Transverse decoherence and coherent spectra in long bunches with space charge

The transverse bunch spectrum and the transverse decoherence/recoherence following an initial bunch offset are important phenomena in synchrotrons and storage rings, and are widely used for beam and lattice measurements. Incoherent shifts of the particles betatron frequency and of the synchrotron frequency modify the transverse spectrum and the bunch decoherence. In this study we analyze the effects of transverse space charge and of the rf nonlinearity on the decoherence signals. The transverse bunch decoherence and the resulting coherent spectra are measured in the SIS18 synchrotron at GSI Darmstadt for different bunch parameters. The frequencies of the bunch head-tail modes provide a direct measure for the self-field space charge tune shift. Particle tracking simulations together with an analytical model are used to describe the modifications in the decoherence signals and in the coherent spectra due to space charge and the rf bucket nonlinearity.