abstract
- © 2022, The Author(s), under exclusive licence to Springer Nature B.V.The aim of this paper is to propose a quasi-invariant technique suitable for describing the transverse dynamics of electrons in a synchrotron and to exhibit that the methodology allows the emergence of resonances in phase space. The proposed technique is implemented by using symbolic computation software, which provides sets of coupled differential equations for functions participating in the nonlinear dynamics, numerically solved with periodic boundary conditions. This approach allows the construction of an approximate invariant in a vicinity of the phase space origin. That portion of phase space is used for holding a stable beam of charge particles in synchrotrons. The submitted approach capability for describing the phase space is tested by comparing numerical results obtained with this technique against tracking simulations performed with available software. Finally, the possibility of applying this technique to control resonances in the optimization of the fourth-generation synchrotron light sources magnetic lattices is discussed.