Theoretical elucidation of space charge effects on the coupled-bunch instability at the 3 GeV rapid cycling synchrotron at the Japan Proton Accelerator Research Complex

The Rapid Cycling Synchrotron (RCS), whose beam energy ranges from 400 MeV to 3 GeV and which is located in the Japan Proton Accelerator Research Complex, is a kicker-impedance dominant machine, which violates the impedance budget from a classical viewpoint. Contrary to conventional understanding, we have succeeded to accelerate a 1-MW equivalent beam. The machine has some interesting features: for instance, the beam tends to be unstable for the smaller transverse beam size, the beam is stabilized by increasing the peak current etc. Space charge effects play an important role in the beam instability at the RCS. In this study, a new theory has been developed to calculate the beam growth rate with the head-tail and coupled-bunch modes (m,mu) while taking space charge effects into account. The theory sufficiently explains the distinctive features of the beam instabilities at the RCS.