Multi-objective optimization of longitudinal injection based on a multi-frequency RF system for fourth-generation storage ring-based light sources

In the fourth-generation storage ring light sources (4GLSs), associated with the extremely strong nonlinearities inherent in the multi-bend achromat design, the dynamic acceptance is usually small and it is difficult to implement traditional off-axis local-bump injection. To release the requirement on dynamic acceptance, on-axis longitudinal injection schemes have been explored. In this paper, we present a multi-objective optimization of longitudinal injection with a multi-frequency RF system, based on the parameters of the Southern Advanced Photon Source, a 4GLS proposed in China. We show that by treating the optimal bunch lengthening condition as an optimizing objective rather than a condition that must be satisfied, a plethora of feasible candidate solutions can be found, showing different trade-offs among multi-objectives. From these candidate solutions, one can find an optimal RF parameter setting that is most adapted to a specific 4GLS physics design and the available technical level of injection kicker. Especially, it would be feasible to realize longitudinal injection within a static bucket enabled by a double-frequency RF system, suggesting an attractive longitudinal injection option for 4GLSs.