Diffusive approach for non-linear beam dynamics in a circular accelerator

In the design phase and simulation of a circular accelerator, it is fundamental to have a proper understanding of the single-particle non-linear betatronic motion, and of how such dynamics interfere with beam quality. In this work we study stochastically-perturbed Hamiltonian systems using a diffusive framework, based on the Fokker-Plank equation. This study is then applied to the analysis of the non-linear betatronic motion and to the Dynamic Aperture problem. In particular, we lay down the basis for formulating an interpolation procedure for Nekhoroshev-like diffusive processes and we pro-pose an experimental procedure for measuring the local diffusive behaviour inside an accelerator. Dynamic Aperture is a key quantity for the long-term behaviour of an accelerator. However, the measure of this quantity via simulation presents serious computational difficulties. Because of that it is in our interest to develop a functional law which models the DA time-dependence