Longitudinal RF capture simulation and BPM signal estimation

In this paper, the theoretical aspects behind longitudinal RF capture are reviewed and the capture process is simulated via a program based on this theory. Four kinds of cases with different initial distribution and capture curve are considered, i.e. uniform distribution with adiabatic capture, uniform distribution with non-adiabatic capture, Gaussian distribution with adiabatic capture and Gaussian distribution with non-adiabatic capture. The simulation results are compared each other and discussed, and Gaussian distribution with adiabatic capture is demonstrated having a higher capture efficiency and leading to a shorter bunch length. In addition, the BPM induced signal is simulated with high input impendence, i.e. $1M\Omega$, and low input impendence, i.e. $50\Omega$, respectively. Finally, the BPM signal of Heavy Ion Medical Machine (HIMM) is estimated and compared with measured one, and a good agreement is achieved.