A code for the optimization of RF voltage waveform and longitudinal beam dynamics simulation in an RCS

In a Rapid Cycling Synchrotron (RCS), the dipole and quadrupole fields oscillate sinusoidally with a high repetition rate. High RF voltage is required to match the rapid change of the dipole field, and the choices of the RF voltage and synchronous phase waveform are important issues in the design of an RCS. The longitudinal beam dynamics simulation plays a key role in optimizing the RF voltage waveform. A code has been developed for both RF voltage waveform optimization and longitudinal beam dynamics simulation in an RCS. The code can be applied to both fundamental and dual harmonic RF systems, with dipole field oscillating as a sine wave or slightly deviated sine wave. In the simulation, the space charge effect is included, and the influence of the higher order modes of RF cavity on the beam can also be simulated. The code was applied to the RCS of China Spallation Neutron Source (CSNS), for optimizing the RF voltage waveform of dual harmonic RF system and beam dynamics simulation study.