Mode-zero Robinson instability in the presence of passive superconducting harmonic cavities

A higher harmonic cavity (HHC) is popularly employed in synchrotron light storage rings to enhance the machine performance, which requires its fundamental mode resonant frequency to be tuned above the radio-frequency harmonic. However, this detuning is likely to cause Robinson instability. In this paper, we focus on a mode-zero Robinson instability driven by the fundamental mode of a passive superconducting harmonic cavity (PSHC). This instability oscillates slightly below the detuning frequency of PSHC and was recently observed in tracking simulations or experiments for several synchrotron light sources, but the underlying mechanisms have not been well understood. To investigate this instability, we modify the conventional Robinson instability equation with the inclusion of the damping effect. By solving directly this modified equation combined with performing macroparticle tracking simulation, it is found that this instability is largely dependent on the momentum compaction factor, the Q value and detuning of PSHC, and even the radiation damping time. Most importantly, this instability can be significantly enhanced by a higher Q of PSHC and a lower radiation damping time, which is completely contrary to the conventional Robinson instability.