Improving beam stability in particle accelerator models by using Hamiltonian control

We derive a Hamiltonian control theory which can be applied to a 4D symplectic map that models a ring particle accelerator composed of elements with sextupole nonlinearity. The controlled system is designed to exhibit a more regular orbital behavior than the uncontrolled one. Using the Smaller Alignement Index (SALI) chaos indicator, we are able to show that the controlled system has a dynamical aperture up to 1.7 times larger than the original mode