Simulation of the electron cloud in the Fermilab Main Injector

We present results from a precision simulation of the electron cloud (EC) problem in the Fermilab Main Injector using the code VORPAL. This is a fully 3d and self consistent treatment of the EC. Both distributions of electrons in 6D phase-space and EM field maps have been generated. Various configurations of the magnetic fields found around the machine have been studied. Plasma waves associated to the fluctuation density of the cloud have been analyzed. Our results have been successfully benchmarked against the POSINST code for the 2D electrostatic case. The response of a Retarding Field Analyzer (RFA) to the EC has been simulated as well as the more challenging microwave absorption experiment. While numerically accurate predictions can be made for a given secondary emission yield (SEY) and initial conditions, the large uncertainties in this SEY and in the spatial distribution of the EC prior to the exponential growth of the EC do make ab-initio prediction difficult. Note also that the RFA response is also uncertain due to the collection efficiency in unknown stray magnetic fields. Nonetheless, our simulations do provide guidance to the experimental program. Moreover, for a reasonable set of initial condition, this calculation shows that no dramatic, non-linear,more » increase of the EC density will occur when the bunch charges increases by a factor of three. Finally, electric field maps or parametric functions are being provided to the Synergia tracking code such that instabilities due to the EC can be simulated over much longer periods of time.« less