Simulation of the Electron Flux Into the Main Injector Electron Cloud Retarding Field Analyzer Using Vorpal

We present results from precision simulations of the electron cloud (EC) in the Fermilab Main Injector (MI), focusing on the dynamics of the EC close to the Retarding Field Analyzer (RFA) detectors. Our simulations are based on the Vorpal plasma simulation package. We find that the presence of a parasitic, weak (few Gauss) magnetic field significantly alters the spatial distribution of electrons in the cloud. The detected flux can easily change by factors of two depending on the location of the RFA. Moreover, the growth rate of the EC is also sensitive to such magnetic fields. Therefore, we suggest to (i) upgrade the RFA preamplifier to  10 MHz bandwidth such that the change in EC growth rate during a complete MI bunch train can be detected; (ii) install a small solenoid (of  25 Gauss maximum) to optionally switch off the EC, and thereby cleanly establish the presence of low energy electrons in the pipe; and (iii) design an RFA that can be inserted in a  2 kGauss field, such that an EC signal can be seen in the environment that matters, i.e., in the MI dipoles.