A preliminary comparative study of the electron-cloud effect for the PSR, ISIS, and the ESS

We present preliminary electron-cloud simulation results for the Proton Storage Ring (PSR) at LANL, ISIS at RAL, and the European Spallation Source (ESS). For each storage ring, we simulate the build-up and dissipation of the electron cloud (EC) in a representative field-free section of the vacuum chamber. For all three cases, we choose the same residual gas temperature, secondary emission yield (SEY), and secondary emission spectrum. Other variables such as proton loss rate, bunch profile, intensity and energy, residual gas pressure and chamber geometry, are set at the corresponding values for each machine. Under these assumptions, we conclude that, of the three machines, the PSR is the most severely affected by the electron cloud effect (ECE), followed by the ESS, with ISIS a distant third. We illustrate a strong sensitivity of the ECE to the longitudinal bunch profile by choosing two different shapes for the case of the PSR, and a weak sensitivity to residual gas pressure. This preliminary study does not address the ECE in other regions of the machine, nor the beam instability that might arise from the EC.