Sequential Bunch Extractions in the los Alamos PSR

In the short-bunch, high-frequency operating mode of the future Proton Storage Ring (PSR) at LAMPF, the extraction scheme will take out one bunch at a time. Because the ring only stores six bunches at most and because the bunching system is heavily beam loaded, each extraction can cause a substantial change in the average beam current and hence affects significantly the total bunching voltage as well as the phase synchronization between those remaining bunches and the voltage waveform. A time-dependent cavity-tuning scheme has been considered to retain the proper bunching voltage and phase relation. This work examines the stability of the phase synchronization in the transient stage of extraction and cavity tuning. An equivalent circuit model is adopted, and the coupled nonlinear differential equations are solved numerically. We find that the relative phase will remain stable and that the voltage variation is tolerable under the PSR proposed operating conditions. A comparison between the numerical and analytical solutions confirms the numerical results.