Dynamical properties of a model for synchro-betatron coupling

The long term stability of betatron motion in presence of multipolar nonlinearities has been extensively investigated for high energy accelerators and the Henon maps has been proposed as a model. In high intensity accelerators the non linear effects due to space charge and synchro-betatron coupling are relevant. We propose a simple model to investigate the coupling between longitudinal and horizontal motion due to chromaticity. The model consists in a standard Chirikov map coupled to a Henon map. Diffusion of orbits is observed and the structure of resonances is inspected by the frequency analysis.