ABSTRACT
MBA cell-based synchrotron light sources have enabled an unprecedented increase in beam coherence and brightness, greatly benefiting the scientific disciplines that rely on X-ray techniques. However, controlling the electron dynamics is a theoretical and technological challenge, due to the large number of parameters to adjust and constraints to satisfy when designing modern synchrotrons. Having versatile tools for the description and manipulation of electron dynamics could favor the design of these accelerators and lead to progress on several fronts in the understanding of matter. In this paper, a formalism based on the use of nonlinear geometric surfaces represented by polynomial quasi-invariants, to analyze and optimize the dynamic aperture of electrons in MBA storage rings, is introduced. The formalism considers on- and off-momentum particle dynamics. Within the optimization scheme, different objective functions defined in terms of the nonlinear surfaces, which are minimized using genetic algorithm methods, are proposed. A remarkable horizontal dynamic aperture exceeding 19 mm is obtained for the design particle of a synchrotron model with 86 pm [Formula: see text] rad emittance along with a dynamic aperture above 5 mm for momentum deviations of ± 3[Formula: see text]. According to the results presented, this formalism could be greatly useful for manipulating the dynamical properties of electrons in synchrotrons light sources close to the diffraction limit.