Influence of chaos on resonance crossings

We undertake a study of particle dynamics in a model fixed-field alternating-gradient (FFAG) synchrotron in which space-charge plays a central role. The space-charge force corresponds to a Gaussian charge distribution in both transverse dimensions. The betatron-tune is linearly ramped through resonance. This ramping alone can cause particles to enter orbits that have chaotic motion. We found that space-charge can lead to spreading of the available tunes which can either increase or decrease the effects of resonance. By applying recently developed techniques to measure complexity in the orbital dynamics, we also determine whether chaoticity can arise in particle trajectories and subsequently influence resonance crossings. Furthermore, we can see that the chaoticity changes drastically in the area around a resonance crossing.