Resistive wall instability in rapid Cycling synchrotron of China spallation neutron source

China Spallation Neutron Source (CSNS) is a high intensity proton accelerator based facility, and its accelerator complex includes two main parts: an H- linac and a rapid cycling synchrotron (RCS). The RCS accumulates the 80 MeV proton beam, and accelerates it to 1.6 GeV, with a repetition rate of 25 Hz. The 1.6 GeV beam is fast extracted for striking the neutron target with average beam power of 100 kW. The collective effect caused by the coupling impedance is one of the serious issues which limit the highest beam power. The impedance estimation of RCS components showed that the resistive wall impedance and its instability are serious. Based on the estimated impedance, the resistive wall instability growth time is theoretically calculated. In order to confirm the analytical results of resistive wall instability, a simplified resistive wall wake field model is used to track the bunch oscillation, and the growth time of resistive wall instability is obtained. In this model, the continuous resistive wall wake field is expressed as an equivalent wake field of one point in the ring, and the long bunch is sliced into many slices longitudinally. By tracking the dynamics of the slices, transverse growth time is obtained. The simulation results with constant energy agree well with the analytical results. The studies of energy ramping process show that if the damping effect of the chromaticity is not considered, the growth time of resistive wall instability is faster than the period of an RCS cycle, and the damping effect of chromaticity will play a key role in suppressing the instability.