OK farmerman has posed some interesting questions. He is correct that most of the existing and earlier applications to which I referred did indeed involve sub critical electrical power applications. A couple of points;
1. The use of nuclear power to put spacecraft in or beyond earth orbit is both infeasible and unnecessary. We have ample rocket engines and the option to stage systems in earth orbit and assemble them there.
2. The use of "mini nuclear detonations" to propel a space craft in deep space is also infeasible and unnecessary. There is a minimum size involved in a supercritical nuclear detonation, and in this case "mini" is pretty large. Moreover, since there is no atmosphere in space there will be no pressure wave and no possibility of efficient capture of released energy by a "capture plate". The only thing that could be "captured" is the momentum of a small fraction of the released radiation and nuclides. That can be far more economically and efficiently done with an ion engine.
The question of a nuclear power reactor supporting long duration space flight is interesting. It isn't much of a trick to design a power reactor with fuel for (say) 50 - 75 years. We have 50 year reactors now in the Nimitz class carriers. (That is accomplished by using highly enriched uranium fuel and by doping the ractor core with consumable neutron absorbers such as boron, so that over the life of the core the product of the available fuel nucleus density and thermal neutron density is roughly constant.) I suspect the most challenging trick would be the engineering of the heat engine required to transform the thermal energy resulting from the capture of fission products into useful electrical energy; and shielding the human crew (if there is one) from the radiation --- and doing all this within the size and weight limitations applicable to space flight. The essential limitation here lies in the intersection of what is required for the design of a long-lived reactor core and what is needed for the heat engine, The metalurgy of a reactor core generally limits its internal temperature to something less than 1,800deg F. That in turn sets an upper limit on the thermodynamic efficiency of the heat engine used to produce the electrical power. This isn't seriously limiting in terrestrial applications, however on a very long space flight it could be limiting.
Fusion power generation has been under fairly constant investigation for about 50 years. We aren't any closer to a feasible containment solution now than we were 30 years ago.