An optical Hamiltonian experiment and the beam dynamics

The analogy between geometric optics and Hamiltonian mechanics is used to propose an experiment that simulates the beam propagation in a focusing magnetic lattice of a particle accelerator. A laser beam is reflected several times by a parabolic mirror and the resulting pattern is registered by a photo camera. This experiment allows to illustrate some aspects of nonlinear beam transport in presence of nonlinearities and stochastic perturbations. The experimental results are discussed and compared with computer simulations.