Fokker-Planck solutions for action diffusion in a noisy symplectic map

We investigate the statistical properties of symplectic maps with noise, describing a FODO cell with a sextupole and current ripples or misalignments in the magnets. Up to some distance from the dynamic aperture, the normal form associated to the map allows to compute analytically the diffusion coefficient due to a stochastic perturbation. The action diffusion is examined and very good agreement between the solutions of the Fokker-Planck (F.P.) equation and the simulations is obtained, for the Henon and SPS maps with a white noise. The corrections appearing for a correlated noise are discussed.