Synchrotron tune shift due to the fundamental mode of the RF cavities

Abstract

A quadratic increase of the synchrotron tune with beam current has been observed during the operation of the Beijing Electron Positron Collider Upgrade (BEPCII). This observation is unexpected considering the conventional theory of the impedance-driven collective effects that the tune shift varies linearly with the beam current. To explain this phenomenon, a simple physical model based on coupled bunch instability theory is developed. The coherent synchrotron frequency is solved directly with a clean form without taking the perturbative approach which is valid for ΔΩ<<ωs. With the model developed, the source of the quadratic increase of the synchrotron tune is found and identified as being due to the interaction with the fundamental mode of the RF cavities. On the other hand, our analysis also offers a new beam-based method to characterize the R/Q and the detuning rate of the fundamental mode of the RF cavity, which can be complementary to laboratory bench measurements.