Suppression of longitudinal coupled-bunch instabilities with RF feedback systems in CEPC main ring

Background Circular electron positron collider (CEPC) is a 100-km electron positron collider proposed by IHEP. The longitudinal coupled-bunch instability (LCBI) of CEPC main ring operating to study the Z particle (Z machine) may be a limiting factor of CEPC and needs to be considered seriously.Purpose The purposes of this paper are to calculate the LCBI caused by the fundamental mode of superconducting RF cavities in CEPC main ring, which is the most critical impedance, and to complete the design of the RF feedback systems suitable for CEPC, whose specifications can suppress the LCBI to a manageable level.Methods The LCBI growth rate in the CEPC main ring is calculated in the frequency domain. Two kinds of RF feedback, i.e., direct feedback and one-turn delay feedback, are simulated with the program to suppress the LCBI. And according to the suppression effect of LCBI growth rate after adding RF feedback, the required design parameters are given.Results Two operation conditions of Z machine have severe LCBI without suppression, and dozens of longitudinal modes are unstable. Only the direct RF feedback is needed to suppress LCBI in the case of Z-30 MW, while both the direct RF feedback with maximum gain and one-turn feedback are needed in the case of Z-50 MW. The LCBI growth rates can be reduced to the order of half frequency of the synchronous oscillation.Conclusion The LCBI of CEPC Z machine has been studied. Selecting appropriate feedback RF feedback can reduce the LCBI to an acceptable value that bunch by bunch feedback can suppress.