A theoretical study of the electron-proton instability in a long proton pulse

The electron-proton instability of a long, intense, and partially neutralized proton bunch is studied by numerically solving the equations of motion for the line centroid of the proton beam and the line centroid of the trapped electrons. The formalism takes into account the effects of variable line densities and alternating-gradient (AG) focusing. Good qualitative agreement between the computational results and experimental observations was obtained when applying the theory to the Los Alamos Proton Storage Ring (PSR). Both the case of a clean extraction gap and the case with a few percent of protons in the extraction gap were studied. It is found that with only a few percent neutralization, the PSR beam can become unstable in both cases. The same equations and method were used to study the stability of the proton beam in the accumulator ring of the proposed LANSCE II spallation-neutron source. The results indicate that the e-p instability can also occur in the LANSCE II accumulator ring for only a few percent neutralization