We use hydrocarbons for aircraft fuel because hydrocarbons have a great many beneficial properties. They have considerable energy density by volume and mass. They remain liquid at a wide range of temperatures, the kinds seen from burning hot deserts to sub-zero temperatures seen at miles into the air. They provide lubrication to pumps. They burn readily when atomized but not when pooled on the ground from a spill. This we all know because of our use of fossil fuels in our every day lives. The point I'm making is that if we could not pump them from the ground then we'd synthesize hydrocarbons for fuel. We know how to produce hydrocarbons from nuclear power, in fact this has been proposed widely as an exit from needing fossil fuels in the real world.
In short, if we could not pump hydrocarbons from the ground for aircraft fuel then we'd make hydrocarbons from whatever raw materials and energy sources were most readily accessible.
Don't try to fit a nuclear reactor into an airplane, just use a nuclear reactor on the ground to make the airplane fuel. The US Navy has been working on this for a very long time, perhaps decades, to allow nuclear powered aircraft carriers to produce the fuel for the aircraft it carries while at sea. If or when this project is successful it would remove the need for a small flotilla of oil tankers to continuously bring fuel to the carrier groups.
As they are heavy, smaller aircrafts have to rely on other fuels. What could those fuels be?
The answer is, in my mind, synthesized kerosene.
If the goal is to have the airborne equivalent of the navy aircraft carrier, a military base that floats in the air instead of floating in the sea, then a nuclear reactor on board starts to make sense. Though with something this large I'd expect a large part of the lift that keeps it in the air to be from a lifting gas. That would mean it's a large armored Zeppelin. Because airplanes are more efficient than helicopters in turning energy into lift, and a moving target is harder to hit than a stationary one, I expect this airborne military base to keep moving and use a flying wing body to provide some of the lift. That doesn't mean it can't hover, only that it does this only when necessary for the mission.
Zeppelins fell out of use because it is so much easier to produce hydrocarbons than to produce helium. 479
Hydrogen is an easily obtained lifting gas but it's so flammable as to be impractical. Perhaps with better materials and techniques Zeppelins filled with hydrogen could be practical. If there's cheap hydrogen for a lifting gas then there's cheap hydrogen for producing synthetic kerosene.
For Zeppelins to be safe and cheap means helium has to be practically gushing out of the ground. Helium is a byproduct of nuclear reactors but I doubt that's a practical source of helium since if there's enough nuclear reactors to make travel by Zeppelins practical then that's a lot of energy going around to make kerosene. Batteries are completely impractical for powering Zeppelins. Mass is a huge issue for keeping a lighter than air vehicle flying. Nobody is going to power a Zeppelin by batteries. They'd be using something far more energy dense. If it's not kerosene being burned in turbine or reciprocating engines then it might be ammonia, hydrogen, or some other lighter than air flammable gas.
If the fuel is also a lifting gas then as it is burned the lifting capacity is diminished so some measure has to be taken to compensate, which could be as simple as dumping sand bags. Perhaps a mix of heavier and lighter than air fuels can be used, burning either as needed to maintain the desired lift. Air density varies with humidity and temperature so having a means to adjust lift during a long flight will be desirable.
A nuclear reactor on a fast moving airplane which could find itself being shot at in a war was likely a liability that few would consider. However, in a big slow moving Zeppelin, used in civilian aviation, a nuclear reactor may actually be safer than kerosene. Consider large civilian nuclear powered lighter than air airliners as an alternative to kerosene powered jet aircraft. It cuts out the conversion losses of producing the kerosene and uses the heat from the reactor directly for propulsion. With a lifting body shape it would still fly largely like an airplane but at a very leisurely cruising speed of something like 50 to 100 knots instead of the 400 to 500 knots of a jet. As a nuclear reactor doesn't need oxygen to burn fuel such an aircraft could reach altitudes a jet never could. 435