This Small Business Innovation Research Phase II project will develop and demonstrate a laboratory prototype of the Advanced Positron Beam Source (APBS) that will provide a high quality pulsed positron beam suitable for a range of analytical instruments for materials science. The project extends the latest developments in techniques to accumulate positrons from a radioactive source in Penning traps. The technical objectives of the Phase I project were fully achieved. The technical objectives of Phase II are: (1) to develop a compact, low-cost, two-stage positron trap; (2) to develop an advanced cryogenic positron moderator system; (3) to develop a high- performance positron buncher; (4) to refine the Phase I approach for extracting positrons from the magnetic field of the trap; and (5) to assemble and demonstrate the APBS system. If successful, this project will provide the basis for commercialization of the APBS in Phase III. A major obstacle to the commercial exploitation of positron-based surface analytical techniques has been the lack of a suitable slow positron beam source. The APBS will fill this need by providing a compact, low-cost, user-friendly positron beam source that can function ultimately as a turnkey system in an industrial environment. The APBS will have advanced performance characteristics that are not available from any other system.