A fission based nuclear thermal propulsion rocket engine. An embodiment provides a source of fissionable material such as plutonium in a carrier gas such as deuterium. A neutron source is provided, such as from a neutron beam generator. By way of engine design geometry, various embodiments may provide for intersection of neutrons with the fissionable material injected by way of the carrier gas, while in a reactor provided in the form of a reaction chamber. Impact of neutrons on fissionable material results in a nuclear fission in sub-critical mass reaction conditions in the reactor, resulting in release of heat energy to the materials within the reactor. The reactor is sized and shaped to receive the reactants and an expandable fluid such as hydrogen, and to confine heated and pressurized gases for discharge out through a throat, into a rocket engine expansion nozzle for propulsive discharge.