Analysis of off-momentum nonlinear driving terms for enlarging off-momentum dynamic apertures

Abstract

Due to scattering, particles in a ring may have large momentum deviations, which will change their dynamics, potentially resulting in particle losses. Optimization of off-momentum nonlinear dynamics is, therefore, important for increasing beam lifetime. When analyzing off-momentum dynamics using the approach of resonance driving terms (RDTs), chromatic RDTs are usually used, which denote the deviations from on-momentum dynamics. In this paper, instead of using chromatic RDTs, we propose using off-momentum RDTs to analyze off-momentum dynamics, which is a more direct way. As in the case of on-momentum dynamics, the nonlinear driving terms for off-momentum particles include off-momentum RDTs and off-momentum amplitude-dependent tune shifts, which are calculated based on off-momentum linear optics. Similar to the analysis of on-momentum dynamics in our previous work [B. Wei et al., Phys. Rev. Accel. Beams 26, 084001 (2023)PRABCJ2469-988810.1103/PhysRevAccelBeams.26.084001], we study the fluctuation or variation of off-momentum RDTs along the longitudinal position, which is very effective for analyzing and optimizing off-momentum dynamic apertures (DAs). Similar results are obtained for the off-momentum case: (i) minimizing the element-by-element average of the RDTs is more effective than minimizing one-turn RDTs in enlarging DAs and (ii) minimizing the average of lower-order RDTs helps reduce higher-order RDTs.