  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. 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.
