Transverse mode coupling instability in the SPS: Headtail simulation and moses calculation

Since 2003, single bunches of protons with high intensity (~ 1.2 1011 protons) and low longitudinal emittance (~ 0.2 eVs) have been observed to suffer from heavy losses in less than one synchrotron period after injection at 26 GeV/c in the CERN Super Proton Synchrotron (SPS) when the vertical chromaticity is corrected (ξy ~ 0). Understanding the mechanisms underlying this instability is crucial to assess the feasibility of an anticipated upgrade of the SPS, which requires bunches of 4 1011 protons. Analytical calculations and particle tracking simulations had already agreed in predicting the intensity threshold of a fast instability. The aim of the present paper is to present a sensitive frequency analysis of the HEADTAIL simulations output using SUSSIX, which brought to light the fine structure of the mode spectrum of the bunch coherent motion. Coupling between the azimuthal modes “-2” and “-3” was clearly observed to be the reason for this fast instability.