Adiabatic theory for slowly varying Hamiltonian systems with applications to beam dynamics

In this work, we present two models in which adiabatic invariance theory can be applied to achieve peculiar effects in beam dynamics, exploiting the phase space separatrix crossing caused by the passage through specific resonances of a system. In particular, we present a 2-d model for the emittance transfer between the two coordinates in the transverse space: we give a theoretical explanation of the mechanism involved and we show how to predict the final emittance values. These results are confirmed by numerical simulation. On the other hand, we present numerical simulation for a 1-d model of a dipolar exciter whose frequency is slowly modulated close to a multiple of the accelerator tune which allow to capture beam particles in a number of stable islands.