You're clearly knowledgeable in this subject, is there a nuclear propulsion design that stands out to you as the most feasible? I like fission fragment rockets(1) because they seem simple and apparently have very high efficiency, but I'm no expert.
There are lots of designs for nuclear rockets, and while I read about them, I did not spend time to poke them and see if there are any obvious issues. The problem with nuclear designs is that things that work on paper don't necessarily work in practice, as Admiral Rickover is known to have ranted once.
Given that, to me the most promising 2 nuclear designs are the nuclear thermal rocket design, and the Orion design.
Here's why.
The Rover/NERVA program [1] is underappreciated. In terms of scientific and engineering achievement it rivals the Manhattan project, while having a fraction of its budget. Just to get a sense of the distance between theory and practice: the idea of a nuclear thermal rocket is to push hydrogen through a nuclear core. It gets in cold, it comes out hot, and voila, you have a nice rocket engine. What could be simpler? There are a few problems. The first is the scale. Here's a quote about the nuclear engine Phoebus 2A [2]:
> This was followed by a test of the larger Phoebus 2A. A preliminary low power (2,000 MW) run was conducted on 8 June 1968, then a full power run on 26 June. The engine was operated for 32 minutes, 12.5 minutes of which was above 4,000 MW, and a peak power of 4,082 MW was reached. At this point the chamber temperature was 2,256 K (1,983 °C), and total flow rate was 118.8 kilograms per second (262 lb/s).
For comparison a full-size nuclear AP1000 reactor like the one that was just started at Vogtle produces about 3.6 GW-thermal, so less than the 4 GWt mentioned here. Such a reactor circulates about 20 tons of water per second through the core. Somehow this rocket engine is able to extract more power using 50 times less coolant by mass, and from a core that literally fits on the bed of a small truck.
The vibrations and temperatures inside this core were tremendous. In various tests parts of the fuel rods ruptured, sometimes the hydrogen would catch fire, sometimes valves would break. All these annoying engineering challenges had to be overcome. But eventually they were overcome. That's the important thing we know about the thermal nuclear engine: we know it can be done, because it was done.
Some people may complain that the ISP from these engines topped at 900 seconds. Considering the technological readiness of this technology, I think this is nothing to sneeze at. There are good reasons to believe with this technology we can reach 1000 seconds, and maybe a bit higher.
The second technology on my list is the Orion project. It was never implemented, but my heuristics are like this: 1. Freeman Dyson was, in the common understanding of the word, a genius. It is true that he did not have a PhD, but aside from that, as a scientific mind, he was probably the equal of Feynman. 2. The thing that makes the spaceship move, the nuclear bombs, are a very mature technology. Pairing that with a pusher plate remains to be validated, but it's highly likely to work. The pusher plate idea was tested with conventional bombs, and we have no particular reason to think it wouldn't work if you increase the yield of the bomb.
Of course, the thing that goes against project Orion is the fact that we live in the real world, and in this world nuclear bombs are a problem. You don't want to start ferrying thousands of nukes to space without thinking twice.
But if we can figure out the non-proliferation aspect of the project Orion, I think it's the most likely configuration to enable us to do deep space travel.
(1) https://en.wikipedia.org/wiki/Fission-fragment_rocket