“For many years, slow positron sources have found uses in diverse fields including medical physics, nuclear physics, biology, surface science, exotic atom research and space science. The purpose of this work is to design and optimize a reactor-based positron source at the Missouri University of Science and Technology Reactor (MSTR) beam port and quantify its intensity. Monte Carlo simulations using the MCNP6 code were used to model the positron production and moderation processes at the MSTR beam port. The thermal neutron flux at the beam port was determined experimentally and used in the source definition of the radiation transport simulations. The source comprised a Cd (n,γ) converter with a tungsten foil grid acting as both pair production target and positron moderator. This work provides rigorously calculated moderator efficiency tabulations for tungsten foil moderators over a relevant range of positron energies and incidence angles. To optimize the positron source for MSTR, slow positron extraction yields were simulated over a range of foil thickness, grid lengths, foil-to-foil pitch sizes, and extraction voltages. A 3 cm in length by 0.2 cm in pitch tungsten grid with 10 μm thick foils was found to maximize the rate of positron extraction in an extraction potential range of 100 to 300 V while longer and narrower grids are more efficient at higher extraction potentials. In its current core configuration, the MSTR would provide a comparatively weak source of positrons. However, several methods for increasing positron yield are suggested including: reconfiguring the core, increasing reactor power, and placing the positron source inside the beam tube”--Abstract, page iii