Positron annihilation spectroscopy provides a useful tool for the non-destructive study of subsurface microscopic defects. Variations in the electronic environment, from that of the bulk of the material, caused by defects introduce Coulombic forces which cause positrons to localize at the site of defects. This lifetime can vary from nanoseconds, if the positron forms a positronium atom before annihilation, to picoseconds if it is involved in pick-off annihilation. By bunching the incident positron beam, the time-resolution of a measurement can greatly be enhanced, allowing the observation of the variation in the lifetime of positrons that undergo pick-off annihilation, which occurs in metals and semiconductors. This is achieved by narrowing the resolution function of the detection system, which allows the measurement of shorter lifetime components. This improved timing resolution, over other techniques, comes at the expense of more complex electronics but is capable of performing measurements over a wide range of timing resolutions. Simulations have been preformed to optimize the design of a bunched slow positron beam to be implemented at North Carolina State University. For the proposed apparatus, the DC beam produced by the positron source at the 1-MW PULSTAR reactor, located at NCSU, must first be chopped into small pulses. This is accomplished by applying a time-varying potential to a re-moderator in the beam line. This waveform accelerates positrons emitted from a transmission moderator, which the incident beam is focused upon, into bunches. This time-varying field has been calculated and is capable of accelerating positrons into pulses approximately 8.5 ns wide with a FWHM of 4 ns. Following this initial chopping stage, the positron pulses undergo further time focusing using applied rf fields to coaxial resonators. Current simulations demonstrate the capability of supplying a 2.4 ns (FWHM) pulse to the double harmonic buncher for final time focusing. The goal is to produce a pulsed positron beam with a time resolution of less than 100 ps capable of implanting positrons with kinetic energy up to 30 kV.