The Solar Wind Around Pluto (SWAP) instrument on New Horizons will measure the interaction between the solar wind and ions created by atmospheric loss from Pluto. These measurements provide a characterization of the total loss rate and allow us to examine the complex plasma interactions at Pluto for the first time. Constrained to fit within minimal resources, SWAP is optimized to make plasma-ion measurements at all rotation angles as the New Horizons spacecraft scans to image Pluto and Charon during the flyby. In order to meet these unique requirements, we combined a cylindrically symmetric retarding potential analyzer (RPA) with small deflectors, a top-hat analyzer, and a redundant/coincidence detection scheme. This configuration allows for highly sensitive measurements and a controllable energy passband at all scan angles of the spacecraft. ; Comment: 78 pages, 42 figures, 7 tables; To appear in a special volume of Space Science Reviews on the New Horizons mission