Nuclear aircraft have the severe downside of the weight of neutron shielding- wiping out most, if not all the gains of nuclear aircraft.
I propose to have a separate drone airplane that carries the nuclear reactor, and from a distance (say a 1km or so), beams laser power to the actual passenger airplane.
This separation should allow for removing the need for most nuclear shielding, with the added bonus of separating the nuclear reactor from the passengers- should anything go wrong, the drone ship can turn away, leaving the passengers safe.
Laser power densities with PCSEL lasers can be as high as 1 MW/m2.
Can enough power be delivered via laser beams to fly a fast airplane?
The Concorde’s engines produce a thrust of ~20 MW x 4 engines = 80 MW (Rolls-Royce Olympus variants - Wikipedia)
The wing surface area is roughly (25m * ½ * 25m) = ~312 m^2
This corresponds to a total deliverable power density of ~300 MW of power via PCSELs, and 300 is indeed greater than 80.
Thus, at first glance, this should be feasible.
Obligatory disclaimer: This is just an idea, probably a bad one, intended primarily to serve as a stepping stone to future ideas.