Decoherence form space-charge

The theory of the Laslett direct space-charge effect is well established since many years. Nevertheless, the fact that transverse coherent tune shifts and decoherence of transverse oscillations have been attributed to direct space-charge, by lack of other explanations, is the origin of a lasting controversy. The observed decoherence in the CERN SPS and the expected decoherence in the CERN LHC have such profound consequences for the construction of transverse feedback systems that lifting the controversy has an interest that is more than purely academic. A collection of beam observations is presented concerning tune shifts and decoherence where the space-charge effect is eminent. A physical model is proposed from which tune shifts and decoherence can easily be derived. The computation can not only be applied to machines where the effect is modest but not negligible, as the SPS and the LHC, but also to the CERN PS and PSB where the effect is massive.