Simulation of the ``little a'' Neutron Beta Decay Experiment at the SNS

We present the GEANT4 Monte Carlo simulation of an experimental apparatus being developed to measure the electron-antineutrino correlation in the free neutron beta decay (``little a'') at the SNS. The proposed method relies on the measurement of the proton time-of-flight distribution using a pair of large area Silicon detectors. The design calls for systematic uncertainties of a few parts in a thousand. We address the practical issues related to a MC simulation of $\simeq 10^9$ events in the 4$\pi$ hermetic magnetic spectrometer. We discuss modeling the required precision of the electromagnetic field maps, p-e coincidence trigger efficiencies, TOF timing spreads due to neutron beam size and position, charged particle detector energy thresholds and backscattering processes.