Study of Robinson instabilities with a higher-harmonic cavity for the HLS phase Ⅱ project

In the Phase Ⅱ Project at the Hefei Light Source, a fourth-harmonic "Landau" cavity will be operated in order to suppress the coupled-bunch instabilities and increase the beam lifetime of the Hefei storage ring. Instabilities limit the utility of the higher-harmonic cavity when the storage ring is operated with a small momentum compaction. Analytical modeling and simulations show that the instabilities result from Robinson mode coupling. In the analytic modeling, we operate an algorithm to consider the Robinson instabilities. To study the evolution of unstable behavior, simulations have been performed in which macroparticles are distributed among the buckets. Both the analytic modeling and simulations agree for passive operation of the harmonic cavity.