Hamiltonian control used to improve the beam stability in particle accelerator models

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 Alignment 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 model.

► Enlargement of dynamical aperture of particle accelerator.
► Development of Hamiltonian control theory in mapping.
► Validation of the method by chaos indicator SALI.