A Simple Model for Multiturn Injection into A.G. Proton Synchrotrons

Analytical expressions are derived in order to compute the optimum injection parameters for betatron stacking into a chosen fraction of the total accelerator acceptance in the Q range N + 0.1 ?? Q ?? N + 0.9. The example of the CERN PS Booster (PSB) is worked out. The efficiency of the process is calculated using standard numerical integration algorithms with a Gaussian distribution of the incoming beam. Other types of distribution can also be dealt with. The results show that the installation of pulsed dipole and quadrupole supplies to obtain steering and focusing conditions which vary during the injection process will improve the injected current by only 3% in the case of the PSB. The measured performance of the PSB injection system is reported and compared with model prediction. Estimates of injected currents prove to be about 10% higher than the actual values. Some considerations on the influence of space-charge forces, which might explain this effect are presented.