Low-mass antimatter-based propulsion systems are well matched to low-mass unmanned spacecraft sent to explore exoplanets and transmit back scientific observations. In the case of nearby habitable-zone exoplanet Proxima b, flyby missions as short as 20 years are being contemplated. In order to achieve spacecraft velocities greater than 2% of the speed of light, exhaust particle velocities commensurate with kinetic energies of at least 1 MeV/nucleon are required. The design of a nuclear propulsion system capable of such particle energies is presented. The scope of this technical note is restricted to the nuclear physics of antiproton-induced fission, classical physics of collimating charged exhaust particles, and the accelerator physics of a particle trap within which the fission events are generated. Other vital issues such as antimatter production and storage are the subject of papers in other journals more appropriate for these subjects.