The interaction of a high-current O(100 µA), medium energy O(10 GeV) electron beam with a thick target O(1m) produces an overwhelming shower of standard model particles in addition to hypothetical light dark matter particles. While most of the radiation (gamma, electron/positron) is contained in the thick target, deep penetrating particles (muons, neutrinos, and light dark matter particles) propagate over a long distance, producing high-intensity secondary beams. Using sophisticated Monte Carlo simulations based on FLUKA and GEANT4, we explored the characteristics of secondary muons and neutrinos and (hypothetical) dark scalar particles produced by the interaction of the Jefferson Lab 11 GeV intense electron beam with the experimental Hall-A beam dump. Considering the possible beam energy upgrade, this study was repeated for a 22 GeV CEBAF beam.