Let us assume that in the next 50 years one of the large nation-states of our world will build nuclear powered planes, for intercontinental flight. Supposedly, the nuclear planes would be bigger, faster, and need less oil in a world where good oil sources are dissapearing (so, assume that peak oil is true and that by 2070 the peak has come and gone). Also, nuclear planes would be a stepping stone to regular suborbital space planes, then to LEO space planes, that would be used to build nuclear pulse propulsion ship (AKA, orion bomb drive). The nation-states have deep pockets and are commited to develop the nuclear planes. We can, if necessary, assume that the nation-state in question can ignore public opinion for a long time, maybe it's a dictatorship like Soviet Union was and can ignore international outrage if something goes wrong.
Having said that, the government does not want a Chernobyl in the sky and would like for the nuclear plane to be as safe as possible. One of the main dangers of such a plane is the radiation emitted by the reactor: that will hurt the crew, irradiate the cargo and damage the control systems. How can the designers contain the radiation without using massive shielding like that used in well-built nuclear power plants? My first idea was to use a tungsten carbide sphere around the reactor to reflect the neutrons back to the fissile material and be able to achieve sustainable fission with less material while at the same time getting rid of the dangerous hot neutrons. I am aware that T.Carbide is heavy but is better then the meters of concrete and lead nuclear power plants use.
The nation-state is ignoring the other danger of the nuclear plane - it crashing and irradiating neighborhoods, there isn't much that can be done about that except placing the airports and the routes far from the cities and critical farmlands.
Would that work? If it won't, why, and what would work?