Coupling local and global rf feedback loops for macroparticle tracking simulations

Radio frequency (rf) control loops are vital components for the optimal operation of rf systems in synchrotron particle accelerators. Modeling these systems in macroparticle tracking simulations provides improved understanding of the complex interaction between the control loops, the beam-induced voltages in the rf cavities, and the circulating beam. This paper details an implementation of local and global rf control loops in the beam longitudinal dynamics (on) simulation suite, which allow for the coupling of the two systems in a macroparticle tracking code for the first time. First, benchmarks of the local control loops in the CERN Super Proton Synchrotron (SPS) and Large Hadron Collider (LHC) are given. The implementation coupling the local and global loops is then tested in the SPS with momentum shifts at constant magnetic field and through the damping of phase offsets at injection into the LHC. Both test cases show the expected behavior and validate the model in on. Finally, the SPS simulation model, which now is able to combine beam-induced voltages, global control loops and local ones, is benchmarked against measurements at the bunch-to-bucket transfer into the real accelerator. The simulations, using the coupled implementation of the loops, are able to reproduce bunch-by-bunch beam parameters at flat bottom as well as uncaptured beam generated at injection.