Quadrupole stability in nonuniform fill patterns

Abstract

In previous publications, the effect of inhomogeneous beam loading of Landau cavities due to a nonuniform fill pattern in a storage ring has been studied with the aim of predicting the resulting longitudinal profiles of the bunches and their time offsets relative to the main rf [T. Olsson et al., Phys. Rev. Accel. Beams 21, 120701 (2018)PRABCJ2469-988810.1103/PhysRevAccelBeams.21.120701]. This work was extended to treat dipolar coupled-bunch modes driven by beam-excited higher-order modes in the rf cavities [F. J. Cullinan et al., Phys. Rev. Accel. Beams 23, 074402 (2020)PRABCJ2469-988810.1103/PhysRevAccelBeams.23.074402]. These coupled-bunch modes are of interest because they can become unstable, leading to an increase in the energy spread. The theory has now been extended once again to cover the case of coupled-bunch quadrupole modes where it is the lengths of the bunches that are oscillating, not their centroids. The theory is outlined and its predictions are thoroughly benchmarked against predictions from macroparticle tracking. Observations of the effects of nonuniform fill patterns on coupled-bunch quadrupole instabilities are made and interpreted. Results of measurements at the MAX IV 3 GeV ring, interpreted using theoretical calculations, are then presented to continue the investigation.