Characterisation of Bunch-by-Bunch Tune Shift Effects in the CERN SPS

After the implementation of major upgrades as part of the LHC Injector Upgrade Project (LIU), the Super Proton Synchrotron (SPS) delivers high intensity bunch trains with 25 ns bunch spacing to the Large Hadron Collider (LHC) at CERN. These beams are exposed to several collective effects in the SPS, such as beam coupling impedance, space charge and electron cloud, leading to relatively large bunch-by-bunch coherent and incoherent tune shifts. Tune correction to the nominal values at injection is crucial to ensure beam stability and good beam transmission. During the beam commissioning of the SPS, measurements of the bunch-by-bunch coherent tune shifts have been conducted under different beam conditions, together with appropriate corrections of the average tunes at each injection. In this paper, we describe the methodology that has been developed to acquire bunch-by-bunch position data and to perform online computations of the coherent tune spectra of each bunch using refined Fourier transform analysis. The experimental data are compared to multiparticle tracking simulations using the SPS impedance model, in view of developing an accurate model for tune correction in the SPS.