abstract
- Fourth-generation synchrotron light sources generate highly brilliant and coherent electromagnetic radiation, valuable in multiple scientific areas. The enhancement of these properties has relied mainly on the use of multi-bend achromat (MBA) cells. Controlling the complex electron dynamics on these magnetic structures is a complicated task. An analytical approach based on polynomial quasi-invariants of motion is introduced to adjust the linear model of a synchrotron light source, attaining a suitable set of linear parameters. Building on a previously developed theory, this work introduces the statistically based concept of the chromatic index. This index provides a quantitative measure of the impact that resonances have on electron dynamics in a fourth-generation synchrotron model. This is done without particle tracking calculations. In particular, the distorted chromatic index is defined incorporating the effect of chromatic sextupoles on electron dynamics. Its minimization proves to be useful in obtaining a suitable set of linear parameters. It is noticeable that the phase advance relation commonly required in accelerator design is preserved without imposing them within the proposed protocol. Nonlinear electron dynamics can be effectively and computationally inexpensively optimized in subsequent stages by using the linear parameters derived from minimizing the distorted chromatic index. The formalism was tested on fourth-generation synchrotron models, with emittances of 81 and 79 pm rad, yielding maximum horizontal stable amplitudes close to 5 mm, for momentum deviations between ¿3% and 3%. The results show that the formalism could be useful for the design of modern synchrotrons. © 2025 The Authors