Injection and capture simulations for a high intensity proton synchrotron

The injection and capture processes in a high intensity, rapid cycling, proton synchrotron are simulated by numerical integration. The equations of motion suitable for rapid numerical simulation are derived so as to maintain symplecticity and second-order accuracy. By careful bookkeeping, the authors can, for each particle that is lost, determine its initial phase space coordinates. They use this information as a guide for different injection schemes and rf voltage programming, so that a minimum of particle losses and dilution are attained. A fairly accurate estimate of the space charge fields is required, as they influence considerably the particle distribution and reduce the capture efficiency. Since the beam is represented by a relatively coarse ensemble of macro particles, the authors study several methods of reducing the statistical fluctuations while retaining the fine structure (high intensity modulations) of the beam distribution. A pre-smoothing of the data is accomplished by the cloud-in-cell method. The program is checked by making sure that it gives correct answers in the absence of space charge, and that it reproduces the negative mass instability properly. Results of simulations for stationary distributions are compared to their analytical predictions. The capture efficiency for the rapid-cycling synchrotron is analyzed with respectmore » to variations in the injected beam energy spread, bunch length, and rf programming.« less