Between 1946 and 1961, the Air Force and the Atomic Energy Commission spent more than $7 billion trying to develop a nuclear-powered aircraft. Although no airplane ever flew under nuclear power, the Air Force converted a B-36 bomber, known as the Nuclear Test Aircraft, to carry an operating three-megawatt air-cooled reactor to assess operational problems (it made 47 flights over Texas and New Mexico between July 1955 and March 1957). The NB-36H carried the reactor in its aft bomb bay and incorporated a new nose section, which housed a 12-ton lead and rubber shielded crew compartment with 12 inch thick leaded-glass windows. Water pockets in the fuselage and behind the crew compartment also absorbed radiation. Due to weight constraints nothing was done to shield the considerable emissions from the top, bottom or sides of the reactor.
In theory, nuclear-powered aircraft could stay in flight for weeks at a time. General Electric built two prototype engines for such a plane. These engines exist today and can be seen outside the EBR-1 complex in Arco, Idaho.
An artist conception is attached:
The Air Force's first operational supersonic bomber was tested in the Arnold Engineering Development Center's 16-foot transonic wind tunnel in 1957. I have not done additional research but it sure looks like the proposed NERA engine.
In 2003 the military and CIA were planning a nuclear powered Drone that can stay up very long periods.