Transverse Mode-Coupling Instability in the CERN SPS: Comparing Moses Analytical Calculations and Headtail Simulations with experiments in the SPS

Since 2003, single bunches of protons with high intensity (1.2e11 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. Understanding the mechanisms underlying this instability is crucial to assess the feasibility of an anticipated upgrade of the SPS, which requires bunches of 4e11 protons. Analytical calculations from MOSES and macroparticle tracking simulations using HEADTAIL with an SPS transverse impedance modelled as a broadband resonator had already qualitatively and quantitatively agreed in predicting the intensity threshold of a fast instability. A sensitive frequency analysis of the HEADTAIL simulations output was performed using SUSSIX, and revealed the fine structure of the mode spectrum of the bunch coherent motion. A coupling between the azimuthal modes "-2"and "-3" was clearly observed to be the reason for this fast instability. The aim of this contribution is to compare the HEADTAIL simulations with dedicated measurements performed in the SPS in 2007.