This article presents the conceptual design of a nuclear space power system based on the ultrahigh temperature vapor-core reactor (UTVR) with magnetohydrodynamic (MHD) energy conversion. This UF4-fueled gas-core cavity reactor operates at a maximum core temperature of 4000 K and 40 atm. Potassium fluoride working fluid cools the reactor cavity wall and mixes with the fissioning fuel in the core. Neutron transport calculations with specialized high temperature gas-core cross-sectional libraries indicate criticality at core radii of 60-80 cm, with BeO reflector thicknesses of —50 cm. The heated core exhaust mixture is directed through a regeneratively cooled nozzle into a disk MHD channel to generate electrical power. The MHD generator operates at fluid conditions below 2300 K and 1 atm. Fission fragment ionization enhances the electrical conductivity in the channel significantly, allowing an overall conversion efficiency of 20%. The mixture is condensed in heat exchangers, and pumped back to the core in a MHD-Rankine thermodynamic cycle. Heat rejection temperatures of 1500-2100 K lead to compact heat exchangers and an overall specific weight of ~1 kg/kWe for 200 MWe. Material experiments, performed with UF4 up to 2200 K (to date), show acceptable compatibility with tungsten-, molybdenum-, and carbon-based materials. This article discusses the supporting nuclear, fluid flow, heat transfer and MHD analysis, materials experiments, and fissioning plasma physics.