Optimizing Dynamic Aperture Studies with Active Learning

Dynamic aperture is an important concept for the study of non-linear beamdynamics in circular accelerators. It describes the extent of the phase-spaceregion where a particle's motion remains bounded over a given number of turns.Understanding the features of dynamic aperture is crucial for the design andoperation of such accelerators, as it provides insights into nonlinear effectsand the possibility of optimising beam lifetime. The standard approach tocalculate the dynamic aperture requires numerical simulations of severalinitial conditions densely distributed in phase space for a sufficient numberof turns to probe the time scale corresponding to machine operations. Thisprocess is very computationally intensive and practically outside the range oftoday's computers. In our study, we introduced a novel method to estimatedynamic aperture rapidly and accurately by utilising a Deep Neural Networkmodel. This model was trained with simulated tracking data from the CERN LargeHadron Collider and takes into account variations in accelerator parameterssuch as betatron tune, chromaticity, and the strength of the Landau octupoles.To enhance its performance, we integrate the model into an innovative ActiveLearning framework. This framework not only enables retraining and updating ofthe computed model, but also facilitates efficient data generation throughsmart sampling. Since chaotic motion cannot be predicted, traditional trackingsimulations are incorporated into the Active Learning framework to deal withthe chaotic nature of some initial conditions. The results demonstrate that theuse of the Active Learning framework allows faster scanning of theconfiguration parameters without compromising the accuracy of the dynamicaperture estimates.