Adiabatic manipulation of longitudinal beam distributions in the presence of energy damping and random perturbations

In recent years, non-linear beam dynamics has been promoted as a means to perform novel manipulations of hadron beams in circular accelerators. This is made possible because of the adiabatic trapping and transport phenomena in phase space for Hamiltonian systems. The extension of the non-linear beam manipulations to circular lepton accelerators has been recently considered, but a rigorous theoretical framework to extend adiabatic theory to stochastically perturbed Hamiltonian systems is still lacking. This project represents a first step in this direction, aiming at analysing the effect of energy damping and random perturbation on adiabatic manipulations. This goal is achieved by studying simple models relevant for beam dynamics, incorporating both analytical and numerical investigations.