchrotron during the long 1.2 s injection flat-bottom. This slow instability has been damped using linear coupling only, i.e. with neither octupoles nor feedbacks. Using the nominal machine and beam parameters for LHC, the sixth head-tail mode number is usually observed. Several other modes were also observed in the past by tuning the chromaticity, and these observations were found to be in good agreement with Sacherer's formula. The purpose of this paper is to present the results of assessing the effect of chromaticity and linear coupling on this slow head-tail instability using the HEADTAIL simulation code, and to compare these simulations with both measurements performed over the last few years, and theoretical calculations.