Electron-cloud simulation studies for the CERN-PS in the framework of the LHC Injectors Upgrade project

The present study aims to provide a consistent picture of the electron cloud effect in the CERN Proton Synchrotron (PS) and to investigate possible future limitations due to the requirements foreseen by the LHC Injectors Upgrade (LIU) project. It consists of a complete simulation survey of the electron cloud build-up in the different beam pipe sections of the ring depending on several controllable beam parameters and vacuum chamber surface properties, covering present and future operation parameters. As the combined function magnets of the accelerator constitute almost the $80\%$ in length of the ring, the implementation of a new feature for the simulation of any external magnetic field on the PyECLOUD code, made it possible to perform this study. All the results of the simulations are given as a function of the vacuum chamber surface properties in order to deduce them, both locally and globally, when compared with experimental data. In a first step, we characterize locally the maximum possible number of beam pipe sections attending to the most repeated combinations of vacuum chamber geometries and external magnetic fields present along the ring. Afterwards, integrating these results, we manage to characterize globally the ring (covering the $78.61\%$ of it) for three different beam production schemes. In particular, assuming a "global" secondary electron yield for the vacuum chamber inner surface of the accelerator around $\delta_{max}^{0}=1.6$, we obtained maximum stable phase shifts per turn due to the electron cloud effect smaller than $0.8^{\circ}$ for the current LHC25 beams and smaller than $0.9^{\circ}$ for the future high intensity LHC25 beams throughout the magnetic cycle; being smaller than $0.2^{\circ}$ for both the current and the future high intensity LHC50 beams. Besides, the BCMS beams have results slightly lower than the ones regarding the LHC25 beams as we take the maximum to characterize the ring, and as the intra-beam steady state is reached before the 48th bunch of the beam. Nevertheless, the electron cloud generated by the BCMS beams is less harmful than the one generated by the LHC25 beams, as the rise time of the electron cloud is bigger and the period without electron cloud in each turn is three times larger. Beyond the characterization of the beam pipe sections or of the whole ring for the different beam production schemes, it seems that the requirements foreseen by the LIU project for the PS are not going to represent a huge limitation in the performance of the machine. This is due to the fact that, as the bunches are not sufficiently short before, the multipacting effect is still going to be develop only after the last bunch splitting (6 ms before extraction to SPS) and to the fact that the number of electrons in the chamber and the energy loss per proton due to the electron cloud effect are quite similar for the current bunch intensities and the future high intensities within the main magnets (which represent almost the $80\%$ in length of the ring). Then, the conditions of exposure time or severity of the effect for the beams to be degraded may not take place; not even for the LHC25 beams, which is the beam production scheme that produces the most adverse electron clouds. Besides, a detailed analysis of the electron cloud build-up in the combined function magnet MU98, ordered by the LIU-PS Commission, is provided in order to support the design of new electron cloud local monitors to be installed there during the 2013-2014 long shut-down. Finally, we partially check the consistency of the simulations with experimental data and, as a result, a more accurate value of the local vacuum chamber surface properties is provided, obtaining a new value for the secondary emission yield in a drift space of $\delta_{max}^{0}=1.55$.