Studies of E-Cloud Build up for the FNAL Main Injector and for the LHC

We present a summary of recent simulation studies of the electron-cloud (EC) build-up for the FNAL MI and for the LHC. In the first case we pay particular attention to the dependence on bunch intensity Nb at injection energy assuming the nominal bunch spacing tb = 19 ns, and we focus on the dipole magnets and field-free regions. The saturated value of the average EC density shows a clear threshold in Nb beyond which the beam will be approximately neutralized on average. For the case of the LHC we limit our discussion to arc dipoles at collision energy, and bunch spacings tb = 25 ns or tb = 75 ns. The main variables exercised in this study are Nb and the peak value of the secondary emission yield (SEY) (delta)max. For tb = 25 ns we conclude that the EC power deposition is comfortably below the available cooling capacity of the cryogenic system if (delta)max is below ∼ 1.2 at nominal Nb. For tb = 75 ns, the EC power deposition is insignificant. As a byproduct of this exercise, we reach a detailed understanding of the significant role played by the backscattered secondary electrons. This article summarizes the results, an slightly extends the discussions, presented in Refs. 1 and 2